New Physics for Muon g-2 anomaly Kazuhiro Tobe (Nagoya University - - PowerPoint PPT Presentation
New Physics for Muon g-2 anomaly Kazuhiro Tobe (Nagoya University and KMI) References M.M. Nojiri, M. Takeuchi, and KT JHEP 1505 (2015) 028 [arXiv:1507.05028] and arXiv:1511.08880 (to be published in PRD), Y. Omura, E. Senaha, KT,
Kazuhiro Tobe (Nagoya University and KMI)
References
★ PRD86, 095025 (2012) [arXiv: 1207.1313], S. Kanemitsu and KT ★ JHEP 1403, 105 (2014) [arXiv:1311.0870], K. Harigaya, T. Igari, M.M. Nojiri, M. Takeuchi, and KT ★JHEP 1505 (2015) 028 [arXiv:1507.05028] and arXiv:1511.08880 (to be published in PRD), Y. Omura, E. Senaha, KT,
素粒子物理学の進展 2016 @ 基研 Sep. 5‒9
★ arXiv:1607.04447, KT
The standard model has been very successful
Discovery of SM Higgs (-like) particle and no discovery of other new particles
But, we believe that there is more fundamental theory of elementary particles!
“Naturalness” has been a strong driving force to think of new physics beyond the SM. SUSY, extra-dimension, little Higgs, etc But, there are no indication of such new physics at the LHC, so far.
Maybe, it is good time to consider new physics differently
e.g. Kobayashi-Maskawa Motivated from the observation of CP violation in Kaon system Three generations in the standard model Good experimental data lead us to the right answer!
Bottom-Up approach
2015: LHC restarted again at √s = 13 TeV 2018?: COMET/Mu2E ( conversion ) start
2018?: SuperKEKB starts
and more … 2017-2019?: New muon g-2 exps. start
But, even now, I think we have lots of interesting data
moment (muon g-2) [3-4σ]
B → K∗µ+µ−
P 0
5
RK
PRL113, 151601 (2014)
RK ≡ B(B+ → K+µ+µ) B(B+ → K+e+e) = 0.745+0.090
0.074 (stat) ± 0.036 (syst) .
龍田さん、清水さん、… 村山さん、大道さん、藤間さん、山本さん、山中さん、… 早川さん、横崎さん、… 山本さん、…
h → τµ
Vub
CMS: arXiv: 1502.07400
R(D(∗)) = BR( ¯ B → D(∗)τ ¯ ν)/BR( ¯ B → D(∗)l¯ ν)
BaBar: PRL 109, 101802(2012), Belle: PRD 92.072014, LHCb: arXiv: 1506.08614
[3.9σ]
BR(B0
s → µ+µ−)/BR(B0 s → µ+µ−)SM = 0.76+0.20 −0.18 [1.2σ]
BR(B0 → µ+µ−)/BR(B0 → µ+µ−)SM = 3.7+1.6
−1.4
[2.2σ]
CMS and LHCb: Nature 522, 68 (2015) Belle: arXiv: 1607.07923, 1608.06391
Vcb
早坂さん、…
北原さん、山本さん、…
LHC run2
ATLAS: ATLAS-CONF-2015-081 CMS: CMS-PAS-EXO-15-004
陣内さん
We have many interesting data!
magnetic moment
H = −~ µ · ~ B,
~ µ = ⇣ e 2m ⌘ ~ S
g
g-factor
g = 2 g 6= 2
anomalous magnetic moment (muon g-2)
γ
It can be a good test of the standard model (including the quantum corrections)
aµ = g − 2 2
早川さん 三部さん
−
QED contribution 11 658 471.808 (0.015) Kinoshita & Nio, Aoyama et al EW contribution 15.4 (0.2) Czarnecki et al Hadronic contributions LO hadronic 694.9 (4.3) HLMNT11 NLO hadronic −9.8 (0.1) HLMNT11 light-by-light 10.5 (2.6) Prades, de Rafael & Vainshtein Theory TOTAL 11 659 182.8 (4.9) Experiment 11 659 208.9 (6.3) world avg Exp − Theory 26.1 (8.0) 3.3 σ discrepancy (in units of 10−10. Numbers taken from HLMNT11, arXiv:1105.3149)
n.b.: hadronic contributions:
. . . .
