Lepton-flavor-violating decays into axion-like particles Lorenzo - - PowerPoint PPT Presentation
3rd International Conference on Charged Lepton Flavor Violation Lepton-flavor-violating decays into axion-like particles Lorenzo Calibbi (Nankai University) Mainly based on work in progress with D. Redigolo, R. Ziegler, and J. Zupan Kyushu
3rd International Conference on Charged Lepton Flavor Violation
Lepton-flavor-violating decays into axion-like particles
Mainly based on work in progress with
Kyushu University, Fukuoka June 18th 2019
Lorenzo Calibbi (Nankai University)
Mu3e I Mu3e II
Motivation
Definitely worth to keep searching, but…
Lorenzo Calibbi (Nankai) LFV into ALPs
Belle/BaBar
Mu3e I Mu3e II
Motivation
What if we haven’t looked (enough) in the right place?
Lorenzo Calibbi (Nankai) LFV into ALPs
Belle/BaBar
Lorenzo Calibbi (Nankai) LFV into ALPs
Introduction Assume there is a light, invisible, new particle “a” with FV couplings to leptons CLFV modes would then be Interesting interplay with cosmo/astro: Light: Invisible:
ma < mμ , mτ
μ → e a, τ → μ a, μ → e γ a, etc .
Lorenzo Calibbi (Nankai) LFV into ALPs
Lepton-flavor-violating ALPs
PNGB: Global symmetry: …
Why should a be light and feebly-coupled? Examples: That’s natural, if it is the (pseudo) Nambu-Goldstone boson (PNGB)
Equivalent possibility: light Z′ of a local U(1), e.g. Li-Lj (with g ≪1)
Heeck ‘16 Wilczek ‘82 Pilaftsis ‘93 Feng et al. ‘97
naturally flavor-violating couplings
Lepton-flavor-violating ALPs
Lorenzo Calibbi (Nankai) LFV into ALPs
Where does lepton flavor violation come from?
La`` = @µa 2fa
ij `iµ`j + CA ij `iµ5`j
General couplings to leptons: Explicit examples at the end of the talk…
naturally flavor-violating couplings
Lepton-flavor-violating ALPs
Lorenzo Calibbi (Nankai) LFV into ALPs
Where does lepton flavor violation come from?
La`` = @µa 2fa
ij `iµ`j + CA ij `iµ5`j
General couplings to leptons: Explicit examples at the end of the talk…
Shift symmetry (PNGB!) → ma from (small) explicit U(1) breaking U(1)-breaking scale → coupling suppression
LFV decays into ALPs: model-independent approach
Lorenzo Calibbi (Nankai) LFV into ALPs
La`` = @µa 2fa
ij `iµ`j + CA ij `iµ5`j
Fij ≡ 2fa q |CV
ij |2 + |CA ij|2
<latexit sha1_base64="UgJGgFEiKJwhr5AYNxEv5pPyXI=">ACKXicbVDLSgMxFM3UV62vqks3wSIQpmpgi6rBXFZwT6g0w6ZNPGZh5NMoWSzu+48VfcKCjq1h8xfSDaeiBwOdcbu5xI0aFNM0PI7W0vLK6l7PbGxube9kd/eqIow5JhUcspDXSQIowGpSCoZqUecIN9lpOb2SmO/NiBc0DC4k8OINH3UCahHMZJacrLFa0fR+8Qm/ZgObI8jrArQc1CibNHnUo1KLVNJplRqwBP4Fi4/BGSxMnmzLw5AVwk1ozkwAxlJ/tit0Mc+ySQmCEhGpYZyaZCXFLMSJKxY0EihHuoQxqaBsgnoqkmlybwSCt6IVcv0DCifp7QiFfiKHv6qSPZFfMe2PxP68RS+iqWgQxZIEeLrIixmUIRzXBtuUEyzZUBOEOdV/hbiLdF1Sl5vRJVjzJy+SaiFvneYLt2e54tWsjQ4AIfgGFjgHBTBDSiDCsDgATyBV/BmPBrPxrvxOY2mjNnMPvgD4+sb5WoOw=</latexit>Γ(`i → `j a) = 1 16⇡ m3
`i
F 2
ij
1 − m2
a
m2
`i
!2
<latexit sha1_base64="DnXvEscDeIybi8iGp/syNEWX9+Y=">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</latexit>Goal: constrain the effective LFV scales Fij using experimental data This generic Lagrangian induces 2-body LFV decays such as:
Feng et al. ‘97
SEARCH FOR RIGHT-HANDED CURRENTS IN MUON DECAY TABLE I. Values of the muon-decay parameters p, 77, g, and 6 in the V -
A model and in the mani-
festly left-right-symmetric (LRS) model with massless neutrinos. Their world-average experimental values (Ref. 21) prior to our experiment are also listed. The values in the LRS model are given to the lowest order in the mass-squared ratio E and mixing angle f for the gauge bosons W I and W2. Decay
V - A
Value in parameter value the LRS model Experimental value
P , is the muon longitudinal polarization from a+
decay at rest.
P, in the y+ rest frame is T-8.
The world-average to -
1, 0, and + 1. The spectrum for unpolarized muons
values2' of the muon-decay parameters p, r ] , (, and 6 mea- corresponds to the cosO=O curve, whose sharp edge at sured prior to our experiment are given in Table I. Also x = 1 played an important role in the spectrometer given there are their values in the L-R-symmetric model, momentum calibration. For cos@= 1, angular-momentum to lowest order in E and [. The V
conservation forces the V - A rate to vanish. The V
+
A to e=C=O. The first-order electromagnetic corrections to the muon-decay spectrum are of order a ln(mP2/me2) (several
76). They can be computed accurately with the four-
fermion contact interaction ~ a m i l t o n i a n , ~ ~ since the heavy intermediate vector bosons contribute negligible ad- ditional terms23 of order a(m, /m
)2. The first-order
corrections have been computed for the general Fermi in- tera~tion,~~ and this general expression was used in Monte Carlo simulations to verify the accuracy of the analysis
spectrum at cose is equivalent to the V-A spectrum at
( -cosf?). The region of greatest experimental sensitivity
to an admixture of right-handed currents is therefore near x =
1 and c o d = 1, where the V -
A rate vanishes while
the V+A rate is maximum. The experiment was designed to measure the positron spectrum for x > 0.85 and cos0 > 0.95. The data analysis was based on a simple property of the muon-decay spectrum: if the weak interaction is predom- inantly V
A, scalar, tensor, or pseudoscalar currents, then the positron spec- were needed. trum near the end point, for cose =
1, can be expressed as
The radiatively corrected muon-decay spectrum for a a sum of the P, cos6= 1 V -A spectrum, which vanishes pure V
linearly at x =
1, and the P, cosB=O V
which is flat near x =
1 with a step to zero at the end
2.0
11 -{P,
c o d
6/p. Measurement of the rate as a function
I
effects
We introduce
1.6
1w
P = l - Q
u 3P,
' case.
L 1.4C
6=1-'6 a I
3
9with p=8 = 0 for a pure V - A interaction, and the decay spectra: S(x,P, cose) is the spectrum for an arbitrary weak coupling (i.e., arbitrary values of {,p,6); SVPA (x,
1
)
is the V - A spectrum at P,cose=l, S V - A ( ~ , O ) is the
V
normalized to S(x,P,, cose). Ignoring the 7 term in (2.11, which is negligible near the end point, and ignoring radia- tive corrections, we can write S(x,P@
C O S ~ ) = ~ ( ~ ) S V - A ( X ,
1)+r(6)Sy-A(~,0) (2.2) where q ( 9)
= CP, C O S ~
+
+p ,
(2.3) Reduced pos~tron energy x and r (9) is the relative rate at the end point:
A radiatively corrected muon-decay spec-
r(e)=(
1
(2.4)
trum plotted for c o d = + 1, 0, and - 1, where T - B is the angle between the positron direction and the muon spin. The effects
TO lowest order in p, 3, and ( 1
, C O S ~ ) ,
r (6) and q (9)
take the simpler forms
Search for RH currents with 1.8×107 polarized 𝜈+
Lorenzo Calibbi (Nankai) LFV into ALPs
Past searches: 𝜈 → e a
(2.5) and When radiative corrections are included, the exact rela- tion (2.2) becomes only an approximation, as does (2.5). For the fitting procedure to be described in Sec. VA, and for a spectrum given by a combination of only V +
A and V - A effective couplings, the radiative corrections were
found to have only a negligible effect on r(8). When this experiment is used for setting limits on the presence of
couplings are taken into account, the radiative corrections likewise do not introduce a significant additional sys- tematic error. Calculations to check this expectation must be made specifically for the particular combination of couplings being investigated, and so are not included here. The highly polarized muons in our experiment were supplied by a "surface" muon beam,25 derived from pions decaying at rest near the surface of the production target. Right-handed currents would reduce the muon polariza- tion in pion decay to P,, = 1
fest left-right symmetry). Including this effect, our final result is given to lowest order in E and f by Since we' are unable to correct for all possible sources of muon depolarization, our result should be interpreted as a lower limit on {PW6/p.
The experiment was performed in the M13 beamline of the TRIUMF cyclotron. Surface muons were transported in vacuum to a stopping target in the muon polarimeter, shown in Fig. 3. High-purity metal foils (Ag, Al, Au, Cu) and liquid He were selected as stopping targets, since in these materials muonium (,u+
atom) formation, lead- ing to muon depolarization, is strongly suppressed. The target region was immersed either in a strong long- itudinal "spin-holding" field (0.3 or 1.1 T) aligned oppo- site to the nominal beam direction, or a vertical (70
G)
spin-precessing field. The longitudinal field quenched the muon depolarization in muonium via the Paschen- Back effect. The data collected with the longitudinal field were used to measure the rate at the spectrum end point, and data with the spin-precessing field were used in the momentum calibration of the spectrometer. The angular acceptance for positrons was significantly increased by the downstream portion of the solenoid, which served as a solenoidal field lens, focusing the posi- trons into the dipole magnet spectrometer. The septum between the target and solenoid bore made the focal length of the solenoid lens nearly independent of the choice of target field orientation. A horizontally focusing spectrometer was chosen in or-
MUON P O L A R I M E T E R Berkeley- Northwestern-TRIUMF
_ _ -
_ _ _ _
tional chambers; S
1
1-D4 are drift
S2, respectively, are not shown. Muons entering the solenoid are
stopped in the target. Decay e + emitted near the beam direc- tion are focused by the solenoid into the spectrometer. der to achieve a high momentum resolution. The win- dows of the vacuum box between the magnet poles were positioned close to the focal planes to minimize the effects
Particle trajectories in the target region (see Fig. 3 inset) were measured by the proportional chambers P1 and P2 for muons, and by the proportional chamber P3 and drift chambers Dl and D2 for positrons. Near the spectrorne- ter magnet, drift chambers D3 and D4 measured positron
trigger signals. The data were accumulated in three running periods
were essentially the same for all three runs, except for minor differences mentioned below and in Appendix A. The longitudinal field in the stopping target region was 1.1 T for runs 1 and 2, and 0.3 and 1.1 T for run 3. A to- tal of 1.8X 10' (1.4X 10') triggers were collected in the spin-holding (spin-precessing) mode on 130 (170) comput- er tapes [I600 BPI (bytes per inch)]. Under optimal con- ditions these data could have been accumulated in -20 d
also collected in many special runs, to be described in Sec. IV, which were used to calibrate the spectrometer.
Very good e+ momentum resolution (~70 KeV at the e.p.)
d2Γ dx d cos ✓ = Γµ ((3 2x) P(2x 1) cos ✓) x2
where x = 2Ee/mµ
µ → e¯ νν
<latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit><latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit><latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit><latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit>Ordinary
SEARCH FOR RIGHT-HANDED CURRENTS IN MUON DECAY TABLE I. Values of the muon-decay parameters p, 77, g, and 6 in the V -
A model and in the mani-
festly left-right-symmetric (LRS) model with massless neutrinos. Their world-average experimental values (Ref. 21) prior to our experiment are also listed. The values in the LRS model are given to the lowest order in the mass-squared ratio E and mixing angle f for the gauge bosons W I and W2. Decay
V - A
Value in parameter value the LRS model Experimental value
P , is the muon longitudinal polarization from a+
decay at rest.
P, in the y+ rest frame is T-8.
The world-average to -
1, 0, and + 1. The spectrum for unpolarized muons
values2' of the muon-decay parameters p, r ] , (, and 6 mea- corresponds to the cosO=O curve, whose sharp edge at sured prior to our experiment are given in Table I. Also x = 1 played an important role in the spectrometer given there are their values in the L-R-symmetric model, momentum calibration. For cos@= 1, angular-momentum to lowest order in E and [. The V
conservation forces the V - A rate to vanish. The V
+
A to e=C=O. The first-order electromagnetic corrections to the muon-decay spectrum are of order a ln(mP2/me2) (several
76). They can be computed accurately with the four-
fermion contact interaction ~ a m i l t o n i a n , ~ ~ since the heavy intermediate vector bosons contribute negligible ad- ditional terms23 of order a(m, /m
)2. The first-order
corrections have been computed for the general Fermi in- tera~tion,~~ and this general expression was used in Monte Carlo simulations to verify the accuracy of the analysis
spectrum at cose is equivalent to the V-A spectrum at
( -cosf?). The region of greatest experimental sensitivity
to an admixture of right-handed currents is therefore near x =
1 and c o d = 1, where the V -
A rate vanishes while
the V+A rate is maximum. The experiment was designed to measure the positron spectrum for x > 0.85 and cos0 > 0.95. The data analysis was based on a simple property of the muon-decay spectrum: if the weak interaction is predom- inantly V
A, scalar, tensor, or pseudoscalar currents, then the positron spec- were needed. trum near the end point, for cose =
1, can be expressed as
The radiatively corrected muon-decay spectrum for a a sum of the P, cos6= 1 V -A spectrum, which vanishes pure V
linearly at x =
1, and the P, cosB=O V
which is flat near x =
1 with a step to zero at the end
2.0
11 -{P,
c o d
6/p. Measurement of the rate as a function
I
effects
We introduce
1.6
1w
P = l - Q
u 3P,
' case.
L 1.4C
6=1-'6 a I
3
9with p=8 = 0 for a pure V - A interaction, and the decay spectra: S(x,P, cose) is the spectrum for an arbitrary weak coupling (i.e., arbitrary values of {,p,6); SVPA (x,
1
)
is the V - A spectrum at P,cose=l, S V - A ( ~ , O ) is the
V
normalized to S(x,P,, cose). Ignoring the 7 term in (2.11, which is negligible near the end point, and ignoring radia- tive corrections, we can write S(x,P@
C O S ~ ) = ~ ( ~ ) S V - A ( X ,
1)+r(6)Sy-A(~,0) (2.2) where q ( 9)
= CP, C O S ~
+
+p ,
(2.3) Reduced pos~tron energy x and r (9) is the relative rate at the end point:
A radiatively corrected muon-decay spec-
r(e)=(
1
(2.4)
trum plotted for c o d = + 1, 0, and - 1, where T - B is the angle between the positron direction and the muon spin. The effects
TO lowest order in p, 3, and ( 1
, C O S ~ ) ,
r (6) and q (9)
take the simpler forms
Search for RH currents with 1.8×107 polarized 𝜈+ interpreted in terms of 𝜈 → ea too Lorenzo Calibbi (Nankai) LFV into ALPs
Past searches: 𝜈 → e a
d2Γ dx d cos ✓ = Γµ ((3 2x) P(2x 1) cos ✓) x2
where x = 2Ee/mµ
µ → e¯ νν
<latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit><latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit><latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit><latexit sha1_base64="HztO89Net8MBGAXm/qGb4HnBmJc=">AB/nicbVDLSgNBEJyNrxhfq+LJy2AQPIVdEfQY9OIxgomB7BJmJ51kyMzsMg8hLAF/xYsHRbz6Hd78GyfJHjSxoKGo6qa7K8k40yYIvr3Syura+kZ5s7K1vbO75+8ftHRqFYUmTXmq2gnRwJmEpmGQztTQETC4SEZ3Uz9h0dQmqXy3owziAUZSNZnlBgndf2jSNjIpBhwlBCVR9JOXHX9alALZsDLJCxIFRVodP2vqJdSK0AayonWnTDITJwTZRjlMKlEVkNG6IgMoOoJAJ0nM/On+BTp/RwP1WupMEz9fdEToTWY5G4TkHMUC96U/E/r2N/yrOmcysAUni/qWY/fvNAvcYwqo4WNHCFXM3YrpkChCjUus4kIF19eJq3zWhjUwruLav26iKOMjtEJOkMhukR1dIsaqIkoytEzekVv3pP34r17H/PWklfMHKI/8D5/ADnElaY=</latexit>Ordinary
dΓ(µ+ → e+ a) d cos θ = Γµ→e a 2 " 1 + 2P cos θ CV
eµCA eµ
(CV
eµ)2 + (CA eµ)2
#
<latexit sha1_base64="yTDiF70iUymABuEYf6rzSYrvU=">ACs3icbVFNb9QwEHXCV1k+uoUjlxErpK2KVkAlQtSw9wXCR2WynJBsfr7FqNk8ieIFZW/iBHbvwbnA+10DKSpaf35o3Hz2mVC42e9tx79y9d/B3sPRo8dPnu6PD54tdVkrxheszEt1kVLNc1HwBQrM+UWlOJVpzs/Ty7NWP/OlRZl8RV3FY8l3RQiE4yipZLxzyhTlJkI+Q806waiT1RKOo1kvToCiLAE3oHXQA+bq7aIlTrCLUfawAer9jM6a2Ksd3D2vgYaEzRzjMfTiCAObQDoB+wuA+Swy3zma1hCt42hiA6bVyuAqs/5o4bQm7sxKbLcbJeOLNvK7gNvAHMCFDzZPxr2hdslryAlOtQ59r8LYUIWC5bwZRbXmFWXdMNDCwsquY5Nl3kDryzhqxU9hQIHfu3w1Cp9U6mtlNS3OqbWkv+TwtrzN7HRhRVjbxg/UVZnYMNtP1AWAvFGeY7CyhTwu4KbEthGi/eWRD8G8+TZYBjP/zSz48nZy8nGIY4+8IC/JlPjkmJyQz2ROFoQ5nrN0Eueb+84N3dRd962uM3iek3/KlX8A8p3RDw=</latexit>𝜈 → e a signal for ma ≈ 0: monochromatic e+ at m𝜈/2
Unless it couples (V-A) like in the SM:
⇒ BR(µ+ → e+a) < 2.6 × 10−6
<latexit sha1_base64="1hdLErDxRKuChBGR8VMIry67QPA=">ACI3icbVDLSgMxFM34rPVdekmWARFLDNFqoiLUjcua7FW6Iwlk6ZtaDIzJHeUMtRvceOvuHGhFDcu/BfTdha+LoQczrmXe8/xI8E12PaHNTM7N7+wmFnKLq+srq3nNjavdRgryuo0FKG68YlmgesDhwEu4kUI9IXrOH3z8d64pzcPgCgYR8yTpBrzDKQFDtXKnbo13e0CUCu8fcOIqiSu14Z4r49sD7EKImfnJPj7DxULJBS6Zxo59mxyWhq1c3i7Yk8J/gZOCPEqr2sqN3HZIY8kCoIJo3XTsCLyEKOBUsGHWjTWLCO2TLmsaGBCzEsmHod41zBt3AmVeQHgCft9IiFS64H0Tack0NO/tTH5n9aMoXPiJTyIYmABnS7qxAIb7+PAcJsrRkEMDCBUcXMrpj2iCAUTa9aE4Py2/BdcFwuOXAuj/LlShpHBm2jHbSHSMyugCVEdUfSIntErerOerBdrZL1PW2esdGYL/Sjr8wvCTqHJ</latexit><latexit sha1_base64="1hdLErDxRKuChBGR8VMIry67QPA=">ACI3icbVDLSgMxFM34rPVdekmWARFLDNFqoiLUjcua7FW6Iwlk6ZtaDIzJHeUMtRvceOvuHGhFDcu/BfTdha+LoQczrmXe8/xI8E12PaHNTM7N7+wmFnKLq+srq3nNjavdRgryuo0FKG68YlmgesDhwEu4kUI9IXrOH3z8d64pzcPgCgYR8yTpBrzDKQFDtXKnbo13e0CUCu8fcOIqiSu14Z4r49sD7EKImfnJPj7DxULJBS6Zxo59mxyWhq1c3i7Yk8J/gZOCPEqr2sqN3HZIY8kCoIJo3XTsCLyEKOBUsGHWjTWLCO2TLmsaGBCzEsmHod41zBt3AmVeQHgCft9IiFS64H0Tack0NO/tTH5n9aMoXPiJTyIYmABnS7qxAIb7+PAcJsrRkEMDCBUcXMrpj2iCAUTa9aE4Py2/BdcFwuOXAuj/LlShpHBm2jHbSHSMyugCVEdUfSIntErerOerBdrZL1PW2esdGYL/Sjr8wvCTqHJ</latexit><latexit sha1_base64="1hdLErDxRKuChBGR8VMIry67QPA=">ACI3icbVDLSgMxFM34rPVdekmWARFLDNFqoiLUjcua7FW6Iwlk6ZtaDIzJHeUMtRvceOvuHGhFDcu/BfTdha+LoQczrmXe8/xI8E12PaHNTM7N7+wmFnKLq+srq3nNjavdRgryuo0FKG68YlmgesDhwEu4kUI9IXrOH3z8d64pzcPgCgYR8yTpBrzDKQFDtXKnbo13e0CUCu8fcOIqiSu14Z4r49sD7EKImfnJPj7DxULJBS6Zxo59mxyWhq1c3i7Yk8J/gZOCPEqr2sqN3HZIY8kCoIJo3XTsCLyEKOBUsGHWjTWLCO2TLmsaGBCzEsmHod41zBt3AmVeQHgCft9IiFS64H0Tack0NO/tTH5n9aMoXPiJTyIYmABnS7qxAIb7+PAcJsrRkEMDCBUcXMrpj2iCAUTa9aE4Py2/BdcFwuOXAuj/LlShpHBm2jHbSHSMyugCVEdUfSIntErerOerBdrZL1PW2esdGYL/Sjr8wvCTqHJ</latexit><latexit sha1_base64="1hdLErDxRKuChBGR8VMIry67QPA=">ACI3icbVDLSgMxFM34rPVdekmWARFLDNFqoiLUjcua7FW6Iwlk6ZtaDIzJHeUMtRvceOvuHGhFDcu/BfTdha+LoQczrmXe8/xI8E12PaHNTM7N7+wmFnKLq+srq3nNjavdRgryuo0FKG68YlmgesDhwEu4kUI9IXrOH3z8d64pzcPgCgYR8yTpBrzDKQFDtXKnbo13e0CUCu8fcOIqiSu14Z4r49sD7EKImfnJPj7DxULJBS6Zxo59mxyWhq1c3i7Yk8J/gZOCPEqr2sqN3HZIY8kCoIJo3XTsCLyEKOBUsGHWjTWLCO2TLmsaGBCzEsmHod41zBt3AmVeQHgCft9IiFS64H0Tack0NO/tTH5n9aMoXPiJTyIYmABnS7qxAIb7+PAcJsrRkEMDCBUcXMrpj2iCAUTa9aE4Py2/BdcFwuOXAuj/LlShpHBm2jHbSHSMyugCVEdUfSIntErerOerBdrZL1PW2esdGYL/Sjr8wvCTqHJ</latexit>⇒ Feµ > 5.5 × 109 GeV
<latexit sha1_base64="8B8QuAOkQu7Wdlao2dKamVorxw=">ACIHicbVDJSgNBEO1xN25Rj14ag+ApzLigXkQU1GMUE4VMD2dStKke2bsrlHCkPyJF3/FiwdF9KZfY2c5uD0oeLxXRVW9IJbCoOt+OCOjY+MTk1PTmZnZufmF7OJSyUSJ5lDkYz0VcAMSBFCEQVKuIo1MBVIuAxaRz3/8ha0EVF4ge0YKo1QlEXnKGVqtkd/1w0msi0ju6of5OwGj2upuCrpEO7+126nd/2USgw1HOv97qprxU9gVKnms25ebcP+pd4Q5IjQxSq2Xe/FvFEQYhcMmPKnhtjJWUaBZfQyfiJgZjxFmtA2dKQ2Z2VtP9gh65ZpUbrkbYVIu2r3ydSpoxpq8B2KoZN89vrif95QTru5VUhHGCEPLBonoiKUa0lxatCQ0cZdsSxrWwt1LeZJpxtJlmbAje75f/ktJG3tvMb5xt5Q4Oh3FMkRWyStaJR3bIATklBVIknNyTR/JMXpwH58l5d4GrSPOcGaZ/IDz+QU6UaJc</latexit>for the isotropic case, they set the limit thus one gets
20 25 30 35 40 45 50
5 10 15 20 25
90% C.I., A = -1
)
2(in MeV/c Mass of X 20 30 40 50 60 70 80
20 25 30 35 40 45 50
5 10 15 20 25
90% C.I., A = 0
Signal Momentum (MeV/c) 20 25 30 35 40 45 50
5 10 15 20 25
90% C.I., A = +1
)
6
10 × Branching Ratio (
V-A (SM-like) V+A (RH curr.) Isotropic
Lorenzo Calibbi (Nankai) LFV into ALPs
Past searches: 𝜈 → e a
Precise measurement of Michel parameters plus dedicated search for 𝜈 → ea in the whole ma range considering anisotropy of the signal
700
Decay Signal 90% C.L. p-value (in ppm) A = 0 Average 9 p = 37.03 MeV/c 26 0.66 Endpoint 21 0.81 A = −1 Average 10 p = 37.28 MeV/c 26 0.60 Endpoint 58 0.80 A = +1 Average 6 p = 19.13 MeV/c 6 0.59 Endpoint 10 0.90
SM-like
Limits (with 5.8×108 𝜈+):
BR(µ → ea) < 5.8 × 10−5
<latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit><latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit><latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit><latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit>For V-A coupl. and ma ≈ 0:
⇒ Feµ > 1.2 × 109 GeV
<latexit sha1_base64="1QUoGgFBWijSGUZ3N2hf5cwT0Y=">ACIHicbVDLSgNBEJz1bXxFPXoZDIKnsBsF9SKioB5VTCJkY5idJIhM7vrTK8SluRPvPgrXjwojf9GiePg6+ChqKqm+6uIJbCoOt+OGPjE5NT0zOzmbn5hcWl7PJKyUSJ5lDkYz0VcAMSBFCEQVKuIo1MBVIKAfto75fvgVtRBReYieGqmLNUDQEZ2ilWnbHvxDNFjKtozvq3ySsTo9rKfgq6dLefo96+YKPQoGhnu910t9regJlLq1bM7NuwPQv8QbkRwZ4ayWfrEU8UhMglM6biuTFWU6ZRcAndjJ8YiBlvsyZULA2Z3VlNBw926YZV6rQRaVsh0oH6fSJlypiOCmynYtgyv72+J9XSbCxW01FGCcIR8uaiSYkT7adG60MBRdixhXAt7K+UtphlHm2nGhuD9fvkvKRXy3la+cL6dOzgcxTFD1sg62SQe2SEH5JSckSLh5J48kmfy4jw4T86r8zZsHXNGM6vkB5zPLy8aolU=</latexit> PHYSICAL REVIEW D VOLUME 38, NUMBER 7 1 OCTOBER 1988
Search for rare muon decays with the Crystal Box detector
G .
Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Hansen Laboratories and Department of Physics, Stanford University, Stanford, California 94305
and S. C. Wright
University of Chicago, Chicago, Illinois 6063 7
Temple University, Philadelphia, Pennsylvania 19122 (Received 16 February 1988) A search with the Crystal Box detector shows no evidence for the lepton-family-number- nonconserving decays p-ey, p-eyy,
The search provides upper limits for the branching ratios of r ( p - e y ) / T ( p - e v V ) < 4 . 9 X 1 0 ~ " (90% C.L.), r ( p - e y y ) / T ( p + e v i s )
< 7 . 2 ~
1 0 ' ' (90% C.L.), and r(p+eee)/r(p+evoi < 3 . 5 ~ lo-'' (90% C.L.). In addition, a limit for the emission of a light scalar or pseudoscalar boson in radiative muon decay is given.
The standard model' of electroweak interactions correctly describes the presently available experimental
divided into three generations or families. However, the multiplicity of generations of particles is not understood. This paper describes a new search for neutrinoless transi- tions from the muon, a second-generation lepton, to the electron of the first generation. The observation of such a lepton-family-number-nonconserving decay would indi- cate a connection between lepton generations and would be direct evidence for physics beyond the standard mod- el. The muon's role in the spectrum of elementary parti- cles has been a mystery since its discovery2 in 1936. For
mediating the strong nuclear force, as predicted by Yu- k a ~ a . ~ However, in 1947 an experiment4 using muons absorbed in dense materials clearly showed that the muon does not interact via the strong force. Subsequent high- precision tests of the electromagnetic and weak couplings
differences between these two particles except for their masses. The normal decay of the muon is to an electron and two neutrinos. Neutrinoless decay modes of the muon, such as p-e y, p-eee, and p-eyy, obey all conserva- tion principles associated with space-time symmetries. However, none of these decays has been observed. To ex- plain this, various lepton-number-conservation laws have been proposed. The first such law was introduced by Konopinski and Mahmoud5 in 1953, followed by the ad- ditive lepton-number-conservation law6 with separate lepton-family numbers in 1957, and a third lepton conser- vation law7 based on a multiplicative lepton number in
decays as well as the process p p Z - e - Z . The add- itive lepton-number-conservation law also prohibits muonium-antimuonium conversion and pt -e
+?,vp.
The latter two lepton-number schemes require separate types of neutrinos for the muon and the electron. Pon- tecorvo and schwartz8 independently proposed experi- ments to reveal their existence. In 1962, an experiment9 confirmed that there were indeed two different types of neutrinos and supported the hypothesis of separate lep- ton numbers. with this discovery, interest in-the search for neutrinoless decay modes of the muon waned and ex- perimentation essentially ended for about 15 years. A resurgence of interest in the search for rare muon decays occurred in 1977 when rumors circulated that an experiment at the Swiss Institute for Nuclear Research (SIN) had found a signal for the decay p-ey. This re- port underscored the fact that conservation of muon number is only empirical and without a fundamental
burst of both theoretical and experimental activity. Theorists found that the suppression of the branching ra- tios for lepton-family-number-nonconserving decays to below the experimental upper limits ( - lop8) was a natu- ral result of the new models. On the experimental side, besides the search at SIN (Ref. lo), two other experi- ments were quickly assembled to search with improved sensitivity for p-ey. One was located at the Tri- University Meson Facility (TRIUMF) (Ref. 1 I), and the
Facility (LAMPF) (Ref. 12). The results from these ex- periments showed no evidence for the decay p-e y at a
2077
@ 1988 The American Physical Society
Lorenzo Calibbi (Nankai) LFV into ALPs
Past searches: 𝜈 → e 𝛿 a
38
2083
apparatus and performed an appropriate action if any sensor reading fell outside its predefined normal operat- ing range. The rms also monitored and controlled the high voltages on the drift chamber. An autodialing modem was connected to the rms providing phone alarms.
There were three major data-taking periods, called I, 11, and 111. During the first, the instantaneous beam in- tensity was - 4 . 9 ~ lo6
y '
s-' with an average duty fac- tor of 6%. The pileup-detection system was not installed for this period. During period 11, the instantaneous beam intensity was -4.7 X lo6 y + s-' with an average duty factor of 9%. The pileup-detection system was partially installed during this period but was not used in the
and utilized during the final data-taking period, which had an average duty factor of 6.6%. Runs with different instantaneous beam intensities, varying from 4X lo6
y + s p l to 9 x 1 0 ~ y + s-I, were interspersed so rate-
dependent effects could be studied. During data taking there were runs to calibrate the plastic-scintillator timing every day, and runs to calibrate the NaI(T1) timing twice a week (see Sec. IV B 2). There were three energy-calibration periods with the drift chamber removed, the liquid-hydrogen target installed, and a .rrp beam incident. One such period occurred dur- ing the period I, one at the end of period 11, and one mid- way through period 111. There were also occasional cali- bration runs with a Pu-a-Be source (whenever the beam went off for a long time) and special runs (such as runs triggered on a pulser and runs triggered on a single pho- ton) at various times. A data run took typically two hours to fill a 2400-ft, 1600-bpi (bits-per-inch) tape with - 35 000 events. Each data run was preceded by a short run to establish the ADC pedestals and a flasher run (see Sec. IVA4) for NaI(T1) channel gain corrections. A total of 1500 mag- netic tapes were used in this experiment; approximately half of them contained production muon data.
A Monte Carlo program was written to simulate the response of the detector to many different types of events (see Table I). The Monte Carlo program followed only electrons, positrons, and photons, as these were the only particles that were detected. As described below, care was taken to ensure that this program faithfully repro- duced the behavior of the detector. The program pro- duced an output file that contained pulse heights and times for each individual detector element in the same format as for actual data; both data and Monte Carlo
It was assumed that all processes initiated by muon de- cays originated with an unpolarized muon decaying in TABLE I. Types of events generated with the Monte Carlo program. Process Trigger
p+-e+y e-Y p++e+yvC e-y, 1-y
P + + ~ + Y Y
e-y-y, e-y p+-e+e+e- e
+ + - -
p+-e e e YV e
p++ef vii
1 -e
p++e+yf (f
=familon)
e-Y "O-yy Y-Y, 1-Y .rr-p+ny
1
the polystyrene target. A small residual polarization would have had a very small effect because the apparatus was symmetric about 90". The muon position distribu- tion on the target was derived from the intersection of the drift-chamber track with the target from data runs triggered on single positrons from y
'
' V V .
Single positrons from y + - t e ' v ~ were generated ac- cording to the Michel di~tribution,~' F ( x ) = ( 2 x
where x =2P,/mp. The parameter x varies between 0 and 1. No radiative corrections were used in the genera- tion of these positrons because the resolution of the NaI(T1) was large enough to mask this effect and because radiated photons tended to enter the same NaI(T1) crys- tals as the positron. For y + - e t y the positron and photon each have en- ergies approximately equal to one-half of the muon mass and are emitted at 180" with respect to each other. The energy of each particle in y '
+e +e - was generated
uniformly over the allowed region of phase space, con- sistent with conservation of energy and momentum. The final-state particle momentum distributions for
y+-e+yy
were calculated from a general local interac- t i ~ n . ~ ' The resulting form of the distribution is where E,, E l , and E, are the energies of the positron, the higher-energy photon, and the lower-energy photon, re- spectively, 8 is the opening angle between the photons, and K is a constant. This equation can be rewritten as where y =(El
2y g x . A nonlocal
interaction, such as a soft photon being emitted from one
+ y , would have a
different distribution; however, the expected branching ratio would then certainly be lower than that for
+
p++e y .
For muon inner bremsstrahlung, y++e + m y , a coin- cident photon and positron were generated according to the distribution given by Fronsdal and ~ b e r a l l . , ~ To reduce the amount of computer time needed for event generation, only positrons and photons with energies above some threshold were generated; this threshold was
2098
R.
38
K)
1 5
20
At
(ns)
rrns
for events with (a) E + P > 110 MeV and ib)
E + P
< 100 MeV. than 10 MeV and E,,, >
45 MeV: for this region of phase space, the prediction is B;3evv
=
1.18
X
The mea- sured branching ratio is B;3evv
= [ l.
l l k0. l l (stat) 20.08 (syst)]X in agreement with the theoretical predic-
the uncertainty in the threshold of the individual NaI(T1) discriminators: the majority of p f -+e +
e +e -vV events
had at least one particle depositing less than 10 MeV in the NaI(T1). The e + y data were also used to search for light scalar
such as familons, axions, and
tive decay p+-e
+y
f, where f is any particular such bo- son. A discussion of the various Lagrangians that could generate p f -e
+y
f and of the resulting differential dis-
tributions was given in Ref. 31. Events from p i -e
+y f, with the light boson undetected, are characterized by the fact that M:, -0, where M:, is the calculated square of the effective mass of the unobserved neutral particle($. Events from muon inner bremsstrahlung satisfy M:, 2 0 while random events have - 1000 < M t f < 500 M ~ v ~ . This is illustrated in Fig. 26. Strictly speaking, the limit is applicable to m f <
2me since heavier bosons would be
expected to rapidly decay into an e +e - pair. To maximize the sensitivity to p +
y
f, the analysis was performed on data set 111, which had the least un- detected pileup. The final cuts were relaxed to E,, > 38 MeV, EeNa1
> 38 MeV, and O,,, > 140". To utilize the
lower energies, the detection efficiency as a function of energy deposited in each NaI(T1) quadrant had to be determined and then put into the Monte Carlo program. The efficiency was determined by comparing EeNaI from
p+-+e+vT, with EeNa1
from le events with no energy
top quadrant. The number of p + -+e
+y
f
events in the 20 015 events with I At,, 1 < 1.5 ns was estimated with the maximum- likelihood method as described above. Here n, (n,, is the estimate of the number of p+-e
+ y
f ( p + - e + v V y )
and At,,,. Fig- ure 26 shows the M : ~ distributions for p+-e
+y
f,
p+-e+vOy,
randoms and for the data events, together with the distribution corresponding to the maximum- likelihood fit. The difference between the fit and data dis-
(a> -
I
" l " l " l '
I B t I I " I " I " I '
, [ , , I , , , , ,
Data
the effective mass of the unobserved neutral particlek) for events from (a) p-eyf; (b)
p-evVy;
(c) random events; and id) the final data set. (a) and (b) were generated with the Monte Carlo program. Also shown in (d) is the sum of p-tevvy and random events with the relative normalization determined by the best likelihood fit.
Lorenzo Calibbi (Nankai) LFV into ALPs
Past searches: 𝜈 → e 𝛿 a
BR(µ ! e a γ) < 1.1 ⇥ 10−9 (90% CL) Analysis for massless familon ma ≈ 0 (with 1.4×1012 stopped 𝜈+ ) yields: ⇡ BR(µ ! e a γ) ⇡ αem 2π I(xmin, ymin)BR(µ ! e a)
I(xmin, ymin) = Z 1
xmin,ymin
dxdy(x 1)(2 xy y) y2(1 x y)
d x = 2Ee/mµ d y = 2Eγ/mµ
Ee > 38 MeV , Eγ > 38 MeV ) xmin = ymin = 0.72
Crystal Box energy thresholds:
Hirsch et al. ‘09
⇒ Feµ > 9.8 × 108 GeV
<latexit sha1_base64="RfNyowvu4uwr9Cx1VjFme0MXZLU=">ACIHicbVDLSgNBEJz1bXxFPXoZDIKnsKuC8SKioB5VTCJkY5idJIhM7vrTK8SluRPvPgrXjwojf9GiePg6+ChqKqm+6uIJbCoOt+OGPjE5NT0zOzmbn5hcWl7PJKyUSJ5lDkYz0VcAMSBFCEQVKuIo1MBVIKAfto75fvgVtRBReYieGqmLNUDQEZ2ilWnbXvxDNFjKtozvq3ySsTo9rKfgq6dLefo/u5Qs+CgWGeu51oZf6WtETKHVr2Zybdwegf4k3Ijkywlkt+7XI54oCJFLZkzFc2Ospkyj4BK6GT8xEDPeZk2oWBoyu7OaDh7s0g2r1Gkj0rZCpAP1+0TKlDEdFdhOxbBlfnt98T+vkmCjUE1FGCcIR8uaiSYkT7adG60MBRdixhXAt7K+UtphlHm2nGhuD9fvkvKW3lve381vlO7uBwFMcMWSPrZJN4ZJckFNyRoqEk3vySJ7Ji/PgPDmvztuwdcwZzaySH3A+vwBD+qJi</latexit>Slightly weaker but independent
Lorenzo Calibbi (Nankai) LFV into ALPs
Past searches: 𝜐 → e a , 𝜐 → 𝜈 a
27 N 50 MeV/c
1400 "''1'' '1'''1'' '1'' 'I'''I'''I'''I''I~A
1000
800 O(m 200 0.2 0.4 06 0,8 I 1.2 1.4 t.6 1.8
Pw [GeWc]
rest frame (points with error bars). The solid line represents a fit to the data assuming no contribution from the decay m + ec~ N 50 MeV/c
''1'' '1' ''I'''I'''I'''I'''I'''I''C 1400 1200
80O 600
400
200 ,q 02 0.4 0.6 0.8 1 t .2 1.4 1,6 1.8
Pp~ [GeV/c]
corrected muon momentum spectrum in the r pseudo rest frame (points with elTor bars). The solid line represents a fit to the data assuming no contribution from the decay 7- ---+ /~c~ in order to ensure good momentum resolution and trigger conditions. The following restrictions were made to reduce the two photon and QED backgrounds to a negligible level. We ap- plied a cut on a relation between the transverse momentum balance and the total visible momentum of the charged par- ticles [8]
4 i=1
> 4.5 9 p~ 9 c _ 0.55 +0.1 GeV/c
i=1 Ecrns
where pm~ is the transverse momentum of the i-th particle. The shower energy of all charged particles on the three- prong side released in the calorimeter was limited to 3.5
tween oppositely charged particles was required to be less than 0.992. To decrease the qq contamination we allowed no more than two photons on the 3-prong side. In a second selection stage we applied cuts specific to the decay channels m -+ euF and m --~ #uF correspondingly. Electrons were required to have momenta greater than 400 MeV/c. In this region the detection efficiency is about 90% and the pion fake rate is 0.5% [4]. The polar angle 0~i~
%- cos(0~is) _> -0.9, where qe is the charge of the detected electron (positron). We have allowed no more than one pho- ton on the one prong side. The photon energy was limited to 300 MeV. The electron sample consisted of 5055 events
[~ 0.06 i, ,,I,,<l~,l,,,i,,,i ,,,i,,,i ,~ ,i, 1
4
1" 004
0.03 0.02 T 0.01 I I I I I I I I P 0.2 0.4 0,6 08 I 1.2 1.4 t.6
c~ Mass [GeV/c 2]
level on the ratio B(T --, s
muons (full squares) with 25 and 17 events resulting from qq contamination and pion misidentification, respectively. For the muon sample the selection procedure depended
momentum Pl~b > 1.5 GeV/c were required to have hit at least one chamber of the outer layer. In this case the detec- tion efficiency is about 85% and pion fake rate is 2.5%. To suppress the r -+ euF decay contribution the electron like- lihood ratio of the charged track was required to be less than 0.5. In order to suppress background from r --+ pu~ we re- quired that no photons be present on the one-prong side and that the shower energy associated with the charged track be less than 0.5 GeV. The use of the r pseudo rest frame method enables the separation of muons from the background at lab-
strategies based on muon penetration through absorber do not work. The backgrounds in this momentum range are mainly due to one-prong r decays into hadrons. A major fraction of two-body hadronic r decays peaks in the high momentum region in the r pseudo rest frame. This com- ponent was rejected by requiring Pv~ < 0.6 GeV/c. The number of events for each part of the muon spectrum is pre- sented in Table 2. The efficiency corrected and background subtracted spectra of electrons and muons in the r pseudo rest frame are shown in Fig. 2 and 3. The background contributions from the r decays and the acceptance for the investigated r decays were estimated from Monte Carlo using the KORALB/TAUOLA generator, the ARGUS detector simulation and subsequent event recon- struction [10-13]. The r decays into a lepton and an unob- servable particle c~ were generated according to the available phase space. The efficiency corrected experimental spectra were fit to a sum of the theoretical expectations for 3- and 2-body r decays for different masses of o~. We have found no excess expected for the r---+ gc~ decays in the whole kinemati- cally allowed region of c~ mass. The upper limits on the ratio of the branching fraction of the decay m --+ gc~ to de- cay r ---+ guF were obtained by a least squares method as a function of c~ mass. In Fig. 4 the results are presented in terms of the ratio of the branching fraction of 2-body decay m ---+ gc~ to the branching fraction of 3-body decay
T --~ ~/J~ .
In summary, a detailed study of the lepton momen- tum spectra for r decays into a lepton and an unobserv-
BR(⌧ → e a) < 2.7 × 10−3 (95% CL) ⇒ Fτe & 4.3 × 106 GeV , BR(⌧ → µ a) < 4.5 × 10−3 (95% CL) ⇒ Fτµ & 3.3 × 106 GeV .
