Feeble Interactions -A Theory Perspective- Martin Bauer March 18, - - PowerPoint PPT Presentation
Feeble Interactions -A Theory Perspective- Martin Bauer March 18, 2019 1 The lifetime gap Example: Axion-like particle with perturbative coupling to photons 2 64 3 f 2 c 2 m 3 a = 4 f a F L = c F
Martin Bauer
March 18, 2019
103 m
1 m
10−3 m 10−6 m 10−9 m 106 m 109 m
Example: Axion-like particle with perturbative coupling to photons
ATLAS /CMS
Supernova Red Giants Ions
a
γ γ
2
Beam dumps
`a = aa Γa
cγγ/f . 1/10 GeV−1
L = cγγ α 4πf a Fµν ˜ F µν
Γa = α2 64π3f 2 c2
γγm3 a
Example: Axion-like particle with perturbative coupling to photons Typically: Long lifetime = Weak couplings and small masses
cγγ/f . 1/10 GeV−1
3
103 m
1 m
10−3 m 10−6 m 10−9 m 106 m 109 m
ATLAS /CMS
Supernova Red Giants Ions Beam dumps
`a = aa Γa
Γa = α2 64π3f 2 c2
γγm3 a
Example: Axion-like particle with perturbative coupling to photons Typically: Long lifetime = Weak couplings and small masses Why would a new particle be light and weakly coupled?
4
1nm
Γa = α2 64π3f 2 c2
γγm3 a
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Light and weak interactions seem to be independent conditions, is this theoretically motivated ? Many UV theories predict new heavy states with sizeable couplings to the SM. New light states with sizeable couplings are largely ruled out.
V (φ) = µ2φφ† + λ (φφ†)2
V (φ) Im φ
µ2 < 0
Re φ
φ = (f + s)eia/f
2 h = |µ2|
m2
s = 4λf 2
m2
a = 0
Every spontaneously broken continuous symmetry gives rise to massless spin-0 fields.
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Since the GB corresponds to the phase of a complex field, it is protected by a shift symmetry
it is protected by a shift symmetry This symmetry forbids a mass term, and all couplings are suppressed by the UV scale
L = 1 2∂µa ∂µa + cµ ∂νa 4πf ¯ µγνµ + . . .
eia(x)/f → ei(a(x)+c)/f = eia(x)/feic/f φ = (f + s)eia/f
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An exactly massless boson is very problematic.
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The global symmetry can be broken by explicit masses or anomalous effects Small masses Small couplings
L = 1 2∂µa ∂µa + cµ ∂νa 4πf ¯ µγνµ + . . .+1
2m2
aa2
ma = µ2 f
The most famous example is the pion
m2
π = mu + md
f 2
π
Λ3
QCD
≈ (140 MeV)2 h¯ qLqRi = Λ3
QCD ≈ GeV3
LQCD = ¯ qLi / D qL + ¯ qRi / D qR + mq ¯ qLqR
ρ, P, N π
The pion mass is controlled by the explicit breaking through light quark masses
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The most famous example is the pion
m2
π = mu + md
f 2
π
Λ3
QCD
≈ (140 MeV)2 h¯ qLqRi = Λ3
QCD ≈ GeV3
LQCD = ¯ qLi / D qL + ¯ qRi / D qR + mq ¯ qLqR
The pion mass is controlled by the explicit breaking through light quark masses
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Scales at f ALP
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LD≤5
eff
= 1 2(∂µa)(∂µa) − m2
a
2 a2 α α
Most general dimension five Lagrangian
ν + ∂µa
f X
i
ci 2 ¯ ψiγµγ5ψi ,
ν + cγγ
α 4πf a Fµν ˜ F µν + cγZ α 4πswcwf a Fµν ˜ Zµν + cZZ α 4πs2
wc2 wf a Zµν ˜
Zµν
+cGG αs 4πf a Gµν ˜ Gµν +
Georgi, Kaplan, Randall, Phys. Lett. 169B, 73 (1986)
Many possible signature. I will focus on photons here.