had. LO µ had. NLO µ γ had. l-by-l µ
Indirect searches for new physics
61 / 86
Status of muon g-2
.895 (0.008): 5-loop calculation (Aoyama et al ’12) 15.4 (0.1): Higgs mass fixed (Grendiger et al ’13)
is comparable to the electroweak contribution
The size of anomaly
δaµ = (26.1 ± 8.0) × 10−10 aEW
µ
= (15.4 ± 0.1) × 10−10
we expect new particles with EW scale mass strong constraints from EW precision data good target at near future experiments
We may be able to discover the new physics before new experiment or/and new (improved) calculation for muon g-2. So, we should study it NOW!
model muon g-2 SUSY ○ Little Higgs × Extra dimension x ．．．．．
Not many (interesting) models can explain it. complementary to known (interesting) models What kind of new physics ? 横崎さん
What is an important point to explain the muon g-2 anomaly while avoiding the experimental constraints?
Not many (interesting) models can explain it.
Contents
in muon g-2
Note: Muon chirality has to be flipped.
If there is some mechanism to enhance the chirality flipping, the new contribution to muon g-2 can be large.
Effective operator for muon g-2
Kanemitsu and KT, PRD86, 095025 (2012) [arXiv: 1207.1313]
New Physics contributions to muon g-2
✴
Model where has new Yukawa interaction with SU(2) singlet scalar ( ) and Dirac fermion ( )
µ φ χ γ µ µ φ γ µ χ (a) (b)
φ φ
Note: The muon chirality is flipped in external fermion line
L = −yN ¯ µRχLφ − mχ ¯ χRχL + h.c. − m2
φφ†φ + · · ·.
µR µR
x µL
µR µR
x
µL χL χL γ
Z, γ
vertex corrections
→ S,T パラメーターで 特徴づけられる
φ, χ
parameters
100 200 300 400 500 100 200 300 400 500
total
χ2/(d.o.f) = 34.8/(22) for SM
100 200 300 400 500 100 200 300 400 500
muon g-2
Constraints from EW observables
✴ Model where and have new Yukawa interactions
scalar mixing
:SU(2) doublet :SU(2) singlet
Φ
The chirality is flipped in the internal fermion line
L = −yL ¯ L2ΦχR − yR¯ µRφχL − mχ ¯ χLχR + h.c.,
x
chirality flip
χL χR
L = y v M 2 ¯ µRσµνµLFµν + h.c.
enhancement of chirality flipping!!
100 200 300 400 500 100 200 300 400 500
Because of the enhancement, even small Yukawa couplings can induce large muon g-2
100 200 300 400 500 100 200 300 400 500
total muon g-2
Constraints from EW observables
χ2/(d.o.f) = 34.8/(22) for SM
enhancement no enhancement
He, Joshi, Lew, Volkas PRD43, 22 (1991), Baek, Deshpande, He, Ko, PRD64 (2001), Ma, Roy, Roy PLB525 (2002),Salvioni, Strumia, Villadoro, Zwirner JHEP (2010), Heeck, Rodejohann PRD84 (2011), Harigaya, Igari, Nojiri, Takeuchi, Tobe JHEP 1403, 105 (2014)…
(Z” model)
U(1)Lµ−Lτ
Fayet PRD75(2007), Pospelov PRD80 (2009),... Davoudiasl, Lee, Marciano PRD86 (2012), Endo, Hamaguchi, Mishima PRD86 (2012), .......