ZEITSCHRIFT FOR PHYSIK C
9 Springer-Verlag 1995
A search for the lepton-flavour violating decays
T > e(]~ T > ~OL
ARGUS Collaboration
~, R. Wurth DESY, Hamburg, Germany
Institut ftir Physik 2, UniversitS.t Dortmund, Germany
Institut far Kern- und Teilchenphysik 3, Technische Universit~it Dresden Germany
Physikalisches Institut 4, Universit~it Erlangen-Ntirnberg, Germany
Universit~it Hamburg, Germany
Institut fur Hochenergiephysik 5, Universit~it Heidelberg, Germany
Max-Planck-Institut fiir Kernphysik, Heidelberg, Germany
6, D. B. MacFarlane 7, J. D. Prentice 6, P. R. B. Saull 7, K. Tzamariudaki 7, R. G. Van de Water 6, T.-S. Yoon 6 Institute of Particle Physics 8, Canada
Institut fiir Experimentelle Kernphysik 9, Universitfit Karlsruhe, Germany
Institut J. Stefan and Oddelek za fiziko I~ Univerza v Ljubljani, Ljubljana, Slovenia
Institute of Theoretical and Experimental Physics, Moscow, Russia Received: 26 April 1995 1 DESY, IfHM Zeuthen 2 Supported by the German Bundesministerium ffir Forschung und Tech- nologie, under contract number 054DO5 IP 3 Supported by the German Bundesministerium ftir Forscbung und Tech- nologie, under contract number 056DO51P 4 Supported by the German Bundesministerium fiir Forschung und Tech- nologie, under contract number 054ER12P 4 Supported by the German Bundesministerium ftir Forschung und Tech- nologie, under contract number 055HD21P 6 University of Toronto, Toronto, Ontario, Canada 7 McGill University, Montreal, Quebec, Canada s Supported by the Natural Sciences and Engineering Research Council, Canada 9 Supported by the German Bundesministerium ftir Forschung und Tecb nologie, under contract number 055KA11P
with the ARGUS detector at the e+e - storage ring DORIS II at DESY using the "pseudo-rest-frame" technique. We have improved upper limits for two-body ~- -decays into a lepton and an unobservable particle. The problem of fermion families remains one of the central problems in particle physics. The standard SU(3) • SU(2) x U(1) model, as well as its possible "vertical" extensions in the one family framework like SU(5), SU(10) etc., cannot 10 Supported by the Ministry of Science and Technology of the Republic
ZEITSCHRIFT FOR PHYSIK C
9 Springer-Verlag 1995
A search for the lepton-flavour violating decays
T > e(]~ T > ~OL
ARGUS Collaboration
~, R. Wurth DESY, Hamburg, Germany
Institut ftir Physik 2, UniversitS.t Dortmund, Germany
Institut far Kern- und Teilchenphysik 3, Technische Universit~it Dresden Germany
Physikalisches Institut 4, Universit~it Erlangen-Ntirnberg, Germany
Universit~it Hamburg, Germany
Institut fur Hochenergiephysik 5, Universit~it Heidelberg, Germany
Max-Planck-Institut fiir Kernphysik, Heidelberg, Germany
6, D. B. MacFarlane 7, J. D. Prentice 6, P. R. B. Saull 7, K. Tzamariudaki 7, R. G. Van de Water 6, T.-S. Yoon 6 Institute of Particle Physics 8, Canada
Institut fiir Experimentelle Kernphysik 9, Universitfit Karlsruhe, Germany
Institut J. Stefan and Oddelek za fiziko I~ Univerza v Ljubljani, Ljubljana, Slovenia
Institute of Theoretical and Experimental Physics, Moscow, Russia Received: 26 April 1995 1 DESY, IfHM Zeuthen 2 Supported by the German Bundesministerium ffir Forschung und Tech- nologie, under contract number 054DO5 IP 3 Supported by the German Bundesministerium ftir Forscbung und Tech- nologie, under contract number 056DO51P 4 Supported by the German Bundesministerium fiir Forschung und Tech- nologie, under contract number 054ER12P 4 Supported by the German Bundesministerium ftir Forschung und Tech- nologie, under contract number 055HD21P 6 University of Toronto, Toronto, Ontario, Canada 7 McGill University, Montreal, Quebec, Canada s Supported by the Natural Sciences and Engineering Research Council, Canada 9 Supported by the German Bundesministerium ftir Forschung und Tecb nologie, under contract number 055KA11P
with the ARGUS detector at the e+e - storage ring DORIS II at DESY using the "pseudo-rest-frame" technique. We have improved upper limits for two-body ~- -decays into a lepton and an unobservable particle. The problem of fermion families remains one of the central problems in particle physics. The standard SU(3) • SU(2) x U(1) model, as well as its possible "vertical" extensions in the one family framework like SU(5), SU(10) etc., cannot 10 Supported by the Ministry of Science and Technology of the Republic
ma ≈ 0 : With 472 pb-1:
□ 𝜐 → ea ■ 𝜐 → 𝜈a
Summary of the model-independent bounds
Lorenzo Calibbi (Nankai) LFV into ALPs
e− + X → e− + a + X
<latexit sha1_base64="SC1znlh3ZW+bcb3tqmXPE/MsnQ=">ACA3icbVDLSgMxFM3UV62vUXe6CRZBEMtMFXRZdOygn1AO5ZMeqcNzWSGJCOU0uLGX3HjQhG3/oQ7/8Z0OgutHrhwcs695N7jx5wp7ThfVm5hcWl5Jb9aWFvf2Nyt3fqKkokhRqNeCSbPlHAmYCaZpDM5ZAQp9Dwx9cTf3GPUjFInGrhzF4IekJFjBKtJE69h7cneBj3MSTto4mePYiqdKxi07JSYH/EjcjRZSh2rE/292IJiEITlRquU6sfZGRGpGOYwL7URBTOiA9KBlqCAhKG+U3jDGh0bp4iCSpoTGqfpzYkRCpYahbzpDovtq3puK/3mtRAcX3oiJONEg6OyjIOFYR3gaCO4yCVTzoSGESmZ2xbRPJKHaxFYwIbjzJ/8l9XLJPS2Vb86KlcsjzaRwfoCLnoHFXQNaqiGqLoAT2hF/RqPVrP1pv1PmvNWdnMLvoF6+Mb8f+UgA=</latexit>ma < O(10) keV
<latexit sha1_base64="wy5mfF6oGUpNlAMoEzyw492k4O8=">ACHicbVDLSsNAFJ3UV62vqEsXDhahbkpSBV24KLpxZwX7gCaEyXTSDp1JwsxEKHdufFX3LhQxK2f4M6/cdJmoa0HLhzOuZd7/FjRqWyrG+jsLS8srpWXC9tbG5t75i7ey0ZJQKTJo5YJDo+koTRkDQVYx0YkEQ9xlp+8PrzG8/ECFpFN6rUxcjvohDShGSkuecg9BCeXE4cjNcCIpbfjim2dTBzB4ZC0oGeWrao1BVwkdk7KIEfDM7+cXoQTkKFGZKya1uxclMkFMWMjEtOIkmM8BD1SVfTEHEi3XT6yBgea6UHg0joChWcqr8nUsSlHFfd2b3ynkvE/zuokKLtyUhnGiSIhni4KEQRXBLBXYo4JgxUaICyovhXiARIK51dSYdgz7+8SFq1qn1ard2dletXeRxFcACOQAXY4BzUwQ1ogCbA4BE8g1fwZjwZL8a78TFrLRj5zD74A+PzBxRmLg=</latexit>Bounds on ALP-electron couplings from energy loss in star systems (red giants, white dwarfs) due to processes like:
F A
ee & 3.7 × 109 GeV
If a lighter than T inside the star
Bertolami at al ‘14
F V,A
ij
≡ 2fa CV,A
ij
<latexit sha1_base64="ldbSBVFT1tFMDSnzyzOYl+f3Mk=">ACF3icbVDLSsNAFJ3UV62vqEs3g0VwISGpgi6rBXFZwT6giWEynbRjJw9nJoUS8hdu/BU3LhRxqzv/xmbRW09MHA451zu3OPFjApmj9aYWl5ZXWtuF7a2Nza3tF395oiSjgmDRyxiLc9JAijIWlIKhlpx5ygwGOk5Q1qY781JFzQKLyTo5g4AeqF1KcYSW5unF9nzZPLjM3pQ8ZtMljQofQ9jnCaQX6LsrS2kwgc/WyaZgTwEVi5aQMctRd/dvuRjgJSCgxQ0J0LDOWToq4pJiRrGQngsQID1CPdBQNUCEk07uyuCRUrQj7h6oYQTdXYiRYEQo8BTyQDJvpj3xuJ/XieR/oWT0jBOJAnxdJGfMCgjOC4JdiknWLKRIghzqv4KcR+pUqSqsqRKsOZPXiTNimGdGpXbs3L1Kq+jCA7AITgGFjgHVXAD6qABMHgCL+ANvGvP2qv2oX1OowUtn9kHf6B9/QLBs5+w</latexit>Fij ≡ 2fa q |CV
ij |2 + |CA ij|2
<latexit sha1_base64="UgJGgFEiKJwhr5AYNxEv5pPyXI=">ACKXicbVDLSgMxFM3UV62vqks3wSIQpmpgi6rBXFZwT6g0w6ZNPGZh5NMoWSzu+48VfcKCjq1h8xfSDaeiBwOdcbu5xI0aFNM0PI7W0vLK6l7PbGxube9kd/eqIow5JhUcspDXSQIowGpSCoZqUecIN9lpOb2SmO/NiBc0DC4k8OINH3UCahHMZJacrLFa0fR+8Qm/ZgObI8jrArQc1CibNHnUo1KLVNJplRqwBP4Fi4/BGSxMnmzLw5AVwk1ozkwAxlJ/tit0Mc+ySQmCEhGpYZyaZCXFLMSJKxY0EihHuoQxqaBsgnoqkmlybwSCt6IVcv0DCifp7QiFfiKHv6qSPZFfMe2PxP68RS+iqWgQxZIEeLrIixmUIRzXBtuUEyzZUBOEOdV/hbiLdF1Sl5vRJVjzJy+SaiFvneYLt2e54tWsjQ4AIfgGFjgHBTBDSiDCsDgATyBV/BmPBrPxrvxOY2mjNnMPvgD4+sb5WoOw=</latexit>ma ≈ 0
Comparison in the case Coupling Lower Bound Process F A
ee
3.7 ⇥ 109 GeV Star cooling Fµe 5.5 ⇥ 109 GeV µ ! e a Fµe (V A) 1.2 ⇥ 109 GeV µ ! e a Fµe 9.8 ⇥ 108 GeV µ ! e a γ Fτe 4.3 ⇥ 106 GeV τ ! e a Fτµ 3.3 ⇥ 106 GeV τ ! µ a
Summary of the model-independent bounds
Lorenzo Calibbi (Nankai) LFV into ALPs
Bounds on ALP-electron couplings from energy loss in star systems (red giants, white dwarfs) due to processes like:
F V,A
ij
≡ 2fa CV,A
ij
<latexit sha1_base64="ldbSBVFT1tFMDSnzyzOYl+f3Mk=">ACF3icbVDLSsNAFJ3UV62vqEs3g0VwISGpgi6rBXFZwT6giWEynbRjJw9nJoUS8hdu/BU3LhRxqzv/xmbRW09MHA451zu3OPFjApmj9aYWl5ZXWtuF7a2Nza3tF395oiSjgmDRyxiLc9JAijIWlIKhlpx5ygwGOk5Q1qY781JFzQKLyTo5g4AeqF1KcYSW5unF9nzZPLjM3pQ8ZtMljQofQ9jnCaQX6LsrS2kwgc/WyaZgTwEVi5aQMctRd/dvuRjgJSCgxQ0J0LDOWToq4pJiRrGQngsQID1CPdBQNUCEk07uyuCRUrQj7h6oYQTdXYiRYEQo8BTyQDJvpj3xuJ/XieR/oWT0jBOJAnxdJGfMCgjOC4JdiknWLKRIghzqv4KcR+pUqSqsqRKsOZPXiTNimGdGpXbs3L1Kq+jCA7AITgGFjgHVXAD6qABMHgCL+ANvGvP2qv2oX1OowUtn9kHf6B9/QLBs5+w</latexit>Fij ≡ 2fa q |CV
ij |2 + |CA ij|2
<latexit sha1_base64="UgJGgFEiKJwhr5AYNxEv5pPyXI=">ACKXicbVDLSgMxFM3UV62vqks3wSIQpmpgi6rBXFZwT6g0w6ZNPGZh5NMoWSzu+48VfcKCjq1h8xfSDaeiBwOdcbu5xI0aFNM0PI7W0vLK6l7PbGxube9kd/eqIow5JhUcspDXSQIowGpSCoZqUecIN9lpOb2SmO/NiBc0DC4k8OINH3UCahHMZJacrLFa0fR+8Qm/ZgObI8jrArQc1CibNHnUo1KLVNJplRqwBP4Fi4/BGSxMnmzLw5AVwk1ozkwAxlJ/tit0Mc+ySQmCEhGpYZyaZCXFLMSJKxY0EihHuoQxqaBsgnoqkmlybwSCt6IVcv0DCifp7QiFfiKHv6qSPZFfMe2PxP68RS+iqWgQxZIEeLrIixmUIRzXBtuUEyzZUBOEOdV/hbiLdF1Sl5vRJVjzJy+SaiFvneYLt2e54tWsjQ4AIfgGFjgHBTBDSiDCsDgATyBV/BmPBrPxrvxOY2mjNnMPvgD4+sb5WoOw=</latexit>ma ≈ 0
Comparison in the case Coupling Lower Bound Process F A
ee
3.7 ⇥ 109 GeV Star cooling Fµe 5.5 ⇥ 109 GeV µ ! e a Fµe (V A) 1.2 ⇥ 109 GeV µ ! e a Fµe 9.8 ⇥ 108 GeV µ ! e a γ Fτe 4.3 ⇥ 106 GeV τ ! e a Fτµ 3.3 ⇥ 106 GeV τ ! µ a
Giannotti at al ‘17
Hints (~3𝜏) for non-standard WD cooling require:
F A
ee ≈ 6 × 109 GeV
<latexit sha1_base64="B5iEDb0t+eIaSBtSzcmxIy2/PDw=">ACE3icbVDJSgNBEO2JW4xb1KOXxiCIhzATxeUWFdRjBLNAZjL0dCpJk56F7h4xDMk3ePFXvHhQxKsXb/6NneWgiQ8KHu9VUVXPiziTyjS/jdTc/MLiUno5s7K6tr6R3dyqyDAWFMo05KGoeUQCZwGUFVMcapEA4nscql73cuhX70FIFgZ3qheB45N2wFqMEqUlN3uArxrnbgLQxwObRJEIHwb42FbMB4kts3E2SGzh42uo9N1szsybI+BZYk1IDk1QcrNfdjOksQ+BopxIWbfMSDkJEYpRDv2MHUuICO2SNtQ1DYje6Sjn/p4TytN3AqFrkDhkfp7IiG+lD3f050+UR057Q3F/7x6rFqnTsKCKFYQ0PGiVsyxCvEwINxkAqjiPU0IFUzfimHCEKVjGjQ7CmX54lULeOswXbo9yxYtJHGm0g3bRPrLQCSqiG1RCZUTRI3pGr+jNeDJejHfjY9yaMiYz2+gPjM8fZedSg=</latexit>e− + X → e− + a + X
<latexit sha1_base64="SC1znlh3ZW+bcb3tqmXPE/MsnQ=">ACA3icbVDLSgMxFM3UV62vUXe6CRZBEMtMFXRZdOygn1AO5ZMeqcNzWSGJCOU0uLGX3HjQhG3/oQ7/8Z0OgutHrhwcs695N7jx5wp7ThfVm5hcWl5Jb9aWFvf2Nyt3fqKkokhRqNeCSbPlHAmYCaZpDM5ZAQp9Dwx9cTf3GPUjFInGrhzF4IekJFjBKtJE69h7cneBj3MSTto4mePYiqdKxi07JSYH/EjcjRZSh2rE/292IJiEITlRquU6sfZGRGpGOYwL7URBTOiA9KBlqCAhKG+U3jDGh0bp4iCSpoTGqfpzYkRCpYahbzpDovtq3puK/3mtRAcX3oiJONEg6OyjIOFYR3gaCO4yCVTzoSGESmZ2xbRPJKHaxFYwIbjzJ/8l9XLJPS2Vb86KlcsjzaRwfoCLnoHFXQNaqiGqLoAT2hF/RqPVrP1pv1PmvNWdnMLvoF6+Mb8f+UgA=</latexit> Summary of the model-independent bounds
Lorenzo Calibbi (Nankai) LFV into ALPs
Bounds on ALP-electron couplings from energy loss in star systems (red giants, white dwarfs) due to processes like:
F V,A
ij
≡ 2fa CV,A
ij
<latexit sha1_base64="ldbSBVFT1tFMDSnzyzOYl+f3Mk=">ACF3icbVDLSsNAFJ3UV62vqEs3g0VwISGpgi6rBXFZwT6giWEynbRjJw9nJoUS8hdu/BU3LhRxqzv/xmbRW09MHA451zu3OPFjApmj9aYWl5ZXWtuF7a2Nza3tF395oiSjgmDRyxiLc9JAijIWlIKhlpx5ygwGOk5Q1qY781JFzQKLyTo5g4AeqF1KcYSW5unF9nzZPLjM3pQ8ZtMljQofQ9jnCaQX6LsrS2kwgc/WyaZgTwEVi5aQMctRd/dvuRjgJSCgxQ0J0LDOWToq4pJiRrGQngsQID1CPdBQNUCEk07uyuCRUrQj7h6oYQTdXYiRYEQo8BTyQDJvpj3xuJ/XieR/oWT0jBOJAnxdJGfMCgjOC4JdiknWLKRIghzqv4KcR+pUqSqsqRKsOZPXiTNimGdGpXbs3L1Kq+jCA7AITgGFjgHVXAD6qABMHgCL+ANvGvP2qv2oX1OowUtn9kHf6B9/QLBs5+w</latexit>Fij ≡ 2fa q |CV
ij |2 + |CA ij|2
<latexit sha1_base64="UgJGgFEiKJwhr5AYNxEv5pPyXI=">ACKXicbVDLSgMxFM3UV62vqks3wSIQpmpgi6rBXFZwT6g0w6ZNPGZh5NMoWSzu+48VfcKCjq1h8xfSDaeiBwOdcbu5xI0aFNM0PI7W0vLK6l7PbGxube9kd/eqIow5JhUcspDXSQIowGpSCoZqUecIN9lpOb2SmO/NiBc0DC4k8OINH3UCahHMZJacrLFa0fR+8Qm/ZgObI8jrArQc1CibNHnUo1KLVNJplRqwBP4Fi4/BGSxMnmzLw5AVwk1ozkwAxlJ/tit0Mc+ySQmCEhGpYZyaZCXFLMSJKxY0EihHuoQxqaBsgnoqkmlybwSCt6IVcv0DCifp7QiFfiKHv6qSPZFfMe2PxP68RS+iqWgQxZIEeLrIixmUIRzXBtuUEyzZUBOEOdV/hbiLdF1Sl5vRJVjzJy+SaiFvneYLt2e54tWsjQ4AIfgGFjgHBTBDSiDCsDgATyBV/BmPBrPxrvxOY2mjNnMPvgD4+sb5WoOw=</latexit>ma ≈ 0
Comparison in the case Coupling Lower Bound Process F A
ee
3.7 ⇥ 109 GeV Star cooling Fµe 5.5 ⇥ 109 GeV µ ! e a Fµe (V A) 1.2 ⇥ 109 GeV µ ! e a Fµe 9.8 ⇥ 108 GeV µ ! e a γ Fτe 4.3 ⇥ 106 GeV τ ! e a Fτµ 3.3 ⇥ 106 GeV τ ! µ a
e− + X → e− + a + X
<latexit sha1_base64="SC1znlh3ZW+bcb3tqmXPE/MsnQ=">ACA3icbVDLSgMxFM3UV62vUXe6CRZBEMtMFXRZdOygn1AO5ZMeqcNzWSGJCOU0uLGX3HjQhG3/oQ7/8Z0OgutHrhwcs695N7jx5wp7ThfVm5hcWl5Jb9aWFvf2Nyt3fqKkokhRqNeCSbPlHAmYCaZpDM5ZAQp9Dwx9cTf3GPUjFInGrhzF4IekJFjBKtJE69h7cneBj3MSTto4mePYiqdKxi07JSYH/EjcjRZSh2rE/292IJiEITlRquU6sfZGRGpGOYwL7URBTOiA9KBlqCAhKG+U3jDGh0bp4iCSpoTGqfpzYkRCpYahbzpDovtq3puK/3mtRAcX3oiJONEg6OyjIOFYR3gaCO4yCVTzoSGESmZ2xbRPJKHaxFYwIbjzJ/8l9XLJPS2Vb86KlcsjzaRwfoCLnoHFXQNaqiGqLoAT2hF/RqPVrP1pv1PmvNWdnMLvoF6+Mb8f+UgA=</latexit>Hints (~3𝜏) for non-standard WD cooling require:
F A
ee ≈ 6 × 109 GeV
<latexit sha1_base64="B5iEDb0t+eIaSBtSzcmxIy2/PDw=">ACE3icbVDJSgNBEO2JW4xb1KOXxiCIhzATxeUWFdRjBLNAZjL0dCpJk56F7h4xDMk3ePFXvHhQxKsXb/6NneWgiQ8KHu9VUVXPiziTyjS/jdTc/MLiUno5s7K6tr6R3dyqyDAWFMo05KGoeUQCZwGUFVMcapEA4nscql73cuhX70FIFgZ3qheB45N2wFqMEqUlN3uArxrnbgLQxwObRJEIHwb42FbMB4kts3E2SGzh42uo9N1szsybI+BZYk1IDk1QcrNfdjOksQ+BopxIWbfMSDkJEYpRDv2MHUuICO2SNtQ1DYje6Sjn/p4TytN3AqFrkDhkfp7IiG+lD3f050+UR057Q3F/7x6rFqnTsKCKFYQ0PGiVsyxCvEwINxkAqjiPU0IFUzfimHCEKVjGjQ7CmX54lULeOswXbo9yxYtJHGm0g3bRPrLQCSqiG1RCZUTRI3pGr+jNeDJejHfjY9yaMiYz2+gPjM8fZedSg=</latexit>Giannotti at al ‘17
Future prospects: Mu3e
Lorenzo Calibbi (Nankai) LFV into ALPs
p [MeV] 20 40 60 80 100 Events per 100keV 0.2 0.4 0.6 0.8 1 1.2
6
10 ×
BG: SM decays(a) Simulated background events. p [MeV] 20 40 60 80 100 Events per 100keV 0.2 0.4 0.6 0.8 1
3
10 ×
=60MeV X Signal: m(b) Simulated µ → eX signal events.
Perrevoort (Mu3e) ‘18
Potential search for performed on momentum histograms filled with online reconstructed short tracks
Future prospects: Mu3e
Lorenzo Calibbi (Nankai) LFV into ALPs
Potential search for performed on momentum histograms filled with online reconstructed short tracks
ma ≈ 0 : BR(µ → e a) < 10−8 = ⇒ Fµe & 9 × 1010 GeV.
<latexit sha1_base64="RBtWNU8Hta49GDemrY0EW1ETzR8=">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</latexit>[MeV]
X
m 10 20 30 40 50 60 70 80 90 Branching Fraction at 90% CL
9 −
10
8 −
10
7 −
10
6 −
10
5 −
10
4 −
10
3 −
10
stops µ
1510 × Mu3e Phase I SIM: 2.6 TWIST 2014 Mu3e online reco. (ext.calib.) Mu3e online reco. (sim. calib.)
Mu3e: Work in progress
Expected limit for phase I (2.6×1015 𝜈+):
Perrevoort (Mu3e) ‘18
Future prospects: COMET/Mu2e
Lorenzo Calibbi (Nankai) LFV into ALPs
20 40 60 80 100 0.00 0.05 0.10 0.15 EeMeV 1 d dEe MeV1 100 101 102 103 104 105 1018 1016 1014 1012 1010 EeMeV 1 d dEe MeV1
Spectrum of 𝜈 → ea emission in orbit (for Al): DIO
B(µ → eJ) ∼ NRRµe fJ Γcapture Γ(µ → eνµ¯ νe) ∼ NRRµe fJ 1.5
Sensitivity in terms of the 𝜈 → e conv. limit:
Fraction of 𝜈 → ea events in the signal region Phase-space correction factor
ma ≈ 0
Future prospects: COMET/Mu2e
Lorenzo Calibbi (Nankai) LFV into ALPs
20 40 60 80 100 0.00 0.05 0.10 0.15 EeMeV 1 d dEe MeV1 100 101 102 103 104 105 1018 1016 1014 1012 1010 EeMeV 1 d dEe MeV1
Spectrum of 𝜈 → ea emission in orbit (for Al): DIO
B(µ → eJ) ∼ NRRµe fJ Γcapture Γ(µ → eνµ¯ νe) ∼ NRRµe fJ 1.5
Sensitivity in terms of the 𝜈 → e conv. limit:
27 (in Al) 2×10-10 (Ee > 100 MeV) 10-17
2×10-6 ma ≈ 0
Fraction of 𝜈 → ea events in the signal region Phase-space correction factor
Future prospects: COMET/Mu2e
Lorenzo Calibbi (Nankai) LFV into ALPs
20 40 60 80 100 0.00 0.05 0.10 0.15 EeMeV 1 d dEe MeV1 100 101 102 103 104 105 1018 1016 1014 1012 1010 EeMeV 1 d dEe MeV1
Spectrum of 𝜈 → ea emission in orbit (for Al): DIO
B(µ → eJ) ∼ NRRµe fJ Γcapture Γ(µ → eνµ¯ νe) ∼ NRRµe fJ 1.5
Sensitivity in terms of the 𝜈 → e conv. limit:
2×10-6
Possible bound at the level of Jodidio et al. Limited by the 𝜈 → e conv. signal region (only the tail included): dedicated search?
ma ≈ 0
Future prospects: MEG II
Lorenzo Calibbi (Nankai) LFV into ALPs
1 101 10-7 10-6 10-5 DEe @MeVD BRHmÆe aL
MEG II- fwd ECAL10 cm - 1014m TRIUMF - ermetic - 107 m
Poor theorists’ estimate of the sensitivity of a dedicate run (2 weeks dedicated run with 108 𝜈+/s):
Jodidio et al.