12
ATLAS, Nature Phys 13, no. 9, 852 (2017) Knapen et al. Phys. Rev. Lett. 118 (2017)
1nm
CMS 1810.04602
Different strategies:
High statistics: Photon fusion in Ion scattering
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a Pb Pb Pb Pb γ γ Ze Ze
CMS, 36 pb1 ATLAS, 3γ 1 nb1 1 n b1 OPAL, 3γ
ATLAS, 2016
5 20 40 60 80 100 ma (GeV) 105 104 103 1/Λ (GeV1)
ATLAS, 2γ Beam Dump OPAL, 2γ
aF e F coupling
1 00 1 0−1 1 0−2
linear p-p ps = 7 TeV Pb-Pb psNN = 5.5 TeV
ATLAS, Nature Phys 13, no. 9, 852 (2017) Knapen et al. Phys. Rev. Lett. 118 (2017)
1nm
CMS 1810.04602
ATLAS/CMS
a Z
MATHUSLA 100 m
100 m 200 m 20 m
γ
γ
MB, Neubert, Thamm, Eur.Phys. J.C 79
a Z
LA m
m m m
γ
γ
MATHUSLA LHC & Z
(Really) displaced vertices: MATHUSLA, FASER, SHiP , CodexB,..
Gligorov et al. Phys. Rev. D 97, no.1 015023, (2018) Feng et. al. Phys. Rev. D 98, 055021 Curtin et al 1806.07396 Alekhin et. al. Rept. Prog. Phys. 79, 124201 (2016)
1nm 14
ATLAS/CMS
a Z
MATHUSLA 100 m
100 m 200 m 20 m
γ
γ
MB, Neubert, Thamm, Eur.Phys. J.C 79
FASER MATHUSLA
Gligorov et al. Phys. Rev. D 97, no.1 015023, (2018) Feng et. al. Phys. Rev. D 98, 055021 Curtin et al 1806.07396 Alekhin et. al. Rept. Prog. Phys. 79, 124201 (2016)
1nm
(Really) displaced vertices: MATHUSLA, FASER, SHiP , CodexB
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Big Advantage of the LHC: The only place to make the Higgs!
h h Z Z h Z a
1nm
h h a a a
φ + cZh f 3 (∂µa)
L>5 = cah f 2 (∂µa) (∂µa) φ†φ +
+c5
Zh
f (∂µa)
µ2
MB, Neubert, Thamm, PRL 117, 181801 (2016)
MB, Neubert, Thamm, JHEP 1712 044 (2017)
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Big Advantage of the LHC: The only place to make the Higgs!
1nm
ceff
Zh = 0.015
Br(h → Za) < 1 o /
f 3 (∂µa)
+c5
Zh
f (∂µa)
µ2
h h a Z Z f
L>5 = cah f 2 (∂µa) (∂µa) φ†φ +
h h Z Z h Z a
Theoretically interesting:
MB, Neubert, Thamm, PRL 117, 181801 (2016)
MB, Neubert, Thamm, JHEP 1712 044 (2017)
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Many experimental signatures:
Low mass, small coupling medium mass, small coupling very small coupling
ATLAS/CMS
a Z
MATHUSLA 100 m 100 m 200 m 20 m
γ
γ
Exotic signatures Very challenging exotic signatures
h → Zγγ
h → Z + ET, miss
a → γγ
Z
h
γγ
a
Z
h
γ γ
a
Always enhanced!