Some examples
Abe, Sato, Yagyu JHEP 1507, 064 (2015), …
横崎さん
SUSY (well-known example)
x
tan β
~ chirality is flipped in the internal line
˜ χR ˜ χL
Figure 3: The SUSY contributions to the muon g − 2 as a function of the lightest smuon mass, m˜
µ1, and the lightest neutralino mass, m˜ χ0
regions, the muon g − 2 discrepancy (1) is explained at the 1σ (2σ) level. The left- right mixing is maximized under the vacuum stability condition. The parameters are m˜
ℓL = m˜ ℓR, tan β = 40 and Msoft = 10 TeV. The stau soft masses are equal to those
Endo, Hamaguchi, Kitahara, Yoshinaga, 1309.3065
enhancement no enhancement
He, Joshi, Lew, Volkas PRD43, 22 (1991), Baek, Deshpande, He, Ko, PRD64 (2001), Ma, Roy, Roy PLB525 (2002),Salvioni, Strumia, Villadoro, Zwirner JHEP (2010), Heeck, Rodejohann PRD84 (2011), Harigaya, Igari, Nojiri, Takeuchi, Tobe JHEP 1403, 105 (2014)…
(Z” model)
U(1)Lµ−Lτ
Fayet PRD75(2007), Pospelov PRD80 (2009),... Davoudiasl, Lee, Marciano PRD86 (2012), Endo, Hamaguchi, Mishima PRD86 (2012), .......
Some examples
Abe, Sato, Yagyu JHEP 1507, 064 (2015), …
Omura, Senaha, Tobe 1507.05028, 1511.08880
横崎さん
Contents
in muon g-2
General two Higgs doublet model (2HDM)
(both Higgs doublets couple to all fermions)
JHEP 1505 (2015) 028 [arXiv:1507.05028] and arXiv:1511.08880 (to be published in PRD), Y. Omura, E. Senaha, KT,
General 2HDM predicts
Flavor-changing phenomena mediated by neutral Higgs bosons This may be a problem if we do not observe any flavor-changing phenomena beyond the standard model. But, now....
Bjorken and Weinberg PRL 38, 622 (1977)
阿部さん
CMS collaboration has reported an excess in h → µτ
Talk by P. Onyisi @FPCP 2015
CMS best fit: 2.4σ excess
BR(h → µτ) = (0.84+0.39
−0.37)%
CMS: arXiv: 1502.07400
ATLAS
BR(h → µτ) = (0.77 ± 0.62)%
ATLAS: JHEP 1511, 211 (2015) [arXiv: 1508.03372]
consistent with CMS
CMS best fit: 2.4σ excess
ATLAS: arXiv: 1508.03372
BR(h → µτ) = (0.84+0.39
−0.37)%
→ μ → τμ τ → τμ σ → τ
τ τ → μ τ τ τ → μ τ
τ μ
H → τμ: ATLAS: BR = 0.53 ± 0.51% < 1.43% (95% CL) CMS: → τ
In Moriond EW 2016 [arXiv: 1604.07730]
Current status
), % τ µ → 95% CL Limit on Br(H
5 10 15 20 25
1.20% (obs.) 1.62% (exp.)
τ µ → H
8.99% (obs.) 7.31% (exp.)
, 2 Jets
e
τ µ
3.04% (obs.) 4.36% (exp.)
, 1 Jet
e
τ µ
1.33% (obs.) 2.24% (exp.)
, 0 Jets
e
τ µ
7.71% (obs.) 6.41% (exp.)
, 2 Jets
had
τ µ
6.35% (obs.) 4.89% (exp.)
, 1 Jet
had
τ µ
4.24% (obs.) 4.17% (exp.)
, 0 Jets
had
τ µ
Observed Expected 1 std deviation ± 2 std deviation ±
8 TeV [Phys. Lett. B 749 (2015) 337]: Observed Expected
(13 TeV)
2.3 fb
CMSPreliminary
Figure 4: Observed and expected 95% CL upper limits on the B(H → µτ) for each individual category and combined. The solid red and dashed black vertical lines correspond, respectively, to the observed and expected 95% CL upper limits obtained at √s = 8 TeV [23].