90% CL bound Positron energy resolution
∆Ee = 1 MeV : BR(µ → ea) < 3 × 10−7
<latexit sha1_base64="G2rNMWK0z8PLiOE85F/NEpM08JQ=">ACLXicbVBdSxtBFJ3VajV+Rfvoy6VBUNCwawqKIha6EvBiolCNobZyU0cMrO7zNwVwrL+oL70rxTB6X0tX+jk5gHvw4MnHvOvdy5J0qVtOT7D97E5Iep6Y8zs6W5+YXFpfLySsMmRFYF4lKzGXELSoZY50kKbxMDXIdKbyI+sdD/+IGjZVJfE6DFua92LZlYKTk9rlk/AEFXH42kY4gADCzTw0Gr5jo9iD21sYVUdnxXqos5ASQL4B+1ALSWq0EPhX+dZO0S5X/Ko/ArwlwZhU2Bin7fJd2ElEpjEmobi1zcBPqZVzQ1IoLEphZjHlos972HQ05m5ZKx9dW8CaUzrQTYx7McFIfT6Rc23tQEeuU3O6tq+9ofie18you9vKZxmhLF4WtTNFLizh9FBRxoUpAaOcGk+yuIa264IBdwyYUQvD75LWlsV4NadfvHl8rh0TiOGbKPrN1FrAdsi+sVNWZ4L9ZL/ZA3v0fn3h/v71PrhDe+cRewPv3H/jkpPA=</latexit>(1014 µ+)
<latexit sha1_base64="gqKdACY5q3zSL4psgrhLIf/pRA=">AB+3icbVDLSgMxFM3UV62vsS7dBItQUcpMLeiy6MZlBfuAzrRk0rQNTJDkhHLML/ixoUibv0Rd/6NaTsLbT1w4XDOvdx7TxAxqrTjfFu5tfWNza38dmFnd2/wD4stlQYS0yaOGSh7ARIEUYFaWqGelEkiAeMNIOJrczv/1IpKheNDTiPgcjQdUoy0kfp2sew6vcStpdC7gB6Pe+dnfbvkVJw54CpxM1ICGRp9+8sbhDjmRGjMkFJd14m0nyCpKWYkLXixIhHCEzQiXUMF4kT5yfz2FJ4aZQCHoTQlNJyrvycSxJWa8sB0cqTHatmbif953VgPr/2EijWRODFomHMoA7hLAg4oJgzaGICypuRXiMZIaxNXwYTgLr+8SlrVintZqd7XSvWbLI48OAYnoAxcAXq4A40QBNg8ASewSt4s1LrxXq3PhatOSubOQJ/YH3+ANWCkl8=</latexit>~1.5 m from the target, radius ~ 10 cm What about a Jodidio-like search at MEG II for ma ≈ 0 with a forward calorimeter?
]
2
[GeV/c
X
m 500 1000 1500
upper limit of Br x10 0.7 0.8 0.9 1 1.1 1.2
τ → µa
<latexit sha1_base64="hjlYaxL5LUMsKmrET3P24rcFqdY=">AB9HicbVDLSgNBEJz1GeMr6tHLYBA8hV0R9Bj04jGCeUB2Cb2T2WTIzOw6j0BY8h1ePCji1Y/x5t84SfagiQUNRVU3V1xpk2v/tra1vbG5tl3bKu3v7B4eVo+OWTq0itElSnqpODJpyJmnTMNpJ1MURMxpOx7dzfz2mCrNUvloJhmNBAwkSxgB46QoNGBDk+JQWAy9StWv+XPgVRIUpIoKNHqVr7CfEiuoNISD1t3Az0yUgzKMcDoth1bTDMgIBrTrqARBdZTPj57ic6f0cZIqV9Lgufp7Igeh9UTErlOAGeplbyb+53WtSW6inMnMGirJYlFiOXZvzhLAfaYoMXziCBDF3K2YDEBMS6nsgshWH5lbQua4FfCx6uqvXbIo4SOkVn6AIF6BrV0T1qoCYi6Ak9o1f05o29F+/d+1i0rnFzAn6A+/zB0NekcA=</latexit><latexit sha1_base64="hjlYaxL5LUMsKmrET3P24rcFqdY=">AB9HicbVDLSgNBEJz1GeMr6tHLYBA8hV0R9Bj04jGCeUB2Cb2T2WTIzOw6j0BY8h1ePCji1Y/x5t84SfagiQUNRVU3V1xpk2v/tra1vbG5tl3bKu3v7B4eVo+OWTq0itElSnqpODJpyJmnTMNpJ1MURMxpOx7dzfz2mCrNUvloJhmNBAwkSxgB46QoNGBDk+JQWAy9StWv+XPgVRIUpIoKNHqVr7CfEiuoNISD1t3Az0yUgzKMcDoth1bTDMgIBrTrqARBdZTPj57ic6f0cZIqV9Lgufp7Igeh9UTErlOAGeplbyb+53WtSW6inMnMGirJYlFiOXZvzhLAfaYoMXziCBDF3K2YDEBMS6nsgshWH5lbQua4FfCx6uqvXbIo4SOkVn6AIF6BrV0T1qoCYi6Ak9o1f05o29F+/d+1i0rnFzAn6A+/zB0NekcA=</latexit><latexit sha1_base64="hjlYaxL5LUMsKmrET3P24rcFqdY=">AB9HicbVDLSgNBEJz1GeMr6tHLYBA8hV0R9Bj04jGCeUB2Cb2T2WTIzOw6j0BY8h1ePCji1Y/x5t84SfagiQUNRVU3V1xpk2v/tra1vbG5tl3bKu3v7B4eVo+OWTq0itElSnqpODJpyJmnTMNpJ1MURMxpOx7dzfz2mCrNUvloJhmNBAwkSxgB46QoNGBDk+JQWAy9StWv+XPgVRIUpIoKNHqVr7CfEiuoNISD1t3Az0yUgzKMcDoth1bTDMgIBrTrqARBdZTPj57ic6f0cZIqV9Lgufp7Igeh9UTErlOAGeplbyb+53WtSW6inMnMGirJYlFiOXZvzhLAfaYoMXziCBDF3K2YDEBMS6nsgshWH5lbQua4FfCx6uqvXbIo4SOkVn6AIF6BrV0T1qoCYi6Ak9o1f05o29F+/d+1i0rnFzAn6A+/zB0NekcA=</latexit><latexit sha1_base64="hjlYaxL5LUMsKmrET3P24rcFqdY=">AB9HicbVDLSgNBEJz1GeMr6tHLYBA8hV0R9Bj04jGCeUB2Cb2T2WTIzOw6j0BY8h1ePCji1Y/x5t84SfagiQUNRVU3V1xpk2v/tra1vbG5tl3bKu3v7B4eVo+OWTq0itElSnqpODJpyJmnTMNpJ1MURMxpOx7dzfz2mCrNUvloJhmNBAwkSxgB46QoNGBDk+JQWAy9StWv+XPgVRIUpIoKNHqVr7CfEiuoNISD1t3Az0yUgzKMcDoth1bTDMgIBrTrqARBdZTPj57ic6f0cZIqV9Lgufp7Igeh9UTErlOAGeplbyb+53WtSW6inMnMGirJYlFiOXZvzhLAfaYoMXziCBDF3K2YDEBMS6nsgshWH5lbQua4FfCx6uqvXbIo4SOkVn6AIF6BrV0T1qoCYi6Ak9o1f05o29F+/d+1i0rnFzAn6A+/zB0NekcA=</latexit>1/ab
]
2
[GeV/c
X
m 500 1000 1500 N S/ 1.2 1.4 1.6 1.8 2 2.2
Yoshinobu Hayasaka (Belle) ‘17
Future prospects: B-factories/Belle-II
Lorenzo Calibbi (Nankai) LFV into ALPs
Simulation of S and B and limit that can be set using the Belle data set (1/ab):
Belle (1/ab) prospect: BR(⌧ → µ a) < 1.1 × 10−4 ⇒ Fτµ & 2.1 × 107 GeV. Belle-II (50/ab) prospect: BR(⌧ → µ a) < 1.4 × 10−5 ⇒ Fτµ & 5.9 × 107 GeV, Estimated by rescaling as
ma ≈ 0 : √ L
<latexit sha1_base64="Jq2aH9H1IM5GTH1U/CLEUAmvj5U=">AB+3icbVDLSsNAFL3xWesr1qWbwSK4KkVdFl048JFBfuAJpTJdNoOnUzizEQsIb/ixoUibv0Rd/6NkzYLbT0wcDjnXu6ZE8ScKe0439bK6tr6xmZpq7y9s7u3bx9U2ipKJKEtEvFIdgOsKGeCtjTnHZjSXEYcNoJte53mkUrFI3OtpTP0QjwQbMoK1kfp2xVMPUqdeiPWYJ7eZlnfrjo1Zwa0TNyCVKFAs29/eYOIJCEVmnCsVM91Yu2nWGpGOM3KXqJojMkEj2jPUIFDqvx0lj1DJ0YZoGEkzRMazdTfGykOlZqGgZnM6pFLxf/83qJHl76KRNxoqkg80PDhCMdobwINGCSEs2nhmAimcmKyBhLTLSpq2xKcBe/vEza9Zp7VqvfnVcbV0UdJTiCYzgFy6gATfQhBYQeIJneIU3K7NerHfrYz6YhU7h/AH1ucP4XKU+w=</latexit> hφi
<latexit sha1_base64="2kily8sN5sd4DnV/O4STspeLYMk=">AB/HicbZDLSsNAFIZPvNZ6i3bpZrAIrkpSBV0W3bisYC/QhDKZTtqhk0mYmQgh1Fdx40IRtz6IO9/GaZqFtv4w8PGfczhn/iDhTGnH+bW1jc2t7YrO9Xdvf2DQ/vouKviVBLaITGPZT/AinImaEczWk/kRHAae9YHo7r/ceqVQsFg86S6gf4bFgISNYG2to1zyOxZhT5CUT5smCh3bdaTiF0Cq4JdShVHtof3mjmKQRFZpwrNTAdRLt51hqRjidVb1U0QSTKR7TgUGBI6r8vDh+hs6M0JhLM0TGhXu74kcR0plUWA6I6wnark2N/+rDVIdXvs5E0mqSCLRWHKkY7RPAk0YpISzTMDmEhmbkVkgiUm2uRVNSG4y19ehW6z4V40mveX9dZNGUcFTuAUzsGFK2jBHbShAwQyeIZXeLOerBfr3fpYtK5Z5UwN/sj6/AG0WZTO</latexit>hφi
<latexit sha1_base64="2kily8sN5sd4DnV/O4STspeLYMk=">AB/HicbZDLSsNAFIZPvNZ6i3bpZrAIrkpSBV0W3bisYC/QhDKZTtqhk0mYmQgh1Fdx40IRtz6IO9/GaZqFtv4w8PGfczhn/iDhTGnH+bW1jc2t7YrO9Xdvf2DQ/vouKviVBLaITGPZT/AinImaEczWk/kRHAae9YHo7r/ceqVQsFg86S6gf4bFgISNYG2to1zyOxZhT5CUT5smCh3bdaTiF0Cq4JdShVHtof3mjmKQRFZpwrNTAdRLt51hqRjidVb1U0QSTKR7TgUGBI6r8vDh+hs6M0JhLM0TGhXu74kcR0plUWA6I6wnark2N/+rDVIdXvs5E0mqSCLRWHKkY7RPAk0YpISzTMDmEhmbkVkgiUm2uRVNSG4y19ehW6z4V40mveX9dZNGUcFTuAUzsGFK2jBHbShAwQyeIZXeLOerBfr3fpYtK5Z5UwN/sj6/AG0WZTO</latexit>hφi
<latexit sha1_base64="2kily8sN5sd4DnV/O4STspeLYMk=">AB/HicbZDLSsNAFIZPvNZ6i3bpZrAIrkpSBV0W3bisYC/QhDKZTtqhk0mYmQgh1Fdx40IRtz6IO9/GaZqFtv4w8PGfczhn/iDhTGnH+bW1jc2t7YrO9Xdvf2DQ/vouKviVBLaITGPZT/AinImaEczWk/kRHAae9YHo7r/ceqVQsFg86S6gf4bFgISNYG2to1zyOxZhT5CUT5smCh3bdaTiF0Cq4JdShVHtof3mjmKQRFZpwrNTAdRLt51hqRjidVb1U0QSTKR7TgUGBI6r8vDh+hs6M0JhLM0TGhXu74kcR0plUWA6I6wnark2N/+rDVIdXvs5E0mqSCLRWHKkY7RPAk0YpISzTMDmEhmbkVkgiUm2uRVNSG4y19ehW6z4V40mveX9dZNGUcFTuAUzsGFK2jBHbShAwQyeIZXeLOerBfr3fpYtK5Z5UwN/sj6/AG0WZTO</latexit>hφi
<latexit sha1_base64="2kily8sN5sd4DnV/O4STspeLYMk=">AB/HicbZDLSsNAFIZPvNZ6i3bpZrAIrkpSBV0W3bisYC/QhDKZTtqhk0mYmQgh1Fdx40IRtz6IO9/GaZqFtv4w8PGfczhn/iDhTGnH+bW1jc2t7YrO9Xdvf2DQ/vouKviVBLaITGPZT/AinImaEczWk/kRHAae9YHo7r/ceqVQsFg86S6gf4bFgISNYG2to1zyOxZhT5CUT5smCh3bdaTiF0Cq4JdShVHtof3mjmKQRFZpwrNTAdRLt51hqRjidVb1U0QSTKR7TgUGBI6r8vDh+hs6M0JhLM0TGhXu74kcR0plUWA6I6wnark2N/+rDVIdXvs5E0mqSCLRWHKkY7RPAk0YpISzTMDmEhmbkVkgiUm2uRVNSG4y19ehW6z4V40mveX9dZNGUcFTuAUzsGFK2jBHbShAwQyeIZXeLOerBfr3fpYtK5Z5UwN/sj6/AG0WZTO</latexit>fL
<latexit sha1_base64="v14wMd3bMTSbY9Z09vXHvlrPFU=">AB6nicbVA9SwNBEJ3zM8avqKXNYhCswl0UtAzaWFhENB+QHGFvs5cs2ds7dueEcOQn2FgoYusvsvPfuEmu0MQHA4/3ZpiZFyRSGHTdb2dldW19Y7OwVdze2d3bLx0cNk2casYbLJaxbgfUcCkUb6BAyduJ5jQKJG8Fo5up3ri2ohYPeI4X5EB0qEglG0kPYu+uVym7FnYEsEy8nZchR75W+uv2YpRFXyCQ1puO5CfoZ1SiY5JNiNzU8oWxEB7xjqaIRN342O3VCTq3SJ2GsbSkM/X3REYjY8ZRYDsjikOz6E3F/7xOiuGVnwmVpMgVmy8KU0kwJtO/SV9ozlCOLaFMC3srYUOqKUObTtG4C2+vEya1Yp3XqneX5Rr13kcBTiGEzgDy6hBrdQhwYwGMAzvMKbI50X5935mLeuOPnMEfyB8/kDGn6NrQ=</latexit>fR
<latexit sha1_base64="9J/vLXB8v6dNBCWpbBft/lJvWY=">AB6nicbVDLSgNBEOz1GeMr6tHLYBA8hd0o6DHoxWN85AHJEmYnvcmQ2dlZlYISz7BiwdFvPpF3vwbJ8keNLGgoajqprsrSATXxnW/nZXVtfWNzcJWcXtnd2+/dHDY1HGqGDZYLGLVDqhGwSU2DcC24lCGgUCW8HoZuq3nlBpHstHM07Qj+hA8pAzaqz0EPbue6WyW3FnIMvEy0kZctR7pa9uP2ZphNIwQbXueG5i/Iwqw5nASbGbakwoG9EBdiyVNELtZ7NTJ+TUKn0SxsqWNGSm/p7IaKT1OApsZ0TNUC96U/E/r5Oa8MrPuExSg5LNF4WpICYm079JnytkRowtoUxeythQ6oMzadog3BW3x5mTSrFe+8Ur27KNeu8zgKcAwncAYeXEINbqEODWAwgGd4hTdHOC/Ou/Mxb1x8pkj+APn8wcjlo2z</latexit>H
<latexit sha1_base64="OmnsBIcI7uL9xT1nclacUzB0Hk=">AB6HicbVDLTgJBEOzF+IL9ehlIjHxRHbRI9ELxwhkUcCGzI79MLI7OxmZtaEL7AiweN8eonefNvHGAPClbSaWqO91dQSK4Nq7eQ2Nre2d/K7hb39g8Oj4vFJS8epYthksYhVJ6AaBZfYNwI7CQKaRQIbAfj+7nfkKleSwfzCRBP6JDyUPOqLFSo9YvltyuwBZJ15GSpCh3i9+9QYxSyOUhgmqdzE+NPqTKcCZwVeqnGhLIxHWLXUkj1P50ceiMXFhlQMJY2ZKGLNTfE1MaT2JAtsZUTPSq95c/M/rpia89adcJqlByZaLwlQE5P512TAFTIjJpZQpri9lbARVZQZm03BhuCtvrxOWpWyd1WuNK5L1bsjycwTlcgc3UIUa1KEJDBCe4RXenEfnxXl3PpatOSebOYU/cD5/AJ7HjNA=</latexit>Froggatt-Nielsen flavor models
small expansion parameter (M=UV scale)
Froggatt Nielsen ‘79 Leurer Seiberg Nir ’92, ’93
…
Lorenzo Calibbi (Nankai) LFV into ALPs
GF could abelian or non-abelian, continuous or discrete, local or global
✓hφi M ◆nf
ij ¯
fL ifR jH
<latexit sha1_base64="fi7A0KldV0J5tUSpX1uHIMnmkI=">ACVXicbVFNaxsxENVu0jRxP+Kkx15ETCEFY3bTQnMJhOSQwpJiZMUy1lmZa2tWKtdpNmAEfqTuZT+k14KlR0fmo8Hgsd7M6PRU14raTFJfkfxyuqrtdfrG603b9+932xvbV/aqjFc9HmlKnOdgxVKatFHiUpc10ZAmStxlU+P5/7VnTBWVvoCZ7UYljDWspAcMEhZW7EScMJBuVOfOWZK+rOZ9jw9oEyJAncpKwxwxTosRKU1RPJzIJ790zI8cT/Hzj9E2ROXnrPWVdynIwrgjTlXehqcH6x76+lJ1u4kvWQB+pykS9IhS5xl7Xs2qnhTCo1cgbWDNKlx6MCg5GDFmusqIFPYSwGgWohR26RSqefgrKiBaVCUcjXaj/dzgorZ2VeaicZ2CfenPxJW/QYLE/dFLXDQrNHy4qGkWxovOI6UgawVHNAgFuZNiV8gmEGDF8RCuEkD598nNyudLv/T2zr92Do+WcayTj2SH7JKUfCOH5ISckT7h5J78iaIojn5Ff+PVeO2hNI6WPR/I8Sb/wD9iLQK</latexit>⟨ϕ⟩ < M
ϵ ≡ ⟨ϕ⟩/M
dictated by the symmetry
nf
ij
Froggatt-Nielsen U(1)
Lorenzo Calibbi (Nankai) LFV into ALPs
LH charges can chosen to give a (quasi-)anarchical PMNS RH charges then responsible for charged leptons hierarchy
φ ¯ Li ei h U(1)
[L]i [e]i
<latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit><latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit><latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit><latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit>Examples:
Altarelli Feruglio Masina Merlo ‘12
([L]1, [L]2, [L]3) = ([L], [L], [L])
<latexit sha1_base64="tAk2raL5uVHc4j4sIqAgG57AsM=">ACDnicbVDLSsNAFJ34rPUVdelmsBRaKCWpBd0IBTcuXFSwD0hDmEwn7dDJMxMhBL6BW78FTcuFHr2p1/46TNQlsPXO7hnHuZucePGZXKsr6NtfWNza3twk5xd2/4NA8Ou7KBGYdHDEItH3kSMctJRVDHSjwVBoc9Iz59cZ37vgQhJI36vpjFxQzTiNKAYKS15Zrni3LqeXRvUst7I+3n1KtNreVU9s2TVrTngKrFzUgI52p75NRhGOAkJV5ghKR3bipWbIqEoZmRWHCSxAhP0Ig4mnIUEum83NmsKyVIQwioYsrOFd/b6QolHIa+noyRGosl71M/M9zEhVcuinlcaIx4uHgoRBFcEsGzikgmDFpogLKj+K8RjJBWOsGiDsFePnmVdBt126rbd81Sq5nHUQCn4AxUgA0uQAvcgDboAwewTN4BW/Gk/FivBsfi9E1I985AX9gfP4AYRWYeQ=</latexit><latexit sha1_base64="tAk2raL5uVHc4j4sIqAgG57AsM=">ACDnicbVDLSsNAFJ34rPUVdelmsBRaKCWpBd0IBTcuXFSwD0hDmEwn7dDJMxMhBL6BW78FTcuFHr2p1/46TNQlsPXO7hnHuZucePGZXKsr6NtfWNza3twk5xd2/4NA8Ou7KBGYdHDEItH3kSMctJRVDHSjwVBoc9Iz59cZ37vgQhJI36vpjFxQzTiNKAYKS15Zrni3LqeXRvUst7I+3n1KtNreVU9s2TVrTngKrFzUgI52p75NRhGOAkJV5ghKR3bipWbIqEoZmRWHCSxAhP0Ig4mnIUEum83NmsKyVIQwioYsrOFd/b6QolHIa+noyRGosl71M/M9zEhVcuinlcaIx4uHgoRBFcEsGzikgmDFpogLKj+K8RjJBWOsGiDsFePnmVdBt126rbd81Sq5nHUQCn4AxUgA0uQAvcgDboAwewTN4BW/Gk/FivBsfi9E1I985AX9gfP4AYRWYeQ=</latexit><latexit sha1_base64="tAk2raL5uVHc4j4sIqAgG57AsM=">ACDnicbVDLSsNAFJ34rPUVdelmsBRaKCWpBd0IBTcuXFSwD0hDmEwn7dDJMxMhBL6BW78FTcuFHr2p1/46TNQlsPXO7hnHuZucePGZXKsr6NtfWNza3twk5xd2/4NA8Ou7KBGYdHDEItH3kSMctJRVDHSjwVBoc9Iz59cZ37vgQhJI36vpjFxQzTiNKAYKS15Zrni3LqeXRvUst7I+3n1KtNreVU9s2TVrTngKrFzUgI52p75NRhGOAkJV5ghKR3bipWbIqEoZmRWHCSxAhP0Ig4mnIUEum83NmsKyVIQwioYsrOFd/b6QolHIa+noyRGosl71M/M9zEhVcuinlcaIx4uHgoRBFcEsGzikgmDFpogLKj+K8RjJBWOsGiDsFePnmVdBt126rbd81Sq5nHUQCn4AxUgA0uQAvcgDboAwewTN4BW/Gk/FivBsfi9E1I985AX9gfP4AYRWYeQ=</latexit><latexit sha1_base64="tAk2raL5uVHc4j4sIqAgG57AsM=">ACDnicbVDLSsNAFJ34rPUVdelmsBRaKCWpBd0IBTcuXFSwD0hDmEwn7dDJMxMhBL6BW78FTcuFHr2p1/46TNQlsPXO7hnHuZucePGZXKsr6NtfWNza3twk5xd2/4NA8Ou7KBGYdHDEItH3kSMctJRVDHSjwVBoc9Iz59cZ37vgQhJI36vpjFxQzTiNKAYKS15Zrni3LqeXRvUst7I+3n1KtNreVU9s2TVrTngKrFzUgI52p75NRhGOAkJV5ghKR3bipWbIqEoZmRWHCSxAhP0Ig4mnIUEum83NmsKyVIQwioYsrOFd/b6QolHIa+noyRGosl71M/M9zEhVcuinlcaIx4uHgoRBFcEsGzikgmDFpogLKj+K8RjJBWOsGiDsFePnmVdBt126rbd81Sq5nHUQCn4AxUgA0uQAvcgDboAwewTN4BW/Gk/FivBsfi9E1I985AX9gfP4AYRWYeQ=</latexit>([L]1, [L]2, [L]3) = ([L] + 1, [L], [L])