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New light gauge bosons have long history
L = −1 4FµνF µν − ✏ 2FµνXµν − 1 4XµνXµν
A0
µ
Bµ A0
µ
Bµ ✏
is a free parameter
✏ ∝ gXe 8⇡2 log Λ2 m2
Kinetic mixing as a renormalizable portal
Charged SM matter is milli- charged under U(1)X
eAµJµ
EM − ✏eA0 µJµ EM
Holdom Phys.Lett 166B, (1986)
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Hidden Photon mass term
L = −1 4FµνF µν − ✏ 2FµνXµν − 1 4XµνXµν
Small masses Small couplings A0
µ
Bµ
✏ ∝ gXe 8⇡2 log Λ2 m2 −1 2DµSDµS
eAµJµ
EM − ✏eA0 µJµ EM
Universal mA0 = gXhSi
New light gauge bosons have long history
Holdom Phys.Lett 166B, (1986)
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eAµJµ
EM − ✏eA0 µJµ EM
Universal
µ+µ−
τ +τ −
had
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MB, Foldenauer Jaeckel, JHEP 1807 094 (2018)
APEX BaBar BaBar Charm E137 E141 E774 KLOE LSND LHCb μμ LHCb μμ NA48 U70 Orsay NuCal g - 2e g - 2μ
Universal
1 µm
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Belle-II DarkLight FASER ATLAS, CMS LHCb D* LHCb μμ LHCb μμ MAMI MESA Mu3e SeaQuest SHiP VEPP3
g - 2μ
100m
1 µm
MB, Foldenauer Jaeckel, JHEP 1807 094 (2018)
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Belle-II DarkLight FASER ATLAS, CMS LHCb D* LHCb μμ LHCb μμ MAMI MESA Mu3e SeaQuest SHiP VEPP3
g - 2μ
Mu3e
100m
1 µm
MB, Foldenauer Jaeckel, JHEP 1807 094 (2018)
[Echenard, Essig, Zhong, 1411.1770]
µ+ → γ0e+νe¯ νµ → e+ee+νe¯ νµ
The Mu3e experiment can search for light hidden photons Displaced vertices
[Mu3E collaboration, in prep.]
A0 W µ e e e ν ν A0 W µ e e e ν ν
A0 W µ e e e ν ν
Universal
Prompt decays
25
26
Belle-II DarkLight FASER ATLAS, CMS LHCb D* LHCb μμ LHCb μμ MAMI MESA Mu3e SeaQuest SHiP VEPP3
g - 2μ
Universal
Mu3e LHCb D*
100m
1 µm
MB, Foldenauer Jaeckel, JHEP 1807 094 (2018)
LHCb can search for hidden photons in rare charm decays
D⇤ → Dγ → Dγ0 → De+e
Taking advantage of large statistics: About 14 Trillion D* mesons in Run III (15 /fb)
Ilten et al. Phys. Rev. Lett. 116, no. 25, 251803 (2016)
A0 π π D∗ D K q ¯ q
Br(D∗ → Dγ) = 38%
Universal
Br(D∗ → Dπ) = 62%
LHCb, Phys. Rev. Lett. 120, 061801 (2018)
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New gauge bosons with gauge couplings to the SM
There is a limited number of possible new light gauge bosons consistent with the SM (= anomaly free, and able to reproduce mixing structures).
Universal B - L Lµ − Lτ Le − Lτ Lµ − Le
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Anomaly cancellation is necessary for gauge invariance.
γ γ ) mγ 6= 0
All triangle diagrams have to vanish
X
Fermions
= 0
[S. Adler (1969). Physical Review. 177 (5): 2426] [Bell, Jackiw (1969) Il Nuovo Cimento A. 60:47]
This fixes the Standard Model hypercharges.
[Gross, Jackiw, Phys. Rev. D6, 477 (1972).
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New gauge bosons with gauge couplings to the SM
There is a limited number of possible new light gauge bosons consistent with the SM (= anomaly free, and able to reproduce mixing structures).
Universal B - L Lµ − Lτ Le − Lτ Lµ − Le
to quarks and leptons
to all charged matter
to muons and electrons
to taus and electrons
to taus and muons
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Lµ − Lτ
Lµ−Lτ
ν¯ ν
e+e−
µ+µ−
τ +τ −
had
…couplings to hadrons and electrons are suppressed.