New 13 TeV result from CMS
CMS PAS HIG-16-005 No excess is observed It is not enough to exclude the 8 TeV
needed.
If the CMS excess in h→μτ is real, …… Two Higgs doublet model (2HDM) can explain it easily. What we found is ……
μ-τflavor violation in 2HDM can explain muon g-2 anomaly
h→μτ muon g-2 anomaly
Maybe related?
H1 = G+
v+φ1+iG √ 2
! , H2 = H+
φ2+iA √ 2
! ,
A basis where one Higgs doublet has vev
G+, G : Nambu-Goldstone bosons H+, A : charged and CP-odd Higgs bosons
(“Higgs basis”) In fermion mass eigenbasis (lepton sector)
General two Higgs doublet model
scalar mixing A basis where one Higgs doublet has vev
: Nambu-Goldstone bosons : charged and CP-odd Higgs bosons mass eigenstates (both Higgs doublets couple to all fermions)
(“Higgs basis”)
− − − ¯ Li
LH1yi eei R − ¯
Li
LH2ρij e ej R,
In fermion mass eigenbasis
flavor violating Yukawa couplings
This model predicts extra-flavor violating sources in Higgs interactions
(In this talk, I assume that is real.)
L =
In fermion mass eigenbasis
flavor violating Yukawa couplings
This model predicts extra-flavor violating sources in Higgs interactions
(In this talk, I assume that is real.)
In fermion mass eigenbasis
flavor violating Yukawa couplings
This model predicts extra-flavor violating sources in Higgs interactions
(In this talk, I assume that is real.)
General two Higgs doublet model
scalar mixing A basis where one Higgs doublet has vev
: Nambu-Goldstone bosons : charged and CP-odd Higgs bosons mass eigenstates (both Higgs doublets couple to all fermions)
(“Higgs basis”)
General two Higgs doublet model
scalar mixing A basis where one Higgs doublet has vev
: Nambu-Goldstone bosons : charged and CP-odd Higgs bosons mass eigenstates (both Higgs doublets couple to all fermions)
(“Higgs basis”)
τ
− − −
βα
− σ σ σ σ − σ − σ δ
neutral Higgs mass spectrum from tree level potential
potential relations among Higgs masses Now, Here, we mainly consider a case with Note: correction to Peskin-Takeuchi T parameter When the small suppresses the correction
−
− − − − − −
ρ ρττ
τ γ
General two Higgs doublet model
ted
scalar mixing A basis where one Higgs doublet has vev
: Nambu-Goldstone bosons : charged and CP-odd Higgs bosons mass eigenstates (both Higgs doublets couple to all fermions)
(“Higgs basis”) In fermion mass eigenbasis
flavor violating Yukawa couplings
This model predicts extra-flavor violating sources in Higgs interactions
(In this talk, I assume that is real.)
ggs
In fermion mass eigenbasis
flavor violating Yukawa couplings
This model predicts extra-flavor violating sources in Higgs interactions
(In this talk, I assume that is real.)
L = ✓ VMNSνL eL ◆
In fermion mass eigenbasis
flavor violating Yukawa couplings
This model predicts extra-flavor violating sources in Higgs interactions
(In this talk, I assume that is real.)