<latexit sha1_base64="C/P6zr9ug4pC6T62vEm64wk9b6Q=">ACEHicbVBNS8NAEN3Ur1q/oh69BIvYinZWtCLUPDiwUMF+wFpCJvtpl262YTdjVBKf4IX/4oXD4p49ejNf+OmzUFbHwz9s0Ms/P8mFGpbPvbyK2srq1v5DcLW9s7u3vm/kFbRonApIUjFomujyRhlJOWoqRbiwICn1GOv7oOq13HoiQNOL3ahwTN0QDTgOKkdKSZ56WnFvXg5VeJc21LJ+Xr1L9DKavNMqeWbSr9gzWMoEZKYIMTc/86vUjnISEK8yQlA60Y+VOkFAUMzIt9BJYoRHaEAcTkKiXQns4Om1olW+lYQCR1cWTP198QEhVKOQ193hkgN5WItFf+rOYkKLt0J5XGiCMfzRUHCLBVZqTtWnwqCFRtrgrCg+q8WHiKBsNIeFrQJcPHkZdKuVaFdhXf1YqOe2ZEHR+AYlAEF6ABbkATtAGj+AZvI348l4Md6Nj3lrzshmDsEfGJ8/SlWY6Q=</latexit><latexit sha1_base64="C/P6zr9ug4pC6T62vEm64wk9b6Q=">ACEHicbVBNS8NAEN3Ur1q/oh69BIvYinZWtCLUPDiwUMF+wFpCJvtpl262YTdjVBKf4IX/4oXD4p49ejNf+OmzUFbHwz9s0Ms/P8mFGpbPvbyK2srq1v5DcLW9s7u3vm/kFbRonApIUjFomujyRhlJOWoqRbiwICn1GOv7oOq13HoiQNOL3ahwTN0QDTgOKkdKSZ56WnFvXg5VeJc21LJ+Xr1L9DKavNMqeWbSr9gzWMoEZKYIMTc/86vUjnISEK8yQlA60Y+VOkFAUMzIt9BJYoRHaEAcTkKiXQns4Om1olW+lYQCR1cWTP198QEhVKOQ193hkgN5WItFf+rOYkKLt0J5XGiCMfzRUHCLBVZqTtWnwqCFRtrgrCg+q8WHiKBsNIeFrQJcPHkZdKuVaFdhXf1YqOe2ZEHR+AYlAEF6ABbkATtAGj+AZvI348l4Md6Nj3lrzshmDsEfGJ8/SlWY6Q=</latexit><latexit sha1_base64="C/P6zr9ug4pC6T62vEm64wk9b6Q=">ACEHicbVBNS8NAEN3Ur1q/oh69BIvYinZWtCLUPDiwUMF+wFpCJvtpl262YTdjVBKf4IX/4oXD4p49ejNf+OmzUFbHwz9s0Ms/P8mFGpbPvbyK2srq1v5DcLW9s7u3vm/kFbRonApIUjFomujyRhlJOWoqRbiwICn1GOv7oOq13HoiQNOL3ahwTN0QDTgOKkdKSZ56WnFvXg5VeJc21LJ+Xr1L9DKavNMqeWbSr9gzWMoEZKYIMTc/86vUjnISEK8yQlA60Y+VOkFAUMzIt9BJYoRHaEAcTkKiXQns4Om1olW+lYQCR1cWTP198QEhVKOQ193hkgN5WItFf+rOYkKLt0J5XGiCMfzRUHCLBVZqTtWnwqCFRtrgrCg+q8WHiKBsNIeFrQJcPHkZdKuVaFdhXf1YqOe2ZEHR+AYlAEF6ABbkATtAGj+AZvI348l4Md6Nj3lrzshmDsEfGJ8/SlWY6Q=</latexit><latexit sha1_base64="C/P6zr9ug4pC6T62vEm64wk9b6Q=">ACEHicbVBNS8NAEN3Ur1q/oh69BIvYinZWtCLUPDiwUMF+wFpCJvtpl262YTdjVBKf4IX/4oXD4p49ejNf+OmzUFbHwz9s0Ms/P8mFGpbPvbyK2srq1v5DcLW9s7u3vm/kFbRonApIUjFomujyRhlJOWoqRbiwICn1GOv7oOq13HoiQNOL3ahwTN0QDTgOKkdKSZ56WnFvXg5VeJc21LJ+Xr1L9DKavNMqeWbSr9gzWMoEZKYIMTc/86vUjnISEK8yQlA60Y+VOkFAUMzIt9BJYoRHaEAcTkKiXQns4Om1olW+lYQCR1cWTP198QEhVKOQ193hkgN5WItFf+rOYkKLt0J5XGiCMfzRUHCLBVZqTtWnwqCFRtrgrCg+q8WHiKBsNIeFrQJcPHkZdKuVaFdhXf1YqOe2ZEHR+AYlAEF6ABbkATtAGj+AZvI348l4Md6Nj3lrzshmDsEfGJ8/SlWY6Q=</latexit>([L]1, [L]2, [L]3) = ([L] + 2, [L] + 1, [L])
<latexit sha1_base64="RK/SozldHqLI7pRzdTciI61wQvQ=">ACEnicbVDLSgMxFM3UV62vUZdugkVoaSmTWtCNUHDjwkUF+4DpMGTStA3NPEgyQhn6DW78FTcuFHryp1/Y6adhbZeSO7JOfdyc48XcSaVZX0bubX1jc2t/HZhZ3dv/8A8POrIMBaEtknIQ9HzsKScBbStmOK0FwmKfY/Trje5TvXuAxWShcG9mkbU8fEoYENGsNKUa5ZL9q3jomq/muZ6ls/LVylfqaevCkrvsmsWrZo1D7gKUAaKIuWa371ByGJfRowrGUNrIi5SRYKEY4nRX6saQRJhM8oraGAfapdJL5SjN4pkBHIZCn0DBOfu7I8G+lFPf05U+VmO5rKXkf5odq+Glk7AgihUNyGLQMOZQhTD1Bw6YoETxqQaYCKb/CskYC0yUdrGgTUDLK6+CTr2GrBq6axSbjcyOPDgBp6AELgATXADWqANCHgEz+AVvBlPxovxbnwsSnNG1nM/oTx+QM21Jla</latexit><latexit sha1_base64="RK/SozldHqLI7pRzdTciI61wQvQ=">ACEnicbVDLSgMxFM3UV62vUZdugkVoaSmTWtCNUHDjwkUF+4DpMGTStA3NPEgyQhn6DW78FTcuFHryp1/Y6adhbZeSO7JOfdyc48XcSaVZX0bubX1jc2t/HZhZ3dv/8A8POrIMBaEtknIQ9HzsKScBbStmOK0FwmKfY/Trje5TvXuAxWShcG9mkbU8fEoYENGsNKUa5ZL9q3jomq/muZ6ls/LVylfqaevCkrvsmsWrZo1D7gKUAaKIuWa371ByGJfRowrGUNrIi5SRYKEY4nRX6saQRJhM8oraGAfapdJL5SjN4pkBHIZCn0DBOfu7I8G+lFPf05U+VmO5rKXkf5odq+Glk7AgihUNyGLQMOZQhTD1Bw6YoETxqQaYCKb/CskYC0yUdrGgTUDLK6+CTr2GrBq6axSbjcyOPDgBp6AELgATXADWqANCHgEz+AVvBlPxovxbnwsSnNG1nM/oTx+QM21Jla</latexit><latexit sha1_base64="RK/SozldHqLI7pRzdTciI61wQvQ=">ACEnicbVDLSgMxFM3UV62vUZdugkVoaSmTWtCNUHDjwkUF+4DpMGTStA3NPEgyQhn6DW78FTcuFHryp1/Y6adhbZeSO7JOfdyc48XcSaVZX0bubX1jc2t/HZhZ3dv/8A8POrIMBaEtknIQ9HzsKScBbStmOK0FwmKfY/Trje5TvXuAxWShcG9mkbU8fEoYENGsNKUa5ZL9q3jomq/muZ6ls/LVylfqaevCkrvsmsWrZo1D7gKUAaKIuWa371ByGJfRowrGUNrIi5SRYKEY4nRX6saQRJhM8oraGAfapdJL5SjN4pkBHIZCn0DBOfu7I8G+lFPf05U+VmO5rKXkf5odq+Glk7AgihUNyGLQMOZQhTD1Bw6YoETxqQaYCKb/CskYC0yUdrGgTUDLK6+CTr2GrBq6axSbjcyOPDgBp6AELgATXADWqANCHgEz+AVvBlPxovxbnwsSnNG1nM/oTx+QM21Jla</latexit><latexit sha1_base64="RK/SozldHqLI7pRzdTciI61wQvQ=">ACEnicbVDLSgMxFM3UV62vUZdugkVoaSmTWtCNUHDjwkUF+4DpMGTStA3NPEgyQhn6DW78FTcuFHryp1/Y6adhbZeSO7JOfdyc48XcSaVZX0bubX1jc2t/HZhZ3dv/8A8POrIMBaEtknIQ9HzsKScBbStmOK0FwmKfY/Trje5TvXuAxWShcG9mkbU8fEoYENGsNKUa5ZL9q3jomq/muZ6ls/LVylfqaevCkrvsmsWrZo1D7gKUAaKIuWa371ByGJfRowrGUNrIi5SRYKEY4nRX6saQRJhM8oraGAfapdJL5SjN4pkBHIZCn0DBOfu7I8G+lFPf05U+VmO5rKXkf5odq+Glk7AgihUNyGLQMOZQhTD1Bw6YoETxqQaYCKb/CskYC0yUdrGgTUDLK6+CTr2GrBq6axSbjcyOPDgBp6AELgATXADWqANCHgEz+AVvBlPxovxbnwsSnNG1nM/oTx+QM21Jla</latexit>([e]1, [e]2, [e]3) = (8 − [L]1, 4 − [L]2, 2 − [L]3)
<latexit sha1_base64="uVpfK5tD6d+VCghso1PwxfcDu6w=">ACGnicbVDLSsNAFJ34rPUVdelmsAgt1JKkBbsRCm5cuKhgH5CGMJlO26GTBzMToYR+hxt/xY0LRdyJG/GSZqFtl4YzuGce7lzjxcxKqRhfGtr6xubW9uFneLu3v7BoX503BVhzDHp4JCFvO8hQRgNSEdSyUg/4gT5HiM9b3qd+r0HwgUNg3s5i4jo3FARxQjqSRXN8s2cVyzOqimaOVYr1yVmxf2beo0MrSqVob1iquXjJqRFVwlZk5KIK+2q38OhiGOfRJIzJAQtmlE0kQlxQzMi8OYkEihKdoTGxFA+QT4STZaXN4rpQhHIVcvUDCTP09kSBfiJnvqU4fyYlY9lLxP8+O5ajpJDSIYkCvFg0ihmUIUxzgkPKCZspgjCnKq/QjxBHGp0iyqEMzlk1dJ16qZRs28a5RajTyOAjgFZ6AMTHAJWuAGtEHYPAInsEreNOetBftXftYtK5p+cwJ+FPa1w91lJwU</latexit><latexit sha1_base64="uVpfK5tD6d+VCghso1PwxfcDu6w=">ACGnicbVDLSsNAFJ34rPUVdelmsAgt1JKkBbsRCm5cuKhgH5CGMJlO26GTBzMToYR+hxt/xY0LRdyJG/GSZqFtl4YzuGce7lzjxcxKqRhfGtr6xubW9uFneLu3v7BoX503BVhzDHp4JCFvO8hQRgNSEdSyUg/4gT5HiM9b3qd+r0HwgUNg3s5i4jo3FARxQjqSRXN8s2cVyzOqimaOVYr1yVmxf2beo0MrSqVob1iquXjJqRFVwlZk5KIK+2q38OhiGOfRJIzJAQtmlE0kQlxQzMi8OYkEihKdoTGxFA+QT4STZaXN4rpQhHIVcvUDCTP09kSBfiJnvqU4fyYlY9lLxP8+O5ajpJDSIYkCvFg0ihmUIUxzgkPKCZspgjCnKq/QjxBHGp0iyqEMzlk1dJ16qZRs28a5RajTyOAjgFZ6AMTHAJWuAGtEHYPAInsEreNOetBftXftYtK5p+cwJ+FPa1w91lJwU</latexit><latexit sha1_base64="uVpfK5tD6d+VCghso1PwxfcDu6w=">ACGnicbVDLSsNAFJ34rPUVdelmsAgt1JKkBbsRCm5cuKhgH5CGMJlO26GTBzMToYR+hxt/xY0LRdyJG/GSZqFtl4YzuGce7lzjxcxKqRhfGtr6xubW9uFneLu3v7BoX503BVhzDHp4JCFvO8hQRgNSEdSyUg/4gT5HiM9b3qd+r0HwgUNg3s5i4jo3FARxQjqSRXN8s2cVyzOqimaOVYr1yVmxf2beo0MrSqVob1iquXjJqRFVwlZk5KIK+2q38OhiGOfRJIzJAQtmlE0kQlxQzMi8OYkEihKdoTGxFA+QT4STZaXN4rpQhHIVcvUDCTP09kSBfiJnvqU4fyYlY9lLxP8+O5ajpJDSIYkCvFg0ihmUIUxzgkPKCZspgjCnKq/QjxBHGp0iyqEMzlk1dJ16qZRs28a5RajTyOAjgFZ6AMTHAJWuAGtEHYPAInsEreNOetBftXftYtK5p+cwJ+FPa1w91lJwU</latexit><latexit sha1_base64="uVpfK5tD6d+VCghso1PwxfcDu6w=">ACGnicbVDLSsNAFJ34rPUVdelmsAgt1JKkBbsRCm5cuKhgH5CGMJlO26GTBzMToYR+hxt/xY0LRdyJG/GSZqFtl4YzuGce7lzjxcxKqRhfGtr6xubW9uFneLu3v7BoX503BVhzDHp4JCFvO8hQRgNSEdSyUg/4gT5HiM9b3qd+r0HwgUNg3s5i4jo3FARxQjqSRXN8s2cVyzOqimaOVYr1yVmxf2beo0MrSqVob1iquXjJqRFVwlZk5KIK+2q38OhiGOfRJIzJAQtmlE0kQlxQzMi8OYkEihKdoTGxFA+QT4STZaXN4rpQhHIVcvUDCTP09kSBfiJnvqU4fyYlY9lLxP8+O5ajpJDSIYkCvFg0ihmUIUxzgkPKCZspgjCnKq/QjxBHGp0iyqEMzlk1dJ16qZRs28a5RajTyOAjgFZ6AMTHAJWuAGtEHYPAInsEreNOetBftXftYtK5p+cwJ+FPa1w91lJwU</latexit>Charged lepton hierarchy: (with )
✏ ≈ 0.2
<latexit sha1_base64="xZXSE028SMy86hGjYCpU0rvZb1s=">AB/HicbVDLSgMxFM34rPU12qWbYBFcDTNF0GXRjcsK9gGdoWTSTBuaSUKSEYeh/obF4q49UPc+Tem7Sy09cCFwzn3cu89sWRUG9/dtbWNza3tis71d29/YND9+i4o0WmMGljwYTqxUgTRjlpG2oY6UlFUBoz0o0nNzO/+0CUpoLfm1ySKEUjThOKkbHSwK2FRGrKBA+RlEo8Qt9rDNy67/lzwFUSlKQOSrQG7lc4FDhLCTeYIa37gS9NVCBlKGZkWg0zTSTCEzQifUs5SomOivnxU3hmlSFMhLFDZyrvycKlGqdp7HtTJEZ62VvJv7n9TOTXEUF5TIzhOPFoiRj0Ag4SwIOqSLYsNwShBW1t0I8RgphY/Oq2hC5ZdXSafhBb4X3F3Um9dlHBVwAk7BOQjAJWiCW9ACbYBDp7BK3hznpwX5935WLSuOeVMDfyB8/kDHc6UZQ=</latexit><latexit sha1_base64="xZXSE028SMy86hGjYCpU0rvZb1s=">AB/HicbVDLSgMxFM34rPU12qWbYBFcDTNF0GXRjcsK9gGdoWTSTBuaSUKSEYeh/obF4q49UPc+Tem7Sy09cCFwzn3cu89sWRUG9/dtbWNza3tis71d29/YND9+i4o0WmMGljwYTqxUgTRjlpG2oY6UlFUBoz0o0nNzO/+0CUpoLfm1ySKEUjThOKkbHSwK2FRGrKBA+RlEo8Qt9rDNy67/lzwFUSlKQOSrQG7lc4FDhLCTeYIa37gS9NVCBlKGZkWg0zTSTCEzQifUs5SomOivnxU3hmlSFMhLFDZyrvycKlGqdp7HtTJEZ62VvJv7n9TOTXEUF5TIzhOPFoiRj0Ag4SwIOqSLYsNwShBW1t0I8RgphY/Oq2hC5ZdXSafhBb4X3F3Um9dlHBVwAk7BOQjAJWiCW9ACbYBDp7BK3hznpwX5935WLSuOeVMDfyB8/kDHc6UZQ=</latexit><latexit sha1_base64="xZXSE028SMy86hGjYCpU0rvZb1s=">AB/HicbVDLSgMxFM34rPU12qWbYBFcDTNF0GXRjcsK9gGdoWTSTBuaSUKSEYeh/obF4q49UPc+Tem7Sy09cCFwzn3cu89sWRUG9/dtbWNza3tis71d29/YND9+i4o0WmMGljwYTqxUgTRjlpG2oY6UlFUBoz0o0nNzO/+0CUpoLfm1ySKEUjThOKkbHSwK2FRGrKBA+RlEo8Qt9rDNy67/lzwFUSlKQOSrQG7lc4FDhLCTeYIa37gS9NVCBlKGZkWg0zTSTCEzQifUs5SomOivnxU3hmlSFMhLFDZyrvycKlGqdp7HtTJEZ62VvJv7n9TOTXEUF5TIzhOPFoiRj0Ag4SwIOqSLYsNwShBW1t0I8RgphY/Oq2hC5ZdXSafhBb4X3F3Um9dlHBVwAk7BOQjAJWiCW9ACbYBDp7BK3hznpwX5935WLSuOeVMDfyB8/kDHc6UZQ=</latexit><latexit sha1_base64="xZXSE028SMy86hGjYCpU0rvZb1s=">AB/HicbVDLSgMxFM34rPU12qWbYBFcDTNF0GXRjcsK9gGdoWTSTBuaSUKSEYeh/obF4q49UPc+Tem7Sy09cCFwzn3cu89sWRUG9/dtbWNza3tis71d29/YND9+i4o0WmMGljwYTqxUgTRjlpG2oY6UlFUBoz0o0nNzO/+0CUpoLfm1ySKEUjThOKkbHSwK2FRGrKBA+RlEo8Qt9rDNy67/lzwFUSlKQOSrQG7lc4FDhLCTeYIa37gS9NVCBlKGZkWg0zTSTCEzQifUs5SomOivnxU3hmlSFMhLFDZyrvycKlGqdp7HtTJEZ62VvJv7n9TOTXEUF5TIzhOPFoiRj0Ag4SwIOqSLYsNwShBW1t0I8RgphY/Oq2hC5ZdXSafhBb4X3F3Um9dlHBVwAk7BOQjAJWiCW9ACbYBDp7BK3hznpwX5935WLSuOeVMDfyB8/kDHc6UZQ=</latexit>ye
ij = ae ij
✓hΦi M ◆[L]i+[e]j
, mν
ij = ν ij
v2 ΛN ✓hΦi M ◆[L]i+[L]j
Lepton sector
Froggatt-Nielsen U(1)
Lorenzo Calibbi (Nankai) LFV into ALPs
Lepton sector LH charges can chosen to give a (quasi-)anarchical PMNS RH charges then responsible for charged leptons hierarchy
φ ¯ Li ei h U(1)
[L]i [e]i
<latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit><latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit><latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit><latexit sha1_base64="e7CzTc7hGFbmhV9KpayKoGRlmwE=">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</latexit>Examples:
Feruglio ‘17
ye
ij = ae ij
✓hΦi M ◆[L]i+[e]j
, mν
ij = ν ij
v2 ΛN ✓hΦi M ◆[L]i+[L]j
XR = [e]1 [e]2 [e]3
<latexit sha1_base64="ehiwiXLRhLpDfGxLgFO6g76T0Ds=">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</latexit><latexit sha1_base64="ehiwiXLRhLpDfGxLgFO6g76T0Ds=">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</latexit><latexit sha1_base64="ehiwiXLRhLpDfGxLgFO6g76T0Ds=">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</latexit><latexit sha1_base64="ehiwiXLRhLpDfGxLgFO6g76T0Ds=">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</latexit>Leptonic FN “familon”
Laff = @µa f ⇣ Cij
V ¯
`iµ`j + Cij
A ¯
`iµ5`j ⌘
<latexit sha1_base64="xtNduHuPUOaCjGogt7Mj3/TkqLA=">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</latexit><latexit sha1_base64="xtNduHuPUOaCjGogt7Mj3/TkqLA=">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</latexit><latexit sha1_base64="xtNduHuPUOaCjGogt7Mj3/TkqLA=">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</latexit><latexit sha1_base64="xtNduHuPUOaCjGogt7Mj3/TkqLA=">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</latexit>CV/A = V †
RXRVR ± V † LXLVL
<latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit><latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit><latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit><latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit>XL = [L]1 [L]2 [L]3
<latexit sha1_base64="zfdHRd38tPSnRdf5a4zM5wewxc=">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</latexit><latexit sha1_base64="zfdHRd38tPSnRdf5a4zM5wewxc=">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</latexit><latexit sha1_base64="zfdHRd38tPSnRdf5a4zM5wewxc=">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</latexit><latexit sha1_base64="zfdHRd38tPSnRdf5a4zM5wewxc=">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</latexit>µ → ea τ → ea τ → µa
<latexit sha1_base64="jNK38htH1MxCQRdYtgDzjh3+bvk=">ACJXicbZDLSsNAFIYn9VbrLerSzWARXJVEBF24KLpxWcG2QhPKyWTSDp1cnJkIJfRl3PgqblxYRHDlqzhJg2jbAzP8fOf8zJzfSziTyrK+jMrK6tr6RnWztrW9s7tn7h90ZJwKQtsk5rF48EBSziLaVkx+pAICqHadcb3eT97hMVksXRvRon1A1hELGAEVAa9c0rJ0yxo2JMTiPKfjFpQn8YryM5zbom3WrYRWF4Vdijoq9U3p4fkzSkSIcpOzZVqLcDIRihNJzUklTYCMYEB7WkYQUulmxZYTfKJj4NY6BMpXNC/jgxCKcehpydDUEM538vhsl4vVcGlm7EoSRWNyOyhIOVYr5lHhn0mKF8rAUQwfRfMRmCAKJ0sDUdgj2/8qLonDVsq2Hfndeb12UcVXSEjtEpstEFaqJb1EJtRNAzekXvaGq8G/Gh/E5G60YpecQ/Svj+weX0aQR</latexit><latexit sha1_base64="jNK38htH1MxCQRdYtgDzjh3+bvk=">ACJXicbZDLSsNAFIYn9VbrLerSzWARXJVEBF24KLpxWcG2QhPKyWTSDp1cnJkIJfRl3PgqblxYRHDlqzhJg2jbAzP8fOf8zJzfSziTyrK+jMrK6tr6RnWztrW9s7tn7h90ZJwKQtsk5rF48EBSziLaVkx+pAICqHadcb3eT97hMVksXRvRon1A1hELGAEVAa9c0rJ0yxo2JMTiPKfjFpQn8YryM5zbom3WrYRWF4Vdijoq9U3p4fkzSkSIcpOzZVqLcDIRihNJzUklTYCMYEB7WkYQUulmxZYTfKJj4NY6BMpXNC/jgxCKcehpydDUEM538vhsl4vVcGlm7EoSRWNyOyhIOVYr5lHhn0mKF8rAUQwfRfMRmCAKJ0sDUdgj2/8qLonDVsq2Hfndeb12UcVXSEjtEpstEFaqJb1EJtRNAzekXvaGq8G/Gh/E5G60YpecQ/Svj+weX0aQR</latexit><latexit sha1_base64="jNK38htH1MxCQRdYtgDzjh3+bvk=">ACJXicbZDLSsNAFIYn9VbrLerSzWARXJVEBF24KLpxWcG2QhPKyWTSDp1cnJkIJfRl3PgqblxYRHDlqzhJg2jbAzP8fOf8zJzfSziTyrK+jMrK6tr6RnWztrW9s7tn7h90ZJwKQtsk5rF48EBSziLaVkx+pAICqHadcb3eT97hMVksXRvRon1A1hELGAEVAa9c0rJ0yxo2JMTiPKfjFpQn8YryM5zbom3WrYRWF4Vdijoq9U3p4fkzSkSIcpOzZVqLcDIRihNJzUklTYCMYEB7WkYQUulmxZYTfKJj4NY6BMpXNC/jgxCKcehpydDUEM538vhsl4vVcGlm7EoSRWNyOyhIOVYr5lHhn0mKF8rAUQwfRfMRmCAKJ0sDUdgj2/8qLonDVsq2Hfndeb12UcVXSEjtEpstEFaqJb1EJtRNAzekXvaGq8G/Gh/E5G60YpecQ/Svj+weX0aQR</latexit><latexit sha1_base64="jNK38htH1MxCQRdYtgDzjh3+bvk=">ACJXicbZDLSsNAFIYn9VbrLerSzWARXJVEBF24KLpxWcG2QhPKyWTSDp1cnJkIJfRl3PgqblxYRHDlqzhJg2jbAzP8fOf8zJzfSziTyrK+jMrK6tr6RnWztrW9s7tn7h90ZJwKQtsk5rF48EBSziLaVkx+pAICqHadcb3eT97hMVksXRvRon1A1hELGAEVAa9c0rJ0yxo2JMTiPKfjFpQn8YryM5zbom3WrYRWF4Vdijoq9U3p4fkzSkSIcpOzZVqLcDIRihNJzUklTYCMYEB7WkYQUulmxZYTfKJj4NY6BMpXNC/jgxCKcehpydDUEM538vhsl4vVcGlm7EoSRWNyOyhIOVYr5lHhn0mKF8rAUQwfRfMRmCAKJ0sDUdgj2/8qLonDVsq2Hfndeb12UcVXSEjtEpstEFaqJb1EJtRNAzekXvaGq8G/Gh/E5G60YpecQ/Svj+weX0aQR</latexit>Lepton-flavor-violating decays into an (invisible) PNGB:
(VL)ij ≈ ✏|[L]i−[L]j|, (VR)ij ≈ ✏|[e]i−[e]j|
<latexit sha1_base64="IHjVGQ9rmUy9p4i1wCYMtTmXBE=">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</latexit><latexit sha1_base64="IHjVGQ9rmUy9p4i1wCYMtTmXBE=">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</latexit><latexit sha1_base64="IHjVGQ9rmUy9p4i1wCYMtTmXBE=">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</latexit><latexit sha1_base64="IHjVGQ9rmUy9p4i1wCYMtTmXBE=">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</latexit>flavor non-universal charges flavor-violating couplings
Γ(`i → `ja) = 1 16⇡ m3
`i
f 2 ⇣ |Cij
V |2 + |Cij A |2⌘
1 − m2
a
m2
`i
!2
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φ = 1 √ 2(f + ρφ)eia/f
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V †
LY eVR = Y e diag
<latexit sha1_base64="M0vkWn8znT52ca3OBEXn6jEGKaY=">ACBnicbZDLSsNAFIYn9VbrLepShMEiuCpJFXQjFN24cFHFpU2DZPJB06uTAzEUroyo2v4saFIm59Bne+jZM2C239YeDjP+dw5vxuwqiQhvGtlRYWl5ZXyquVtfWNzS19e8cScoxaeGYxbzjIkEYjUhLUslIJ+EhS4jbXd4mdfbD4QLGkd3cpQO0RBRH2KkVSWo+9bznW/56EA3vcJtJxbeJ6Tk3kUBWNHrxo1YyI4D2YBVCo6ehfPS/GaUgiRkSomsaibQzxCXFjIwrvVSQBOEhCkhXYRCIuxscsYHirHg37M1YsknLi/JzIUCjEKXdUZIjkQs7Xc/K/WTaV/Zmc0SlJIjxd5KcMyhjmUCPcoIlGylAmFP1V4gHiCMsVXIVFYI5e/I8WPWaeVyr35xUGxdFHGWwBw7AETDBKWiAK9AELYDBI3gGr+BNe9JetHftY9pa0oqZXfBH2ucPGiyXoA=</latexit>U(1)FN charges L and R rotations to the lepton mass basis
LFV decays into a leptonic familon
Cij
V ≈ −Cij A
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V ≈ Cij A
<latexit sha1_base64="LQf26NSgH7diZfonSL2L23R+S0=">ACAnicbVDLSgMxFM34rPU16krcBIvgqsyIoMtqNy4r2Ae045BJM21sJglJRixDceOvuHGhiFu/wp1/Y9rOQlsPXDicy/3hNJRrXxvG9nYXFpeW1sFZc39jc2nZ3dhtapAqTOhZMqFaENGUk7qhpGWVAQlESPNaFAd+817ojQV/MYMJQkS1OM0phgZK4XufvU2o3ejsAE7SEolHmAuXIRuySt7E8B54uekBHLUQver0xU4TQg3mCGt274nTZAhZShmZFTspJpIhAeoR9qWcpQHWSTF0bwyCpdGAtlixs4UX9PZCjRephEtjNBpq9nvbH4n9dOTXweZJTL1BCOp4vilEj4DgP2KWKYMOGliCsqL0V4j5SCBubWtG4M+PE8aJ2XfK/vXp6XKZR5HARyAQ3AMfHAGKuAK1EAdYPAInsEreHOenBfn3fmYti4+cwe+APn8wfMg5cI</latexit><latexit sha1_base64="LQf26NSgH7diZfonSL2L23R+S0=">ACAnicbVDLSgMxFM34rPU16krcBIvgqsyIoMtqNy4r2Ae045BJM21sJglJRixDceOvuHGhiFu/wp1/Y9rOQlsPXDicy/3hNJRrXxvG9nYXFpeW1sFZc39jc2nZ3dhtapAqTOhZMqFaENGUk7qhpGWVAQlESPNaFAd+817ojQV/MYMJQkS1OM0phgZK4XufvU2o3ejsAE7SEolHmAuXIRuySt7E8B54uekBHLUQver0xU4TQg3mCGt274nTZAhZShmZFTspJpIhAeoR9qWcpQHWSTF0bwyCpdGAtlixs4UX9PZCjRephEtjNBpq9nvbH4n9dOTXweZJTL1BCOp4vilEj4DgP2KWKYMOGliCsqL0V4j5SCBubWtG4M+PE8aJ2XfK/vXp6XKZR5HARyAQ3AMfHAGKuAK1EAdYPAInsEreHOenBfn3fmYti4+cwe+APn8wfMg5cI</latexit><latexit sha1_base64="LQf26NSgH7diZfonSL2L23R+S0=">ACAnicbVDLSgMxFM34rPU16krcBIvgqsyIoMtqNy4r2Ae045BJM21sJglJRixDceOvuHGhiFu/wp1/Y9rOQlsPXDicy/3hNJRrXxvG9nYXFpeW1sFZc39jc2nZ3dhtapAqTOhZMqFaENGUk7qhpGWVAQlESPNaFAd+817ojQV/MYMJQkS1OM0phgZK4XufvU2o3ejsAE7SEolHmAuXIRuySt7E8B54uekBHLUQver0xU4TQg3mCGt274nTZAhZShmZFTspJpIhAeoR9qWcpQHWSTF0bwyCpdGAtlixs4UX9PZCjRephEtjNBpq9nvbH4n9dOTXweZJTL1BCOp4vilEj4DgP2KWKYMOGliCsqL0V4j5SCBubWtG4M+PE8aJ2XfK/vXp6XKZR5HARyAQ3AMfHAGKuAK1EAdYPAInsEreHOenBfn3fmYti4+cwe+APn8wfMg5cI</latexit><latexit sha1_base64="LQf26NSgH7diZfonSL2L23R+S0=">ACAnicbVDLSgMxFM34rPU16krcBIvgqsyIoMtqNy4r2Ae045BJM21sJglJRixDceOvuHGhiFu/wp1/Y9rOQlsPXDicy/3hNJRrXxvG9nYXFpeW1sFZc39jc2nZ3dhtapAqTOhZMqFaENGUk7qhpGWVAQlESPNaFAd+817ojQV/MYMJQkS1OM0phgZK4XufvU2o3ejsAE7SEolHmAuXIRuySt7E8B54uekBHLUQver0xU4TQg3mCGt274nTZAhZShmZFTspJpIhAeoR9qWcpQHWSTF0bwyCpdGAtlixs4UX9PZCjRephEtjNBpq9nvbH4n9dOTXweZJTL1BCOp4vilEj4DgP2KWKYMOGliCsqL0V4j5SCBubWtG4M+PE8aJ2XfK/vXp6XKZR5HARyAQ3AMfHAGKuAK1EAdYPAInsEreHOenBfn3fmYti4+cwe+APn8wfMg5cI</latexit>µ → ea
<latexit sha1_base64="Jjq8ykqmH4qo2ZJjk/uClJA7ZBs=">AB8XicbVDLSsNAFL2pr1pfVZduBovgqiQi6LoxmUF+8AmlMn0ph06mYSZiVBC/8KNC0Xc+jfu/BunbRbaemDgcM69zD0nTAXxnW/ndLa+sbmVnm7srO7t39QPTxq6yRTDFsEYnqhlSj4BJbhuB3VQhjUOBnXB8O/M7T6g0T+SDmaQYxHQoecQZNVZ69OPMNwlBQvVmlt35yCrxCtIDQo0+9Uvf5CwLEZpmKBa9zw3NUFOleFM4LTiZxpTysZ0iD1LJY1RB/n84ik5s8qARImyTxoyV39v5DTWehKHdjKmZqSXvZn4n9fLTHQd5FymUHJFh9FmSA25Cw+GXCFzIiJZQpbm8lbEQVZcaWVLEleMuRV0n7ou65de/+sta4Keowmcwjl4cAUNuIMmtICBhGd4hTdHOy/Ou/OxGC05xc4x/IHz+QPg1JBh</latexit><latexit sha1_base64="Jjq8ykqmH4qo2ZJjk/uClJA7ZBs=">AB8XicbVDLSsNAFL2pr1pfVZduBovgqiQi6LoxmUF+8AmlMn0ph06mYSZiVBC/8KNC0Xc+jfu/BunbRbaemDgcM69zD0nTAXxnW/ndLa+sbmVnm7srO7t39QPTxq6yRTDFsEYnqhlSj4BJbhuB3VQhjUOBnXB8O/M7T6g0T+SDmaQYxHQoecQZNVZ69OPMNwlBQvVmlt35yCrxCtIDQo0+9Uvf5CwLEZpmKBa9zw3NUFOleFM4LTiZxpTysZ0iD1LJY1RB/n84ik5s8qARImyTxoyV39v5DTWehKHdjKmZqSXvZn4n9fLTHQd5FymUHJFh9FmSA25Cw+GXCFzIiJZQpbm8lbEQVZcaWVLEleMuRV0n7ou65de/+sta4Keowmcwjl4cAUNuIMmtICBhGd4hTdHOy/Ou/OxGC05xc4x/IHz+QPg1JBh</latexit><latexit sha1_base64="Jjq8ykqmH4qo2ZJjk/uClJA7ZBs=">AB8XicbVDLSsNAFL2pr1pfVZduBovgqiQi6LoxmUF+8AmlMn0ph06mYSZiVBC/8KNC0Xc+jfu/BunbRbaemDgcM69zD0nTAXxnW/ndLa+sbmVnm7srO7t39QPTxq6yRTDFsEYnqhlSj4BJbhuB3VQhjUOBnXB8O/M7T6g0T+SDmaQYxHQoecQZNVZ69OPMNwlBQvVmlt35yCrxCtIDQo0+9Uvf5CwLEZpmKBa9zw3NUFOleFM4LTiZxpTysZ0iD1LJY1RB/n84ik5s8qARImyTxoyV39v5DTWehKHdjKmZqSXvZn4n9fLTHQd5FymUHJFh9FmSA25Cw+GXCFzIiJZQpbm8lbEQVZcaWVLEleMuRV0n7ou65de/+sta4Keowmcwjl4cAUNuIMmtICBhGd4hTdHOy/Ou/OxGC05xc4x/IHz+QPg1JBh</latexit><latexit sha1_base64="Jjq8ykqmH4qo2ZJjk/uClJA7ZBs=">AB8XicbVDLSsNAFL2pr1pfVZduBovgqiQi6LoxmUF+8AmlMn0ph06mYSZiVBC/8KNC0Xc+jfu/BunbRbaemDgcM69zD0nTAXxnW/ndLa+sbmVnm7srO7t39QPTxq6yRTDFsEYnqhlSj4BJbhuB3VQhjUOBnXB8O/M7T6g0T+SDmaQYxHQoecQZNVZ69OPMNwlBQvVmlt35yCrxCtIDQo0+9Uvf5CwLEZpmKBa9zw3NUFOleFM4LTiZxpTysZ0iD1LJY1RB/n84ik5s8qARImyTxoyV39v5DTWehKHdjKmZqSXvZn4n9fLTHQd5FymUHJFh9FmSA25Cw+GXCFzIiJZQpbm8lbEQVZcaWVLEleMuRV0n7ou65de/+sta4Keowmcwjl4cAUNuIMmtICBhGd4hTdHOy/Ou/OxGC05xc4x/IHz+QPg1JBh</latexit>differential decay rate: LH rotations dominate: RH rotations dominate: Anarchical model
Γ(µ → ea) ≈ 1 16π m3
µ
f 2 |(VR)12|2
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µ
f 2 |(VL)12|2
<latexit sha1_base64="tYWrcL1j6dEadJ8PYXxeBejisko=">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</latexit><latexit sha1_base64="tYWrcL1j6dEadJ8PYXxeBejisko=">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</latexit><latexit sha1_base64="tYWrcL1j6dEadJ8PYXxeBejisko=">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</latexit><latexit sha1_base64="tYWrcL1j6dEadJ8PYXxeBejisko=">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</latexit>O(me/mµ)
<latexit sha1_base64="a0KFelfzpWuiMr2VbQtgSxMV+H8=">AB/3icbVDLSgMxFM3UV62vUcGNm2AR6qbOiKDLoht3VrAP6AxDJs20oUlmSDJCGbvwV9y4UMStv+HOvzHTzkJbDwQO59zLPTlhwqjSjvNtlZaWV1bXyuVjc2t7R17d6+t4lRi0sIxi2U3RIowKkhLU81IN5E8ZCRTji6zv3OA5GKxuJejxPiczQNKIYaSMF9oHkR5ixLbSY0H5JQHk9PArvq1J0p4CJxC1IFBZqB/eX1Y5xyIjRmSKme6yTaz5DUFDMyqXipIgnCIzQgPUMF4kT52T/B4bpQ+jWJonNJyqvzcyxJUa89BM5mnVvJeL/3m9VEeXfkZFkmoi8OxQlDKoY5iXAftUEqzZ2BCEJTVZIR4ibA2lVMCe78lxdJ+6zuOnX37rzauCrqKINDcARqwAUXoAFuQBO0AaP4Bm8gjfryXqx3q2P2WjJKnb2wR9Ynz+AtZW/</latexit><latexit sha1_base64="a0KFelfzpWuiMr2VbQtgSxMV+H8=">AB/3icbVDLSgMxFM3UV62vUcGNm2AR6qbOiKDLoht3VrAP6AxDJs20oUlmSDJCGbvwV9y4UMStv+HOvzHTzkJbDwQO59zLPTlhwqjSjvNtlZaWV1bXyuVjc2t7R17d6+t4lRi0sIxi2U3RIowKkhLU81IN5E8ZCRTji6zv3OA5GKxuJejxPiczQNKIYaSMF9oHkR5ixLbSY0H5JQHk9PArvq1J0p4CJxC1IFBZqB/eX1Y5xyIjRmSKme6yTaz5DUFDMyqXipIgnCIzQgPUMF4kT52T/B4bpQ+jWJonNJyqvzcyxJUa89BM5mnVvJeL/3m9VEeXfkZFkmoi8OxQlDKoY5iXAftUEqzZ2BCEJTVZIR4ibA2lVMCe78lxdJ+6zuOnX37rzauCrqKINDcARqwAUXoAFuQBO0AaP4Bm8gjfryXqx3q2P2WjJKnb2wR9Ynz+AtZW/</latexit><latexit sha1_base64="a0KFelfzpWuiMr2VbQtgSxMV+H8=">AB/3icbVDLSgMxFM3UV62vUcGNm2AR6qbOiKDLoht3VrAP6AxDJs20oUlmSDJCGbvwV9y4UMStv+HOvzHTzkJbDwQO59zLPTlhwqjSjvNtlZaWV1bXyuVjc2t7R17d6+t4lRi0sIxi2U3RIowKkhLU81IN5E8ZCRTji6zv3OA5GKxuJejxPiczQNKIYaSMF9oHkR5ixLbSY0H5JQHk9PArvq1J0p4CJxC1IFBZqB/eX1Y5xyIjRmSKme6yTaz5DUFDMyqXipIgnCIzQgPUMF4kT52T/B4bpQ+jWJonNJyqvzcyxJUa89BM5mnVvJeL/3m9VEeXfkZFkmoi8OxQlDKoY5iXAftUEqzZ2BCEJTVZIR4ibA2lVMCe78lxdJ+6zuOnX37rzauCrqKINDcARqwAUXoAFuQBO0AaP4Bm8gjfryXqx3q2P2WjJKnb2wR9Ynz+AtZW/</latexit><latexit sha1_base64="a0KFelfzpWuiMr2VbQtgSxMV+H8=">AB/3icbVDLSgMxFM3UV62vUcGNm2AR6qbOiKDLoht3VrAP6AxDJs20oUlmSDJCGbvwV9y4UMStv+HOvzHTzkJbDwQO59zLPTlhwqjSjvNtlZaWV1bXyuVjc2t7R17d6+t4lRi0sIxi2U3RIowKkhLU81IN5E8ZCRTji6zv3OA5GKxuJejxPiczQNKIYaSMF9oHkR5ixLbSY0H5JQHk9PArvq1J0p4CJxC1IFBZqB/eX1Y5xyIjRmSKme6yTaz5DUFDMyqXipIgnCIzQgPUMF4kT52T/B4bpQ+jWJonNJyqvzcyxJUa89BM5mnVvJeL/3m9VEeXfkZFkmoi8OxQlDKoY5iXAftUEqzZ2BCEJTVZIR4ibA2lVMCe78lxdJ+6zuOnX37rzauCrqKINDcARqwAUXoAFuQBO0AaP4Bm8gjfryXqx3q2P2WjJKnb2wR9Ynz+AtZW/</latexit>O(✏)
<latexit sha1_base64="oJa5WcKVThA+dEVDxvB2+8plP4U=">AB/nicbVDLSsNAFL2pr1pfUXHlJliEuimJCLosunFnBfuAJpTJdNIOncyEmYlQsFfceNCEbd+hzv/xkmbhbYeGDicy/3zAkTRpV23W+rtLK6tr5R3qxsbe/s7tn7B20lUolJCwsmZDdEijDKSUtTzUg3kQTFISOdcHyT+51HIhUV/EFPEhLEaMhpRDHSRurbR36M9Agjlt1Naz5JFGWCn/Xtqlt3Z3CWiVeQKhRo9u0vfyBwGhOuMUNK9Tw30UGpKaYkWnFTxVJEB6jIekZylFMVJDN4k+dU6MnEhI87h2ZurvjQzFSk3i0EzmYdWil4v/eb1UR1dBRnmSasLx/FCUMkcLJ+/CGVBJsGYTQxCW1GR18AhJhLVprGJK8Ba/vEza53XPrXv3F9XGdVFHGY7hBGrgwSU04Ba0AIMGTzDK7xZT9aL9W59zEdLVrFzCH9gf4ANqGVoQ=</latexit><latexit sha1_base64="oJa5WcKVThA+dEVDxvB2+8plP4U=">AB/nicbVDLSsNAFL2pr1pfUXHlJliEuimJCLosunFnBfuAJpTJdNIOncyEmYlQsFfceNCEbd+hzv/xkmbhbYeGDicy/3zAkTRpV23W+rtLK6tr5R3qxsbe/s7tn7B20lUolJCwsmZDdEijDKSUtTzUg3kQTFISOdcHyT+51HIhUV/EFPEhLEaMhpRDHSRurbR36M9Agjlt1Naz5JFGWCn/Xtqlt3Z3CWiVeQKhRo9u0vfyBwGhOuMUNK9Tw30UGpKaYkWnFTxVJEB6jIekZylFMVJDN4k+dU6MnEhI87h2ZurvjQzFSk3i0EzmYdWil4v/eb1UR1dBRnmSasLx/FCUMkcLJ+/CGVBJsGYTQxCW1GR18AhJhLVprGJK8Ba/vEza53XPrXv3F9XGdVFHGY7hBGrgwSU04Ba0AIMGTzDK7xZT9aL9W59zEdLVrFzCH9gf4ANqGVoQ=</latexit><latexit sha1_base64="oJa5WcKVThA+dEVDxvB2+8plP4U=">AB/nicbVDLSsNAFL2pr1pfUXHlJliEuimJCLosunFnBfuAJpTJdNIOncyEmYlQsFfceNCEbd+hzv/xkmbhbYeGDicy/3zAkTRpV23W+rtLK6tr5R3qxsbe/s7tn7B20lUolJCwsmZDdEijDKSUtTzUg3kQTFISOdcHyT+51HIhUV/EFPEhLEaMhpRDHSRurbR36M9Agjlt1Naz5JFGWCn/Xtqlt3Z3CWiVeQKhRo9u0vfyBwGhOuMUNK9Tw30UGpKaYkWnFTxVJEB6jIekZylFMVJDN4k+dU6MnEhI87h2ZurvjQzFSk3i0EzmYdWil4v/eb1UR1dBRnmSasLx/FCUMkcLJ+/CGVBJsGYTQxCW1GR18AhJhLVprGJK8Ba/vEza53XPrXv3F9XGdVFHGY7hBGrgwSU04Ba0AIMGTzDK7xZT9aL9W59zEdLVrFzCH9gf4ANqGVoQ=</latexit><latexit sha1_base64="oJa5WcKVThA+dEVDxvB2+8plP4U=">AB/nicbVDLSsNAFL2pr1pfUXHlJliEuimJCLosunFnBfuAJpTJdNIOncyEmYlQsFfceNCEbd+hzv/xkmbhbYeGDicy/3zAkTRpV23W+rtLK6tr5R3qxsbe/s7tn7B20lUolJCwsmZDdEijDKSUtTzUg3kQTFISOdcHyT+51HIhUV/EFPEhLEaMhpRDHSRurbR36M9Agjlt1Naz5JFGWCn/Xtqlt3Z3CWiVeQKhRo9u0vfyBwGhOuMUNK9Tw30UGpKaYkWnFTxVJEB6jIekZylFMVJDN4k+dU6MnEhI87h2ZurvjQzFSk3i0EzmYdWil4v/eb1UR1dBRnmSasLx/FCUMkcLJ+/CGVBJsGYTQxCW1GR18AhJhLVprGJK8Ba/vEza53XPrXv3F9XGdVFHGY7hBGrgwSU04Ba0AIMGTzDK7xZT9aL9W59zEdLVrFzCH9gf4ANqGVoQ=</latexit>Anisotropy (thus exp. bound) depends on the model:
BR(µ → ea) < 2.6 × 10−6
<latexit sha1_base64="gBsiDfnbofDickjIbErZEpS4YZA=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6KkQoWBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0OumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqODCS2kYJ4qEeH4oSBjUyaf9wD4VBCs21gRhQfVfIR4igbDSLRZ0Cc5i5GXSqliObTk3Z8VaPasjD47AMSgB5yDGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCk45rq</latexit><latexit sha1_base64="gBsiDfnbofDickjIbErZEpS4YZA=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6KkQoWBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0OumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqODCS2kYJ4qEeH4oSBjUyaf9wD4VBCs21gRhQfVfIR4igbDSLRZ0Cc5i5GXSqliObTk3Z8VaPasjD47AMSgB5yDGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCk45rq</latexit><latexit sha1_base64="gBsiDfnbofDickjIbErZEpS4YZA=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6KkQoWBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0OumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqODCS2kYJ4qEeH4oSBjUyaf9wD4VBCs21gRhQfVfIR4igbDSLRZ0Cc5i5GXSqliObTk3Z8VaPasjD47AMSgB5yDGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCk45rq</latexit><latexit sha1_base64="gBsiDfnbofDickjIbErZEpS4YZA=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6KkQoWBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0OumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqODCS2kYJ4qEeH4oSBjUyaf9wD4VBCs21gRhQfVfIR4igbDSLRZ0Cc5i5GXSqliObTk3Z8VaPasjD47AMSgB5yDGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCk45rq</latexit>Hierarchical model