µ, τ
ˆ Bµ
✏ = − e g 8⇡2 log m2
τ
m2
µ
A0
µ
BRs very different from the universal case
≈ g 50
31
Borexino BaBar 4 μ BaBar Charm II E137 KLOE NA64 g - 2e g - 2μ White Dwarfs
Borexino g - 2μ White Dwarfs
Lµ − Lτ
MB, Foldenauer Jaeckel, JHEP 1807 094 (2018) 32
Belle-II Belle - II γνν DarkLight LHCb μμ Mu3e SHiP SHiP VEPP3
Lµ − Lτ
Mu3e
MB, Foldenauer Jaeckel, JHEP 1807 094 (2018) 33
Belle-II Belle - II γνν DarkLight LHCb μμ Mu3e SHiP SHiP VEPP3
e−
e+
P P
A0
Lµ − Lτ
Mu3e
double suppression
[MB, Foldenauer, Jaeckel, 1803.05466]
34
Belle-II Belle - II γνν DarkLight LHCb μμ Mu3e SHiP SHiP VEPP3
Lµ − Lτ
Mu3e
A0 W µ e e e ν ν A0 W µ e e e ν ν
[MB, Foldenauer, Jaeckel, 1803.05466]
35
Cosmological solutions to the Hierarchy problem predict feebly interacting particles Nnaturalness Relaxion
36
α
Λ/ (ϕ) ϕ α
〈〉≠
Λ3
cε ⌧ Λ
for g ⌧ 1 hat large field excursions for φ needed: φ
predicts new axion-like state
[Graham, Kaplan, Rajendran, 1504.07551]
predicts (many) new hidden photons.
Arkani-Hamed et al. PRL 117 (2016) 251801
37
Apart from small couplings, very off-shell propagators can result in suppressed width and therefore long-lived particles
`B = ΓB ≈ 7 mm
The B meson is not light with respect to its decay products, but the off-shell decay and the boost factor lead to a displaced vertex. b
¯ u
B−
W −
`−
¯ ν`
c
⇒ Γ(B → Xc`⌫) = g4 192⇡3 |Vcb|2 2 m5
b
M 4
W
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Example: Split SUSY Theories with large mass splittings between mediators and decay products lead to long lifetimes, even for particles with sizeable couplings and masses.
˜ B
˜ g ˜ q q q
⇒ Γ(˜ g → q˜ qχ) = ααs 192πs2
W
M 5
˜ g
˜ m4
`˜
g =
Γ˜
g
≈ 0.3 m − 3 km
h ˜ q ˜ g, ˜ χ
Large Split
[Giudice, Romanian Nucl. Phys. B 699, 65 (2004)]
39
Example: Emerging Jets Chirality suppressed decays lead to further suppressions without very large mass splittings.
W −
b
¯ u
B−
`−
¯ ν`
Γ(B− → `¯ ⌫) = g4 16⇡2 |Vub|2 m2
`MB
M 4
W
Xd
πdark d ¯ d
Γ(πd → d ¯ d) = g4
X
32π f 2
πdm2 dmπd
M 4
Xd
Xd
Dark QCD QCD
[Schwaller et al. JHEP 1505, 059 (2015)]
cτ0 = c~ Γ ≈ 80 mm × 1 κ4 × ✓2 GeV fπd ◆2 ✓100 MeV mdown ◆2 ✓2 GeV mπd ◆ ✓ MXd 1 TeV ◆4
Only scratched the surface: Sterile neutrinos, dark matter, charged particles, displaced hadronic decays, compressed spectra…
40
New, feebly interacting particles with decay length between microscopic and astrophysical decay length are poorly constrained. Goldstone bosons and new gauge bosons are well- motivated to be weakly coupled and light. Search strategies range from LHC searches (displaced vertices, exotic Higgs/Z decays), new detectors, excited meson decays (LHCb), muon decays (Mu3e), etc.
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Fraction of surviving Particles Distance
e+e− µ+µ− τ +τ − c ¯ c b¯ b γγ gg
3π
Partial ALP widths for all Wilson coefficients set to 1.
Jaeckel, Spannowsky, Phys. Lett. B 753, 482 (2016) Armengaud et al., JCAP 1311, 067 (2013) …and others
MB, Neubert, Thamm, 1708.00443
If the alps are light, they are strongly boosted! The LHC only has a finite angular resolution putting a limit on the angle for which single photons can be separated from pairs,
8 > > > > > > > < > > > > > > > : m2
h − m2 Z + m2 a
2mamh , for h → Za , mh 2ma , for h → aa .