General two Higgs doublet model
scalar mixing A basis where one Higgs doublet has vev
: Nambu-Goldstone bosons : charged and CP-odd Higgs bosons mass eigenstates (both Higgs doublets couple to all fermions)
(“Higgs basis”)
General two Higgs doublet model
scalar mixing A basis where one Higgs doublet has vev
: Nambu-Goldstone bosons : charged and CP-odd Higgs bosons mass eigenstates (both Higgs doublets couple to all fermions)
(“Higgs basis”)
τ
− − −
βα
− σ σ σ σ − σ − σ δ
neutral Higgs mass spectrum from tree level potential
potential relations among Higgs masses Now, Here, we mainly consider a case with Note: correction to Peskin-Takeuchi T parameter When the small suppresses the correction
−
− − − − − −
ρ ρττ
τ γ
ρf (f = d, u, e) : flavor violating Yukawa couplings
✓ φ1 φ2 ◆ = ✓ cos θβα sin θβα − sin θβα cos θβα ◆ ✓ H h ◆ .
scalar mixing
mass eigenstates
sβα = sin θβα, cβα = cos θβα
cβα → 0 SM limit
In mass eigenstates of Higgs bosons,
L = − X
φ=h,H,A
yφij ¯ fLiφfRj − ¯ νLi(V †
MNSρe)ijH+eRj
− ¯ ui(VCKMρdPR − ρ†
uVCKMPL)ijH+dj + h.c.,
yhij = mi
f
v sβαδij + ρij
f
√ 2cβα, yHij = mi
f
v cβαδij − ρij
f
√ 2sβα, yAij = ⎧ ⎨ ⎩ −
iρij
f
√ 2 , (f = u), iρij
f
√ 2 , (f = d, e),
Note: When sβα → 1 (or cβα → 0), the SM-like Higgs (h) interactions approach to the SM ones. The flavor-violating couplings are suppressed by cβα
sβα = sin θβα, cβα = cos θβα
neutral Higgs mass spectrum from tree level potential
potential relations among Higgs masses
V = M 2
11H† 1H1 + M 2 22H† 2H2 −
⇣ M 2
12H† 1H2 + h.c.
⌘ + λ1 2 (H†
1H1)2 + λ2
2 (H†
2H2)2 + λ3(H† 1H1)(H† 2H2) + λ4(H† 1H2)(H† 2H1)
+ λ5 2 (H†
1H2)2 +
n λ6(H†
1H1) + λ7(H† 2H2)
1H2) + h.c..
m2
H+ = M 2 22 + v2
2 λ3, m2
A m2 H+ = v2
2 (λ5 λ4), (m2
H m2 h)2 =
A + (λ5 λ1)v2 2 + 4λ2 6v4,
sin 2θβα = 2λ6v2 m2
H m2 h
.
Now, cβα ⌧ 1 Here, we mainly consider a case with Note: correction to Peskin-Takeuchi T parameter When
mA ' mH+,
the small suppresses the correction cβα m2
h ' λ1v2,
m2
H ' m2 A + λ5v2,
m2
H+ = m2 A λ4 λ5
2 v2, m2
A = M 2 22 + λ3 + λ4 λ5
2 v2. suming λ4 = λ5 = 0.5 λ6 ⌧ 1
Solution to the CMS excess in and the muon g-2 anomaly
h → µτ
yhij = mi
f
v sβαδij + ρij
f
√ 2cβα,
h μ τ ρµτ
e
e
can explain it
BR(h → µτ) = c2
βα(|ρµτ e |2 + |ρτµ e |2)mh
16πΓh , re Γ is a total decay width of Higgs boson h an
CMS result 2HDM prediction result
BR(h → µτ) = (0.84+0.39
−0.37)%
¯ ρµτ ⌘ r |ρµτ
e |2 + |ρτµ e |2
2 ' 0.26 ✓0.01 cβα ◆ r BR(h ! µτ) 0.84 ⇥ 10−2 . | |
General 2HDM can explain it easily