CV/A = V †
RXRVR ± V † LXLVL
<latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit><latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit><latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit><latexit sha1_base64="WBURvIgEuB12Pmy8ZNdSC9LZSKA=">ACFnicbVDLSgMxFM3UV62vUZdugkVwY50RQTdCtRsXdRip4XOGQyaRuaeZBkhDL0K9z4K25cKOJW3Pk3ZtoRtPVAyLn3EtyjxczKqRhfGmFhcWl5ZXiamltfWNzS9/esUSUcExaOGIR73hIEZD0pJUMtKJOUGBx0jbG9Yyv31PuKBReCtHMXEC1A9pj2IkleTqRzU3tY4vxfQcpt3to/6sOM2s8KOA3XVf7R6Vrh62agYE8B5YuakDHI0XP3T9iOcBCSUmCEhuqYRSydFXFLMyLhkJ4LECA9Rn3QVDVFAhJNO1hrDA6X4sBdxdUIJ+rviRQFQowCT3UGSA7ErJeJ/3ndRPbOnZSGcSJiKcP9RIGZQSzjKBPOcGSjRBmFP1V4gHiCMsVZIlFYI5u/I8sU4qplExb07L1as8jiLYA/vgEJjgDFTBNWiAFsDgATyBF/CqPWrP2pv2Pm0taPnMLvgD7eMbQ2qc6w=</latexit>Stronger exp. limit applies: But suppressed rate: Weaker exp. limit applies:
BR(µ → ea) < 5.8 × 10−5
<latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit><latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit><latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit><latexit sha1_base64="60zTzkA581nQeRGg4tGaPpyhqg=">ACEnicbVC7TsMwFHXKq5RXgJHFokJqB6IEUdGBoSoLY0H0ITWhclyntWonke0gVG/gYVfYWEAIVYmNv4Gt80ALUeydHTOvbo+x48Zlcq2v43cyura+kZ+s7C1vbO7Z+4ftGSUCEyaOGKR6PhIEkZD0lRUMdKJBUHcZ6Ttj6mfvuBCEmj8E6NY+JxNAhpQDFSWuqZ5dQVHNZvJyWXJ9BVESQleElrFhV1FOJHTs+/S0MumZRduyZ4DLxMlIEWRo9Mwvtx/hJNQYak7Dp2rLwUCUxI5OCm0gSIzxCA9LVNET6mJfOIk3giVb6MIiEfqGCM/X3Roq4lGPu60mO1FAuelPxP6+bqKDqpTSME0VCPD8UJAzq5N+YJ8KghUba4KwoPqvEA+RQFjpFgu6BGcx8jJpnVmObTk358VaPasjD47AMSgB1yAGrgGDdAEGDyCZ/AK3own48V4Nz7mozkj2zkEf2B8/gCrPpru</latexit>But larger rate:
Lorenzo Calibbi (Nankai) LFV into ALPs
dΓ(µ+ → e+ a) d cos θ = Γµ→e a 2 " 1 + 2P cos θ CV
eµCA eµ
(CV
eµ)2 + (CA eµ)2
#
<latexit sha1_base64="yTDiF70iUymABuEYf6rzSYrvU=">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</latexit> Bounds on the flavor-breaking scale f
Anarchical model Hierarchical model
µ → e a γ
<latexit sha1_base64="A1sgrA2zQYSPyK+oLA4fasVTds=">AB/nicbVBNS8NAEN34WetXVDx5WSyCh1ISEfRY9OKxgv2AJpTJdtMu3d2E3Y1QsG/4sWDIl79Hd78N27bHLT1wcDjvRlm5kUpZ9p43rezsrq2vrFZ2ipv7+zu7bsHhy2dZIrQJkl4ojoRaMqZpE3DKedVFEQEaftaHQ79duPVGmWyAczTmkoYCBZzAgYK/Xc40BkgUkwxUEVgioOBiAE9NyKV/NmwMvEL0gFWj03K+gn5BMUGkIB627vpeaMAdlGOF0Ug4yTVMgIxjQrqUSBNVhPjt/gs+s0sdxomxJg2fq74kchNZjEdlOAWaoF72p+J/XzUx8HeZMpmhkswXxRnH9t9pFrjPFCWGjy0Bopi9FZMhKCDGJla2IfiLy+T1kXN92r+/WlflPEUIn6BSdIx9doTq6Qw3URATl6Bm9ojfnyXlx3p2PeuKU8wcoT9wPn8Ai6iUjw=</latexit><latexit sha1_base64="A1sgrA2zQYSPyK+oLA4fasVTds=">AB/nicbVBNS8NAEN34WetXVDx5WSyCh1ISEfRY9OKxgv2AJpTJdtMu3d2E3Y1QsG/4sWDIl79Hd78N27bHLT1wcDjvRlm5kUpZ9p43rezsrq2vrFZ2ipv7+zu7bsHhy2dZIrQJkl4ojoRaMqZpE3DKedVFEQEaftaHQ79duPVGmWyAczTmkoYCBZzAgYK/Xc40BkgUkwxUEVgioOBiAE9NyKV/NmwMvEL0gFWj03K+gn5BMUGkIB627vpeaMAdlGOF0Ug4yTVMgIxjQrqUSBNVhPjt/gs+s0sdxomxJg2fq74kchNZjEdlOAWaoF72p+J/XzUx8HeZMpmhkswXxRnH9t9pFrjPFCWGjy0Bopi9FZMhKCDGJla2IfiLy+T1kXN92r+/WlflPEUIn6BSdIx9doTq6Qw3URATl6Bm9ojfnyXlx3p2PeuKU8wcoT9wPn8Ai6iUjw=</latexit><latexit sha1_base64="A1sgrA2zQYSPyK+oLA4fasVTds=">AB/nicbVBNS8NAEN34WetXVDx5WSyCh1ISEfRY9OKxgv2AJpTJdtMu3d2E3Y1QsG/4sWDIl79Hd78N27bHLT1wcDjvRlm5kUpZ9p43rezsrq2vrFZ2ipv7+zu7bsHhy2dZIrQJkl4ojoRaMqZpE3DKedVFEQEaftaHQ79duPVGmWyAczTmkoYCBZzAgYK/Xc40BkgUkwxUEVgioOBiAE9NyKV/NmwMvEL0gFWj03K+gn5BMUGkIB627vpeaMAdlGOF0Ug4yTVMgIxjQrqUSBNVhPjt/gs+s0sdxomxJg2fq74kchNZjEdlOAWaoF72p+J/XzUx8HeZMpmhkswXxRnH9t9pFrjPFCWGjy0Bopi9FZMhKCDGJla2IfiLy+T1kXN92r+/WlflPEUIn6BSdIx9doTq6Qw3URATl6Bm9ojfnyXlx3p2PeuKU8wcoT9wPn8Ai6iUjw=</latexit><latexit sha1_base64="A1sgrA2zQYSPyK+oLA4fasVTds=">AB/nicbVBNS8NAEN34WetXVDx5WSyCh1ISEfRY9OKxgv2AJpTJdtMu3d2E3Y1QsG/4sWDIl79Hd78N27bHLT1wcDjvRlm5kUpZ9p43rezsrq2vrFZ2ipv7+zu7bsHhy2dZIrQJkl4ojoRaMqZpE3DKedVFEQEaftaHQ79duPVGmWyAczTmkoYCBZzAgYK/Xc40BkgUkwxUEVgioOBiAE9NyKV/NmwMvEL0gFWj03K+gn5BMUGkIB627vpeaMAdlGOF0Ug4yTVMgIxjQrqUSBNVhPjt/gs+s0sdxomxJg2fq74kchNZjEdlOAWaoF72p+J/XzUx8HeZMpmhkswXxRnH9t9pFrjPFCWGjy0Bopi9FZMhKCDGJla2IfiLy+T1kXN92r+/WlflPEUIn6BSdIx9doTq6Qw3URATl6Bm9ojfnyXlx3p2PeuKU8wcoT9wPn8Ai6iUjw=</latexit>µ → e a
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<latexit sha1_base64="tcVqlXbMAtzQLKn/Aj0NwMWo=">ACAXicbVBNS8NAEJ3Ur1q/ol4EL4tF8CAlkYoeCx70WMF+QBPLZrtpl+4mYXcjlFAv/hUvHhTx6r/w5r9x2+agrQ8GHu/NMDMvSDhT2nG+rcLS8srqWnG9tLG5tb1j7+41VZxKQhsk5rFsB1hRziLa0Exz2k4kxSLgtBUMryZ+64FKxeLoTo8S6gvcj1jICNZG6toHVU8zQRVynftz7zTzpEDXtDlGXbvsVJwp0CJxc1KGHPWu/eX1YpIKGmnCsVId10m0n2GpGeF0XPJSRNMhrhPO4ZG2Gz1s+kHY3RslB4KY2kq0miq/p7IsFBqJALTKbAeqHlvIv7ndVIdXvoZi5JU04jMFoUpRzpGkzhQj0lKNB8Zgolk5lZEBlhiok1oJROCO/yImeVyn4t5Wy7VqHkcRDuEITsCFC6jBDdShAQe4Rle4c16sl6sd+tj1lqw8pl9+APr8wcWYZVQ</latexit><latexit sha1_base64="tcVqlXbMAtzQLKn/Aj0NwMWo=">ACAXicbVBNS8NAEJ3Ur1q/ol4EL4tF8CAlkYoeCx70WMF+QBPLZrtpl+4mYXcjlFAv/hUvHhTx6r/w5r9x2+agrQ8GHu/NMDMvSDhT2nG+rcLS8srqWnG9tLG5tb1j7+41VZxKQhsk5rFsB1hRziLa0Exz2k4kxSLgtBUMryZ+64FKxeLoTo8S6gvcj1jICNZG6toHVU8zQRVynftz7zTzpEDXtDlGXbvsVJwp0CJxc1KGHPWu/eX1YpIKGmnCsVId10m0n2GpGeF0XPJSRNMhrhPO4ZG2Gz1s+kHY3RslB4KY2kq0miq/p7IsFBqJALTKbAeqHlvIv7ndVIdXvoZi5JU04jMFoUpRzpGkzhQj0lKNB8Zgolk5lZEBlhiok1oJROCO/yImeVyn4t5Wy7VqHkcRDuEITsCFC6jBDdShAQe4Rle4c16sl6sd+tj1lqw8pl9+APr8wcWYZVQ</latexit><latexit sha1_base64="tcVqlXbMAtzQLKn/Aj0NwMWo=">ACAXicbVBNS8NAEJ3Ur1q/ol4EL4tF8CAlkYoeCx70WMF+QBPLZrtpl+4mYXcjlFAv/hUvHhTx6r/w5r9x2+agrQ8GHu/NMDMvSDhT2nG+rcLS8srqWnG9tLG5tb1j7+41VZxKQhsk5rFsB1hRziLa0Exz2k4kxSLgtBUMryZ+64FKxeLoTo8S6gvcj1jICNZG6toHVU8zQRVynftz7zTzpEDXtDlGXbvsVJwp0CJxc1KGHPWu/eX1YpIKGmnCsVId10m0n2GpGeF0XPJSRNMhrhPO4ZG2Gz1s+kHY3RslB4KY2kq0miq/p7IsFBqJALTKbAeqHlvIv7ndVIdXvoZi5JU04jMFoUpRzpGkzhQj0lKNB8Zgolk5lZEBlhiok1oJROCO/yImeVyn4t5Wy7VqHkcRDuEITsCFC6jBDdShAQe4Rle4c16sl6sd+tj1lqw8pl9+APr8wcWYZVQ</latexit><latexit sha1_base64="tcVqlXbMAtzQLKn/Aj0NwMWo=">ACAXicbVBNS8NAEJ3Ur1q/ol4EL4tF8CAlkYoeCx70WMF+QBPLZrtpl+4mYXcjlFAv/hUvHhTx6r/w5r9x2+agrQ8GHu/NMDMvSDhT2nG+rcLS8srqWnG9tLG5tb1j7+41VZxKQhsk5rFsB1hRziLa0Exz2k4kxSLgtBUMryZ+64FKxeLoTo8S6gvcj1jICNZG6toHVU8zQRVynftz7zTzpEDXtDlGXbvsVJwp0CJxc1KGHPWu/eX1YpIKGmnCsVId10m0n2GpGeF0XPJSRNMhrhPO4ZG2Gz1s+kHY3RslB4KY2kq0miq/p7IsFBqJALTKbAeqHlvIv7ndVIdXvoZi5JU04jMFoUpRzpGkzhQj0lKNB8Zgolk5lZEBlhiok1oJROCO/yImeVyn4t5Wy7VqHkcRDuEITsCFC6jBDdShAQe4Rle4c16sl6sd+tj1lqw8pl9+APr8wcWYZVQ</latexit>5 × 103 GeV
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<latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit><latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit><latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit><latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit>106 GeV
<latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit><latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit><latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit><latexit sha1_base64="E1Z6ze2+UK9ftjOlnc+R512UBvk=">AB+XicbVBNSwMxEM3Wr1q/Vj16CRbBg5RdKeqx4EGPFewHdNeSTadtaJdkmyhLP0nXjwo4tV/4s1/Y9ruQVsfDzem2FmXpRwpo3nfTuFtfWNza3idmlnd2/wD08auo4VRQaNOaxakdEA2cSGoYZDu1EARERh1Y0up35rTEozWL5aCYJhIMJOszSoyVuq7re09XwUWKIHvoDnFXbfsVbw58Crxc1JGOepd9yvoxTQVIA3lROuO7yUmzIgyjHKYloJUQ0LoiAygY6kAnSYzS+f4jOr9HA/VrakwXP190RGhNYTEdlOQcxQL3sz8T+vk5r+TZgxmaQGJF0s6qcmxjPYsA9poAaPrGEUMXsrZgOiSLU2LBKNgR/+eV0rys+F7Ff6iWa9U8jiI6QafoHPnoGtXQPaqjBqJojJ7RK3pzMufFeXc+Fq0FJ585Rn/gfP4AcO+SLw=</latexit>Present bounds
f > 2 × 107 GeV
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Lorenzo Calibbi (Nankai) LFV into ALPs
To be compared to the bound (from the coupling to electrons) from star cooling:
f > 2 × 1010 GeV
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<latexit sha1_base64="wy5mfF6oGUpNlAMoEzyw492k4O8=">ACHicbVDLSsNAFJ3UV62vqEsXDhahbkpSBV24KLpxZwX7gCaEyXTSDp1JwsxEKHdufFX3LhQxK2f4M6/cdJmoa0HLhzOuZd7/FjRqWyrG+jsLS8srpWXC9tbG5t75i7ey0ZJQKTJo5YJDo+koTRkDQVYx0YkEQ9xlp+8PrzG8/ECFpFN6rUxcjvohDShGSkuecg9BCeXE4cjNcCIpbfjim2dTBzB4ZC0oGeWrao1BVwkdk7KIEfDM7+cXoQTkKFGZKya1uxclMkFMWMjEtOIkmM8BD1SVfTEHEi3XT6yBgea6UHg0joChWcqr8nUsSlHFfd2b3ynkvE/zuokKLtyUhnGiSIhni4KEQRXBLBXYo4JgxUaICyovhXiARIK51dSYdgz7+8SFq1qn1ard2dletXeRxFcACOQAXY4BzUwQ1ogCbA4BE8g1fwZjwZL8a78TFrLRj5zD74A+PzBxRmLg=</latexit> Bounds on the flavor-breaking scale f
Anarchical model Hierarchical model
µ → e a γ
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<latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit>Future sensitivity f > 8 × 108 GeV
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? ?
4 × 1010 GeV
<latexit sha1_base64="+RLU7X21gRWBdis6ihI3+Ht5YBk=">ACBHicbVDLSgMxFM3UV62vUZfdBIvgQkoiBV0WXeiygn1AZyZNOGZjJDkhHKMAs3/obF4q49SPc+Temj4W2HrhwOde7r0nSATXBqFvp7Cyura+UdwsbW3v7O65+wctHaeKsiaNRaw6AdFMcMmahvBOoliJAoEawejq4nfmBK81jemXHC/IgMJA85JcZKPbdc8wyPmIY3WcY5d4pzDwVwWvWyntuBVXRFHCZ4DmpgDkaPfL68c0jZg0VBCtuxglxs+IMpwKlpe8VLOE0BEZsK6lktjFfjZ9IofHVunDMFa2pIFT9fdERiKtx1FgOyNihnrRm4j/ed3UhBd+xmWSGibpbFGYCmhiOEkE9rli1IixJYQqbm+FdEgUocbmVrIh4MWXl0nrIpRFd/WKvXLeRxFUAZH4ARgcA7q4AY0QBNQ8AiewSt4c56cF+fd+Zi1Fpz5zCH4A+fzB10PlqA=</latexit><latexit sha1_base64="+RLU7X21gRWBdis6ihI3+Ht5YBk=">ACBHicbVDLSgMxFM3UV62vUZfdBIvgQkoiBV0WXeiygn1AZyZNOGZjJDkhHKMAs3/obF4q49SPc+Temj4W2HrhwOde7r0nSATXBqFvp7Cyura+UdwsbW3v7O65+wctHaeKsiaNRaw6AdFMcMmahvBOoliJAoEawejq4nfmBK81jemXHC/IgMJA85JcZKPbdc8wyPmIY3WcY5d4pzDwVwWvWyntuBVXRFHCZ4DmpgDkaPfL68c0jZg0VBCtuxglxs+IMpwKlpe8VLOE0BEZsK6lktjFfjZ9IofHVunDMFa2pIFT9fdERiKtx1FgOyNihnrRm4j/ed3UhBd+xmWSGibpbFGYCmhiOEkE9rli1IixJYQqbm+FdEgUocbmVrIh4MWXl0nrIpRFd/WKvXLeRxFUAZH4ARgcA7q4AY0QBNQ8AiewSt4c56cF+fd+Zi1Fpz5zCH4A+fzB10PlqA=</latexit><latexit sha1_base64="+RLU7X21gRWBdis6ihI3+Ht5YBk=">ACBHicbVDLSgMxFM3UV62vUZfdBIvgQkoiBV0WXeiygn1AZyZNOGZjJDkhHKMAs3/obF4q49SPc+Temj4W2HrhwOde7r0nSATXBqFvp7Cyura+UdwsbW3v7O65+wctHaeKsiaNRaw6AdFMcMmahvBOoliJAoEawejq4nfmBK81jemXHC/IgMJA85JcZKPbdc8wyPmIY3WcY5d4pzDwVwWvWyntuBVXRFHCZ4DmpgDkaPfL68c0jZg0VBCtuxglxs+IMpwKlpe8VLOE0BEZsK6lktjFfjZ9IofHVunDMFa2pIFT9fdERiKtx1FgOyNihnrRm4j/ed3UhBd+xmWSGibpbFGYCmhiOEkE9rli1IixJYQqbm+FdEgUocbmVrIh4MWXl0nrIpRFd/WKvXLeRxFUAZH4ARgcA7q4AY0QBNQ8AiewSt4c56cF+fd+Zi1Fpz5zCH4A+fzB10PlqA=</latexit><latexit sha1_base64="+RLU7X21gRWBdis6ihI3+Ht5YBk=">ACBHicbVDLSgMxFM3UV62vUZfdBIvgQkoiBV0WXeiygn1AZyZNOGZjJDkhHKMAs3/obF4q49SPc+Temj4W2HrhwOde7r0nSATXBqFvp7Cyura+UdwsbW3v7O65+wctHaeKsiaNRaw6AdFMcMmahvBOoliJAoEawejq4nfmBK81jemXHC/IgMJA85JcZKPbdc8wyPmIY3WcY5d4pzDwVwWvWyntuBVXRFHCZ4DmpgDkaPfL68c0jZg0VBCtuxglxs+IMpwKlpe8VLOE0BEZsK6lktjFfjZ9IofHVunDMFa2pIFT9fdERiKtx1FgOyNihnrRm4j/ed3UhBd+xmWSGibpbFGYCmhiOEkE9rli1IixJYQqbm+FdEgUocbmVrIh4MWXl0nrIpRFd/WKvXLeRxFUAZH4ARgcA7q4AY0QBNQ8AiewSt4c56cF+fd+Zi1Fpz5zCH4A+fzB10PlqA=</latexit>ma ≈ 0
Lorenzo Calibbi (Nankai) LFV into ALPs
To be compared to the bound (from the coupling to electrons) from star cooling:
f > 2 × 1010 GeV
<latexit sha1_base64="xaZUeXrd7fxLpkiU2sxKsljJgHg=">ACB3icbVDLSgMxFM34rPU16lKQYBFcSEmKoCsputBlBfuAzlgyaYNTWaGJCOUoTs3/obF4q49Rfc+Tem7Sy09cCFwzn3cu89QSK4Ngh9OwuLS8srq4W14vrG5ta2u7Pb0HGqKvTWMSqFRDNBI9Y3XAjWCtRjMhAsGYwuBr7zQemNI+jOzNMmC9JL+Ihp8RYqeMehBew4hkumY3WcYjbwTmHlKwmvWGHXcEiqjCeA8wTkpgRy1jvldWOaShYZKojWbYwS42dEGU4FGxW9VLOE0AHpsbalEbGL/WzyxwgeWaULw1jZigycqL8nMiK1HsrAdkpi+nrWG4v/e3UhOd+xqMkNSyi0VhKqCJ4TgU2OWKUSOGlhCquL0V0j5RhBobXdGgGdfnieNShmjMr49LVUv8zgKYB8cgmOAwRmoghtQA3VAwSN4Bq/gzXlyXpx352PauDkM3vgD5zPHwhil4A=</latexit><latexit sha1_base64="xaZUeXrd7fxLpkiU2sxKsljJgHg=">ACB3icbVDLSgMxFM34rPU16lKQYBFcSEmKoCsputBlBfuAzlgyaYNTWaGJCOUoTs3/obF4q49Rfc+Tem7Sy09cCFwzn3cu89QSK4Ngh9OwuLS8srq4W14vrG5ta2u7Pb0HGqKvTWMSqFRDNBI9Y3XAjWCtRjMhAsGYwuBr7zQemNI+jOzNMmC9JL+Ihp8RYqeMehBew4hkumY3WcYjbwTmHlKwmvWGHXcEiqjCeA8wTkpgRy1jvldWOaShYZKojWbYwS42dEGU4FGxW9VLOE0AHpsbalEbGL/WzyxwgeWaULw1jZigycqL8nMiK1HsrAdkpi+nrWG4v/e3UhOd+xqMkNSyi0VhKqCJ4TgU2OWKUSOGlhCquL0V0j5RhBobXdGgGdfnieNShmjMr49LVUv8zgKYB8cgmOAwRmoghtQA3VAwSN4Bq/gzXlyXpx352PauDkM3vgD5zPHwhil4A=</latexit><latexit sha1_base64="xaZUeXrd7fxLpkiU2sxKsljJgHg=">ACB3icbVDLSgMxFM34rPU16lKQYBFcSEmKoCsputBlBfuAzlgyaYNTWaGJCOUoTs3/obF4q49Rfc+Tem7Sy09cCFwzn3cu89QSK4Ngh9OwuLS8srq4W14vrG5ta2u7Pb0HGqKvTWMSqFRDNBI9Y3XAjWCtRjMhAsGYwuBr7zQemNI+jOzNMmC9JL+Ihp8RYqeMehBew4hkumY3WcYjbwTmHlKwmvWGHXcEiqjCeA8wTkpgRy1jvldWOaShYZKojWbYwS42dEGU4FGxW9VLOE0AHpsbalEbGL/WzyxwgeWaULw1jZigycqL8nMiK1HsrAdkpi+nrWG4v/e3UhOd+xqMkNSyi0VhKqCJ4TgU2OWKUSOGlhCquL0V0j5RhBobXdGgGdfnieNShmjMr49LVUv8zgKYB8cgmOAwRmoghtQA3VAwSN4Bq/gzXlyXpx352PauDkM3vgD5zPHwhil4A=</latexit><latexit sha1_base64="xaZUeXrd7fxLpkiU2sxKsljJgHg=">ACB3icbVDLSgMxFM34rPU16lKQYBFcSEmKoCsputBlBfuAzlgyaYNTWaGJCOUoTs3/obF4q49Rfc+Tem7Sy09cCFwzn3cu89QSK4Ngh9OwuLS8srq4W14vrG5ta2u7Pb0HGqKvTWMSqFRDNBI9Y3XAjWCtRjMhAsGYwuBr7zQemNI+jOzNMmC9JL+Ihp8RYqeMehBew4hkumY3WcYjbwTmHlKwmvWGHXcEiqjCeA8wTkpgRy1jvldWOaShYZKojWbYwS42dEGU4FGxW9VLOE0AHpsbalEbGL/WzyxwgeWaULw1jZigycqL8nMiK1HsrAdkpi+nrWG4v/e3UhOd+xqMkNSyi0VhKqCJ4TgU2OWKUSOGlhCquL0V0j5RhBobXdGgGdfnieNShmjMr49LVUv8zgKYB8cgmOAwRmoghtQA3VAwSN4Bq/gzXlyXpx352PauDkM3vgD5zPHwhil4A=</latexit>ma < O(10) keV