γa ==
8 > > > > > > > < > > > > > > > :
γa < 625
Z γ
h
Z
h
γ
a
2 2
σeff(h → Zγ) = Exciting possibility:
[95] ATLAS Collaboration, ATLAS-CONF-2012-079.
colliders
Z → aγ
e+ e−
µ− µ−
µ+ µ− a
e+ e−
µ− µ−
µ+ µ− a MB, Neubert, Thamm, 1708.00443
The reach for future searches for h -> Za decays is immense
Ceff
Zh = 0.1
Ceff
Zh = 0.015
Ceff
Zh = 0.72
Br(a → γγ) & 2 × 10−4
Br(a → γγ) & 0.011
Br(a → γγ) & 0.46
Ask for 100 events within the full 300 /fb dataset.
Future: The anomalous magnetic moment of the muon
[Gohn 1506.00608]
aexp
µ
− aSM
µ
= (288 ± 63 ± 49) · 10−11
aµ = (g − 2)µ/2
Currently:
3.6 σ discrepancy & 5 σ ?
µ µ γ
µ µ γ
W ±
ν
δaW
µ ≈
g2 20π2 m2
µ
M 2
W
≈ 400 × 10−11
SM NP M = O(TeV)
Marciano, Masiero, Paradisi, Passera, Phys. Rev. D 94, 115033 (2016) µ µ µ γ γ µ a Z/γ µ µ µ a
δaµ = m2
µ
Λ2 ( Kaµ(µ) − (cµµ)2 16π2 h1 ✓m2
a
m2
µ
◆ − 2α π cµµ Cγγ ln µ2 m2
µ
+ ✓ ◆ + 3 − h2 ✓m2
a
m2
µ
◆
− α 2π 1 − 4s2
w
swcw cµµ CγZ ✓ ln µ2 m2
Z
+ − + 3 2 ◆
(g-2)μ for rather sizable photon couplings
MB, Neubert, Thamm, JHEP 1712 044 (2017)
h h h a a a a a a f Z/W ± h h a Z Z a f W ± h Z a
Γ(h → Za) = m3
h
16πΛ2
Zh
✓m2
Z
m2
h
, m2
a
m2
h
◆ x − y)2 − 4xy, and we have defined
− − − Ceff
Zh ≈ C(5) Zh − 0.016 ctt + 0.030 C(7) Zh
1 TeV Λ 2 .
Γ(h → aa) = v2m3
h
32⇡Λ4
ah
1 − 2m2
a
m2
h
◆2 s 1 − 4m2
a
m2
h
.
Ceff
ah ≈ Cah(Λ) + 0.173 c2 tt − 0.0025
WW + C2 ZZ
B − L
Lµ−Le
Lτ −Le
ν¯ ν ν¯ ν ν¯ ν ν¯ ν
e+e− e+e− e+e− e+e−
µ+µ− µ+µ− µ+µ− µ+µ−
Lτ −Lµ
τ +τ − τ +τ − τ +τ −
had had had had
This is not new. Integrating out New Physics leads to the operators
induce the operator O1 = c1 αs 4πv2 Ga
µνGµν a H†H
O O2 = c2 αs 8π Ga
µνGµν a log
H†H v2
Pierce, Thaler, Wang, JHEP 0705, 070 (2007)
with consequences for Higgs pair production. The top
c2
C(5)
Zh
Vectorlike Quarks
Pierce, Thaler, Wang, JHEP 0705, 070 (2007)
· −Lmass = λ1
HBc + λ2
HT + QcHB
c1 = 4 3 −β (1 − β)2
generate
β ≡ 2mAmB λ1λ2v2 . , c2 = 4 3 1 (1 − β)2,
O1 = c1 αs 4πv2 Ga
µνGµν a H†H
O O2 = c2 αs 8π Ga
µνGµν a log
H†H v2