Sierra and Vicente, 1409.7690, Crivellin et al., 1501.00993, Lima et al., 1501.06923, … Before the CMS excess, see Pilaftsis, PLB 285, 68 (1992); Assamagan et al, PRD 67, 035001 (2003); Brignole and Rossi, PLB 566, 217 (2003); Kanemura et al, PLB 599, 83 (2004); Arganda et al, PRD 71, 035011 (2005); ……, Blankenburg, Ellis, Isidori, PLB712, 386 (2012),……
µL τR τL µR mτ h, H, A γ ρµτ
e
ρτµ
e
muon g-2 induced by the μ-τ flavor violating coupling chirality flipping
O ✓mτ mµ ◆
enhancement
Note: need both ρµτ
e
and ρτµ
e
(For , we need only ) ρµτ
e
e
h → µτ
Both anomalies in the muon g-2 and can be accommodated in the general 2HDM
h → µτ
muon g-2
σ σ σ − σ − σ − σ
βα
− − − − − τ
δ
−2σ BR( )[%]
µ
δa
A
2σ µτ 3σ 1σ 1 0.8 0.6 0.4 0.2 −0.002 −0.006 −0.01
−1σ −3σ h
m = 350 GeV
Omura, Senaha, Tobe (2015)
1-loop contributions yφττ
φ = h, H, A
τL τR τL µL ρτµ
e
(L ↔ R) 2-loop contributions φ = h, H, A γ γ t, b, τ W (L ↔ R) τL µR µR ρτµ
e
yφff
Chang, Hou, Keung, PRD48, 217 (1993)
γ, Z
BR(τ → µγ)exp. < 4.4 × 10−8 For a case with ρττ
e
= ρtt
u = 0 −
γ
βα
− − − − − τ
A
1.0
BR( ) [10 ]
−9
1.5
−0.01 −0.006 −0.002 1 0.6 0.8 0.4 0.2 BR( )[%] h µτ
τ µγ 0.5 m = 350 GeV
σ σ σ − σ − σ − σ
βα
− − − − − τ
δ
−2σ BR( )[%]
µ
δa
A
2σ µτ 3σ 1σ 1 0.8 0.6 0.4 0.2 −0.002 −0.006 −0.01
cβα
−1σ −3σ h
m = 350 GeV
muon g-2
Omura, Senaha, Tobe (2015)
−8
4.4 0.1 4.4 m = 350 GeV τ µγ
A
h µτ
BR( ) [10 ] BR( ) = 0.84%
−
τ γ τ
5, cβα = −0.007
−
τ γ τ
t, δaµ = 2.2 × 10−9
For a case with ρττ
e
6= 0, ρtt
u 6= 0
The size of the rate can be within the reach of the future B-factory
Omura, Senaha, Tobe (2015)
τ µ ρµτ
e
ρτµ
e
H− νµ ¯ ντ
Correction to τ → µν¯
Γ(τ → µν¯ ν) = m5
τG2 F
192π3 (1 + δ), δ = |ρµτ
e |2|ρτµ e |2
32G2
F m4 H+
.
(experimental colleague) Hayasaka-san asked me. What about the Michel parameters in τ decay?
τ µ ρµτ
e
ρτµ
e
H− νµ ¯ ντ Correction to τ → µν¯
ν decay
Γ(τ → µν¯ ν) = m5
τG2 F
192π3 (1 + δ), δ = |ρµτ
e |2|ρτµ e |2
32G2
F m4 H+
.
Michel parameters in τ decay
dΓ(τ − → µ−ν¯ ν) dxd cos θµ = mτw4 2π3 q x2 − x2
0G2 Fµ [F1(x) − F2(x)Pτ cos θµ]
F1(x) = x(1 − x) + 2ρ 9 (4x2 − 3x − x2
0) + ηx0(1 − x)
F2(x) = −ξ p x2 − x2 3 " 1 − x + 2δ(4x − 4 + p 1 − x2
0)
3 #
w = m2
τ + m2 µ
2mτ
x = Eµ/w, x0 = mµ/w
Pτ :
tau polarization
ξ ' 1 2δ
Note: flavor conserving case
∆ξ ' 2(∆η)2, (|∆η| |∆ξ|)
arXiv:1607.04447, KT
Michel parameter
There are interesting correlation between muon g-2 and Δξ
muon g-2 is explained by
±1σ
BR( µτ)[%]
H+
h
m = 350 GeV
−5
10
−4
10 10
−2 −3
10 ∆ξµ
|∆ξ| (∆ξ < 0)
±2σ
Note: BABAR collaboration +others lepton universality measurement
PRL 105, 051602 (2010)
ge 2
Þ Bð ! e eÞ fðm2
e=m2 Þ
fðm2
=m2 Þ ;
The precise measurement will be important. Belle and future B-factory result would be very interesting.