<latexit sha1_base64="wy5mfF6oGUpNlAMoEzyw492k4O8=">ACHicbVDLSsNAFJ3UV62vqEsXDhahbkpSBV24KLpxZwX7gCaEyXTSDp1JwsxEKHdufFX3LhQxK2f4M6/cdJmoa0HLhzOuZd7/FjRqWyrG+jsLS8srpWXC9tbG5t75i7ey0ZJQKTJo5YJDo+koTRkDQVYx0YkEQ9xlp+8PrzG8/ECFpFN6rUxcjvohDShGSkuecg9BCeXE4cjNcCIpbfjim2dTBzB4ZC0oGeWrao1BVwkdk7KIEfDM7+cXoQTkKFGZKya1uxclMkFMWMjEtOIkmM8BD1SVfTEHEi3XT6yBgea6UHg0joChWcqr8nUsSlHFfd2b3ynkvE/zuokKLtyUhnGiSIhni4KEQRXBLBXYo4JgxUaICyovhXiARIK51dSYdgz7+8SFq1qn1ard2dletXeRxFcACOQAXY4BzUwQ1ogCbA4BE8g1fwZjwZL8a78TFrLRj5zD74A+PzBxRmLg=</latexit> Bounds on the flavor-breaking scale f
Lorenzo Calibbi (Nankai) LFV into ALPs
… and hints for non-standard energy loss in star systems that could be fitted in this model with:
ma < O(10) keV
<latexit sha1_base64="wy5mfF6oGUpNlAMoEzyw492k4O8=">ACHicbVDLSsNAFJ3UV62vqEsXDhahbkpSBV24KLpxZwX7gCaEyXTSDp1JwsxEKHdufFX3LhQxK2f4M6/cdJmoa0HLhzOuZd7/FjRqWyrG+jsLS8srpWXC9tbG5t75i7ey0ZJQKTJo5YJDo+koTRkDQVYx0YkEQ9xlp+8PrzG8/ECFpFN6rUxcjvohDShGSkuecg9BCeXE4cjNcCIpbfjim2dTBzB4ZC0oGeWrao1BVwkdk7KIEfDM7+cXoQTkKFGZKya1uxclMkFMWMjEtOIkmM8BD1SVfTEHEi3XT6yBgea6UHg0joChWcqr8nUsSlHFfd2b3ynkvE/zuokKLtyUhnGiSIhni4KEQRXBLBXYo4JgxUaICyovhXiARIK51dSYdgz7+8SFq1qn1ard2dletXeRxFcACOQAXY4BzUwQ1ogCbA4BE8g1fwZjwZL8a78TFrLRj5zD74A+PzBxRmLg=</latexit>Anarchical model Hierarchical model
µ → e a γ
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<latexit sha1_base64="Xw6xtvHSqofG0AFI2sRz5kbECbw=">AB83icbVDLSgNBEJyNrxhfUY9eBoPgQcKuCHoMevEYwTwgu4TZSW8yZGZ2mYcQlvyGFw+KePVnvPk3TpI9aGJBQ1HVTXdXnHGmje9/e6W19Y3NrfJ2ZWd3b/+genjU1qlVFo05anqxkQDZxJahkO3UwBETGHTjy+m/mdJ1CapfLRTDKIBlKljBKjJPCUNjQpBhweEH61Zpf9+fAqyQoSA0VaParX+EgpVaANJQTrXuBn5koJ8owymFaCa2GjNAxGULPUkE6Cif3zFZ04Z4CRVrqTBc/X3RE6E1hMRu05BzEgvezPxP69nTXIT5Uxm1oCki0WJ5di9OQsAD5gCavjEUIVc7diOiKUONiqrgQguWXV0n7sh749eDhqta4LeIoxN0is5RgK5RA92jJmohijL0jF7Rm2e9F+/d+1i0lrxi5hj9gf5AwAokP0=</latexit><latexit sha1_base64="Xw6xtvHSqofG0AFI2sRz5kbECbw=">AB83icbVDLSgNBEJyNrxhfUY9eBoPgQcKuCHoMevEYwTwgu4TZSW8yZGZ2mYcQlvyGFw+KePVnvPk3TpI9aGJBQ1HVTXdXnHGmje9/e6W19Y3NrfJ2ZWd3b/+genjU1qlVFo05anqxkQDZxJahkO3UwBETGHTjy+m/mdJ1CapfLRTDKIBlKljBKjJPCUNjQpBhweEH61Zpf9+fAqyQoSA0VaParX+EgpVaANJQTrXuBn5koJ8owymFaCa2GjNAxGULPUkE6Cif3zFZ04Z4CRVrqTBc/X3RE6E1hMRu05BzEgvezPxP69nTXIT5Uxm1oCki0WJ5di9OQsAD5gCavjEUIVc7diOiKUONiqrgQguWXV0n7sh749eDhqta4LeIoxN0is5RgK5RA92jJmohijL0jF7Rm2e9F+/d+1i0lrxi5hj9gf5AwAokP0=</latexit><latexit sha1_base64="Xw6xtvHSqofG0AFI2sRz5kbECbw=">AB83icbVDLSgNBEJyNrxhfUY9eBoPgQcKuCHoMevEYwTwgu4TZSW8yZGZ2mYcQlvyGFw+KePVnvPk3TpI9aGJBQ1HVTXdXnHGmje9/e6W19Y3NrfJ2ZWd3b/+genjU1qlVFo05anqxkQDZxJahkO3UwBETGHTjy+m/mdJ1CapfLRTDKIBlKljBKjJPCUNjQpBhweEH61Zpf9+fAqyQoSA0VaParX+EgpVaANJQTrXuBn5koJ8owymFaCa2GjNAxGULPUkE6Cif3zFZ04Z4CRVrqTBc/X3RE6E1hMRu05BzEgvezPxP69nTXIT5Uxm1oCki0WJ5di9OQsAD5gCavjEUIVc7diOiKUONiqrgQguWXV0n7sh749eDhqta4LeIoxN0is5RgK5RA92jJmohijL0jF7Rm2e9F+/d+1i0lrxi5hj9gf5AwAokP0=</latexit><latexit sha1_base64="Xw6xtvHSqofG0AFI2sRz5kbECbw=">AB83icbVDLSgNBEJyNrxhfUY9eBoPgQcKuCHoMevEYwTwgu4TZSW8yZGZ2mYcQlvyGFw+KePVnvPk3TpI9aGJBQ1HVTXdXnHGmje9/e6W19Y3NrfJ2ZWd3b/+genjU1qlVFo05anqxkQDZxJahkO3UwBETGHTjy+m/mdJ1CapfLRTDKIBlKljBKjJPCUNjQpBhweEH61Zpf9+fAqyQoSA0VaParX+EgpVaANJQTrXuBn5koJ8owymFaCa2GjNAxGULPUkE6Cif3zFZ04Z4CRVrqTBc/X3RE6E1hMRu05BzEgvezPxP69nTXIT5Uxm1oCki0WJ5di9OQsAD5gCavjEUIVc7diOiKUONiqrgQguWXV0n7sh749eDhqta4LeIoxN0is5RgK5RA92jJmohijL0jF7Rm2e9F+/d+1i0lrxi5hj9gf5AwAokP0=</latexit>τ → e a
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<latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit>Future sensitivity f > 8 × 108 GeV
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<latexit sha1_base64="V1m1hbRwkqwkSrpOfQpqKxznCWY=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkoixXoseNBjBfsBTSyb7aZdutmE3YlQnvxr3jxoIhX/4U3/43bNgdtfTDweG+GmXlBIrgGx/m2VlbX1jc2C1vF7Z3dvX374LCp41R1qCxiFU7IJoJLlkDOAjWThQjUSBYKxheT/3WI1Oax/IeRgnzI9KXPOSUgJG69nHVAx4xjV3nIbscTzJPRfiGNcdu+SUnRnwMnFzUkI56l37y+vFNI2YBCqI1h3XScDPiAJOBRsXvVSzhNAh6bOoZKYrX42+2CMz4zSw2GsTEnAM/X3REYirUdRYDojAgO96E3F/7xOCuGVn3GZpMAknS8KU4EhxtM4cI8rRkGMDCFUcXMrpgOiCAUTWtGE4C6+vEyaF2XKbt3lVKtksdRQCfoFJ0jF1VRDd2iOmogiboGb2iN+vJerHerY9564qVzxyhP7A+fwBa5pYi</latexit><latexit sha1_base64="V1m1hbRwkqwkSrpOfQpqKxznCWY=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkoixXoseNBjBfsBTSyb7aZdutmE3YlQnvxr3jxoIhX/4U3/43bNgdtfTDweG+GmXlBIrgGx/m2VlbX1jc2C1vF7Z3dvX374LCp41R1qCxiFU7IJoJLlkDOAjWThQjUSBYKxheT/3WI1Oax/IeRgnzI9KXPOSUgJG69nHVAx4xjV3nIbscTzJPRfiGNcdu+SUnRnwMnFzUkI56l37y+vFNI2YBCqI1h3XScDPiAJOBRsXvVSzhNAh6bOoZKYrX42+2CMz4zSw2GsTEnAM/X3REYirUdRYDojAgO96E3F/7xOCuGVn3GZpMAknS8KU4EhxtM4cI8rRkGMDCFUcXMrpgOiCAUTWtGE4C6+vEyaF2XKbt3lVKtksdRQCfoFJ0jF1VRDd2iOmogiboGb2iN+vJerHerY9564qVzxyhP7A+fwBa5pYi</latexit><latexit sha1_base64="V1m1hbRwkqwkSrpOfQpqKxznCWY=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkoixXoseNBjBfsBTSyb7aZdutmE3YlQnvxr3jxoIhX/4U3/43bNgdtfTDweG+GmXlBIrgGx/m2VlbX1jc2C1vF7Z3dvX374LCp41R1qCxiFU7IJoJLlkDOAjWThQjUSBYKxheT/3WI1Oax/IeRgnzI9KXPOSUgJG69nHVAx4xjV3nIbscTzJPRfiGNcdu+SUnRnwMnFzUkI56l37y+vFNI2YBCqI1h3XScDPiAJOBRsXvVSzhNAh6bOoZKYrX42+2CMz4zSw2GsTEnAM/X3REYirUdRYDojAgO96E3F/7xOCuGVn3GZpMAknS8KU4EhxtM4cI8rRkGMDCFUcXMrpgOiCAUTWtGE4C6+vEyaF2XKbt3lVKtksdRQCfoFJ0jF1VRDd2iOmogiboGb2iN+vJerHerY9564qVzxyhP7A+fwBa5pYi</latexit><latexit sha1_base64="V1m1hbRwkqwkSrpOfQpqKxznCWY=">ACAXicbVBNS8NAEN34WetX1IvgZbEInkoixXoseNBjBfsBTSyb7aZdutmE3YlQnvxr3jxoIhX/4U3/43bNgdtfTDweG+GmXlBIrgGx/m2VlbX1jc2C1vF7Z3dvX374LCp41R1qCxiFU7IJoJLlkDOAjWThQjUSBYKxheT/3WI1Oax/IeRgnzI9KXPOSUgJG69nHVAx4xjV3nIbscTzJPRfiGNcdu+SUnRnwMnFzUkI56l37y+vFNI2YBCqI1h3XScDPiAJOBRsXvVSzhNAh6bOoZKYrX42+2CMz4zSw2GsTEnAM/X3REYirUdRYDojAgO96E3F/7xOCuGVn3GZpMAknS8KU4EhxtM4cI8rRkGMDCFUcXMrpgOiCAUTWtGE4C6+vEyaF2XKbt3lVKtksdRQCfoFJ0jF1VRDd2iOmogiboGb2iN+vJerHerY9564qVzxyhP7A+fwBa5pYi</latexit>2 × 107 GeV
<latexit sha1_base64="TzSJ1mf27T23tujIq5T5ay/R45U=">ACAXicbVBNS8NAEN3Ur1q/ol4EL4tF8FSUqjHgc9VrCt0MSy2W7apZtN2J0IJbQX/4oXD4p49V9489+4bXPQ1gcDj/dmJkXJIJrcJxvq7C2vrG5Vdwu7ezu7R/Yh0dtHaeKshaNRazuA6KZ4JK1gINg94liJAoE6wSjq5nfeWRK81jewThfkQGkoecEjBSz6pesAjprHrPGT1yTzVISvWXvSs8tOxZkDrxI3J2WUo9mzv7x+TNOISaCaN1nQT8jCjgVLBJyUs1SwgdkQHrGiqJ2epn8w8m+NwofRzGypQEPFd/T2Qk0nocBaYzIjDUy95M/M/rphBe+hmXSQpM0sWiMBUYjyLA/e5YhTE2BCFTe3YjokilAwoZVMCO7y6ukXa24TsW9rZUbtTyOIjpFZ+gCuaiOGugGNVELUTRFz+gVvVlP1ov1bn0sWgtWPnOM/sD6/AFUbpYe</latexit><latexit sha1_base64="TzSJ1mf27T23tujIq5T5ay/R45U=">ACAXicbVBNS8NAEN3Ur1q/ol4EL4tF8FSUqjHgc9VrCt0MSy2W7apZtN2J0IJbQX/4oXD4p49V9489+4bXPQ1gcDj/dmJkXJIJrcJxvq7C2vrG5Vdwu7ezu7R/Yh0dtHaeKshaNRazuA6KZ4JK1gINg94liJAoE6wSjq5nfeWRK81jewThfkQGkoecEjBSz6pesAjprHrPGT1yTzVISvWXvSs8tOxZkDrxI3J2WUo9mzv7x+TNOISaCaN1nQT8jCjgVLBJyUs1SwgdkQHrGiqJ2epn8w8m+NwofRzGypQEPFd/T2Qk0nocBaYzIjDUy95M/M/rphBe+hmXSQpM0sWiMBUYjyLA/e5YhTE2BCFTe3YjokilAwoZVMCO7y6ukXa24TsW9rZUbtTyOIjpFZ+gCuaiOGugGNVELUTRFz+gVvVlP1ov1bn0sWgtWPnOM/sD6/AFUbpYe</latexit><latexit sha1_base64="TzSJ1mf27T23tujIq5T5ay/R45U=">ACAXicbVBNS8NAEN3Ur1q/ol4EL4tF8FSUqjHgc9VrCt0MSy2W7apZtN2J0IJbQX/4oXD4p49V9489+4bXPQ1gcDj/dmJkXJIJrcJxvq7C2vrG5Vdwu7ezu7R/Yh0dtHaeKshaNRazuA6KZ4JK1gINg94liJAoE6wSjq5nfeWRK81jewThfkQGkoecEjBSz6pesAjprHrPGT1yTzVISvWXvSs8tOxZkDrxI3J2WUo9mzv7x+TNOISaCaN1nQT8jCjgVLBJyUs1SwgdkQHrGiqJ2epn8w8m+NwofRzGypQEPFd/T2Qk0nocBaYzIjDUy95M/M/rphBe+hmXSQpM0sWiMBUYjyLA/e5YhTE2BCFTe3YjokilAwoZVMCO7y6ukXa24TsW9rZUbtTyOIjpFZ+gCuaiOGugGNVELUTRFz+gVvVlP1ov1bn0sWgtWPnOM/sD6/AFUbpYe</latexit><latexit sha1_base64="TzSJ1mf27T23tujIq5T5ay/R45U=">ACAXicbVBNS8NAEN3Ur1q/ol4EL4tF8FSUqjHgc9VrCt0MSy2W7apZtN2J0IJbQX/4oXD4p49V9489+4bXPQ1gcDj/dmJkXJIJrcJxvq7C2vrG5Vdwu7ezu7R/Yh0dtHaeKshaNRazuA6KZ4JK1gINg94liJAoE6wSjq5nfeWRK81jewThfkQGkoecEjBSz6pesAjprHrPGT1yTzVISvWXvSs8tOxZkDrxI3J2WUo9mzv7x+TNOISaCaN1nQT8jCjgVLBJyUs1SwgdkQHrGiqJ2epn8w8m+NwofRzGypQEPFd/T2Qk0nocBaYzIjDUy95M/M/rphBe+hmXSQpM0sWiMBUYjyLA/e5YhTE2BCFTe3YjokilAwoZVMCO7y6ukXa24TsW9rZUbtTyOIjpFZ+gCuaiOGugGNVELUTRFz+gVvVlP1ov1bn0sWgtWPnOM/sD6/AFUbpYe</latexit>Mu3e phase I Belle2 (50/ab)
? ?
4 × 1010 GeV
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Bounds on the flavor-breaking scale f
Lorenzo Calibbi (Nankai) LFV into ALPs
ma range
100 keV
m𝜈 m𝜐
Anarchical model Hierarchical model
µ → e a γ
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<latexit sha1_base64="JDs8SLOf7ThJ6bvKc9nT0zPFU=">AB9HicbVBNS8NAEJ3Ur1q/qh69LBbBg5REBD0WvXisYD+gCWz3bRLN5u4OymU0t/hxYMiXv0x3vw3btsctPXBwO9GWbmhakUBl32ymsrW9sbhW3Szu7e/sH5cOjpkyzXiDJTLR7ZAaLoXiDRQoeTvVnMah5K1weDfzWyOujUjUI45THsS0r0QkGEUrBT7SzMeEcOJf0G654lbdOcgq8XJSgRz1bvnL7yUsi7lCJqkxHc9NMZhQjYJPi35meEpZUPa5x1LFY25CSbzo6fkzCo9EiXalkIyV39PTGhszDgObWdMcWCWvZn4n9fJMLoJkKlGXLFouiTBL75iwB0hOaM5RjSyjTwt5K2IBqytDmVLIheMsvr5LmZdVzq97DVaV2m8dRhBM4hXPw4BpqcA91aACDJ3iGV3hzRs6L8+58LFoLTj5zDH/gfP4Ax6KRbw=</latexit><latexit sha1_base64="JDs8SLOf7ThJ6bvKc9nT0zPFU=">AB9HicbVBNS8NAEJ3Ur1q/qh69LBbBg5REBD0WvXisYD+gCWz3bRLN5u4OymU0t/hxYMiXv0x3vw3btsctPXBwO9GWbmhakUBl32ymsrW9sbhW3Szu7e/sH5cOjpkyzXiDJTLR7ZAaLoXiDRQoeTvVnMah5K1weDfzWyOujUjUI45THsS0r0QkGEUrBT7SzMeEcOJf0G654lbdOcgq8XJSgRz1bvnL7yUsi7lCJqkxHc9NMZhQjYJPi35meEpZUPa5x1LFY25CSbzo6fkzCo9EiXalkIyV39PTGhszDgObWdMcWCWvZn4n9fJMLoJkKlGXLFouiTBL75iwB0hOaM5RjSyjTwt5K2IBqytDmVLIheMsvr5LmZdVzq97DVaV2m8dRhBM4hXPw4BpqcA91aACDJ3iGV3hzRs6L8+58LFoLTj5zDH/gfP4Ax6KRbw=</latexit><latexit sha1_base64="JDs8SLOf7ThJ6bvKc9nT0zPFU=">AB9HicbVBNS8NAEJ3Ur1q/qh69LBbBg5REBD0WvXisYD+gCWz3bRLN5u4OymU0t/hxYMiXv0x3vw3btsctPXBwO9GWbmhakUBl32ymsrW9sbhW3Szu7e/sH5cOjpkyzXiDJTLR7ZAaLoXiDRQoeTvVnMah5K1weDfzWyOujUjUI45THsS0r0QkGEUrBT7SzMeEcOJf0G654lbdOcgq8XJSgRz1bvnL7yUsi7lCJqkxHc9NMZhQjYJPi35meEpZUPa5x1LFY25CSbzo6fkzCo9EiXalkIyV39PTGhszDgObWdMcWCWvZn4n9fJMLoJkKlGXLFouiTBL75iwB0hOaM5RjSyjTwt5K2IBqytDmVLIheMsvr5LmZdVzq97DVaV2m8dRhBM4hXPw4BpqcA91aACDJ3iGV3hzRs6L8+58LFoLTj5zDH/gfP4Ax6KRbw=</latexit><latexit sha1_base64="JDs8SLOf7ThJ6bvKc9nT0zPFU=">AB9HicbVBNS8NAEJ3Ur1q/qh69LBbBg5REBD0WvXisYD+gCWz3bRLN5u4OymU0t/hxYMiXv0x3vw3btsctPXBwO9GWbmhakUBl32ymsrW9sbhW3Szu7e/sH5cOjpkyzXiDJTLR7ZAaLoXiDRQoeTvVnMah5K1weDfzWyOujUjUI45THsS0r0QkGEUrBT7SzMeEcOJf0G654lbdOcgq8XJSgRz1bvnL7yUsi7lCJqkxHc9NMZhQjYJPi35meEpZUPa5x1LFY25CSbzo6fkzCo9EiXalkIyV39PTGhszDgObWdMcWCWvZn4n9fJMLoJkKlGXLFouiTBL75iwB0hOaM5RjSyjTwt5K2IBqytDmVLIheMsvr5LmZdVzq97DVaV2m8dRhBM4hXPw4BpqcA91aACDJ3iGV3hzRs6L8+58LFoLTj5zDH/gfP4Ax6KRbw=</latexit>τ → µ a
<latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit><latexit sha1_base64="kzsPuvsF5tpy316QDfv8/YNkE8Y=">AB+HicbVDLSsNAFJ3UV62PRl26GSyCymJCLosunFZwT6gCeVmOmHziRhHkIN/RI3LhRx6e482+ctlo64ELh3Pu5d57owzpT3v2ymtrW9sbpW3Kzu7e/tV9+CwrVIjCW2RlKeyG4GinCW0pZnmtJtJCiLitBONb2d+5FKxdLkQU8yGgoYJixmBLSV+m410GACneJAGBycQ9+teXVvDrxK/ILUIFm3/0KBikxgiacFCq53uZDnOQmhFOp5XAKJoBGcOQ9ixNQFAV5vPDp/jUKgMcp9JWovFc/T2Rg1BqIiLbKUCP1LI3E/zekbH12HOksxompDFothwbB+dpYAHTFKi+cQSIJLZWzEZgQSibVYVG4K/PIqaV/Ufa/u31/WGjdFHGV0jE7QGfLRFWqgO9RELUSQc/oFb05T86L8+58LFpLTjFzhP7A+fwB3OaSjQ=</latexit>Future sensitivity f > 8 × 108 GeV
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? ?
4 × 1010 GeV
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𝜈→e modes can compete with stars 𝜈→e dominates Only 𝜐 decays!
Conclusions
Lorenzo Calibbi (Nankai) LFV into ALPs
In general, PNGBs from non-universal global U(1) give rise to lepton-flavor-violating decays Very large symmetry-breaking scales can be probed Future CLFV limits (e.g. on a leptonic familon) can supersede stellar bounds even in the small mass range We have huge room for improvement over the old limits Essantial interplay among 𝜈, 𝜐, and astrophysical bounds