✓gµ ge ◆
τ
= 1.0036 ± 0.0020 (BaBar) = 1.0018 ± 0.0014 (world average) ' 1 ∆ξ 4 (2HDM)
Summary
★ muon g-2 anomaly may be a hint for new physics ★ If there is a mechanism to enhance the chirality flipping
★ μ-τflavor violating Higgs interactions in general 2HDM can induce large correction to muon g-2 and explain the muon g-2 anomaly as well as the CMS excess in h→μτ ★ τ→μγ and correction to τ→μνν are interesting to probe this scenario ★ Run 2 result of h→μτ will be very interesting
★ Other interesting physics may be explained by this scenario.
Electroweak Baryogengesis
Chiang, Fuyuto, Senaha, arXiv: 1607.07316
★μ-τ flavor violating gauge interactions can similarly explain the muon g-2 anomaly.
Altmannshofer, Chen, Bhopal Dev, Soni, arXiv: 1607.06832
★ Flavor violations in quark sector should be studied.
flavor violation in quark sector is expected
New discovery may start from small deviation!
I want to thank organizers for this nice workshop!!
Backup slides
( )
τ µ µ µ ρµτ(τµ)
e
φ = h, H, A
yφµµ Even if other ρf (other than ρµτ(τµ)
e
) are negligible, non-zero rate of is predicted
τ → 3µ
but it is very small O(10−13 − 10−12) (since muon Yukawa is very small) BR(τ → 3µ)exp. < 2.1 × 10−8 yµ = √ 2mµ v ∼ 6 × 10−4
τ µ µ µ ρµτ(τµ)
e
φ = h, H, A
yφµµ
BR(τ → 3µ)exp. < 2.1 × 10−8
c = −0.007
βα
1 2 3 4 5 6 7 8 3 2 4 1 3µ BR( )/10 τ
ρe
µµ /10 −3 λ = λ = 0.5
4 5
m = 350 GeV
A
−8
τ
ρ
−
βα −
λ λ −
Other lepton flavor violating Yukawa couplings (e-τ, e-μ couplings) are strongly constrained from μ→eγ process
µL τR τL µR mτ h, H, A γ ρµτ
e
ρτµ
e
e-τ flavor violation
eR
ρτe
e
large enhancement
τ −5
τ e e
−1.0 0.5 1.0 1.5 −1.5
5.7 1.0 0.1 0.01
−0.5 −1.0 −1.5 0.5 1.0 1.5 −0.5
−5 e e
−13
µ eγ BR( ) [10 ]
strongly constrained
e-μ flavor violation similar to τ→μγ, 2-loop contributions are important
e e −4
µ −4
4 2 −4 −2 −4 −2 2 4
1.0 5.7 0.1 0.01 µ e γ
µe e
BR( ) [10 ]
−13
Muon electric dipole moment (muon EDM)
µL τR τL µR mτ h, H, A γ ρµτ
e
ρτµ
e
e ρτµ e
e ρτµ e |eiφ,
imaginary parts of the Yukawas induce the muon EDM A relation between δaµ and δdµ
δdµ = −3 × 10−22 e · cm × ✓tan φ 1.0 ◆ ✓ δaµ 3 × 10−9 ◆
Prediction Current limit
|dµ| < 1.9 × 10−19 e · cm (95% C.L.),
Future (J-PARC)
dµ ∼ 10−24 e · cm
future J-PARC experiment may have a sensitivity