1. Muon Physics Yasuhiro Okada (KEK) November 18, 2005
ISS Physics working group meeting
Imperial College London

2. Muon in the particle physics
We have learned many important things from muons.
(Generation structure, Lepton flavor conservation, V-A interaction, VEV of the Higgs field: ,etc)
Muon is simple. (almost 100% decay to
enn , a pure Dirac fermion)
Muon is a clean laboratory for new physics.

3. Plan of this talk Comments on muon g-2 and EDM Lepton Flavor Violation
Three muon processes
Polarized muon decays
Z-dependence of mu-e conversion rate
New physics examples

4. Muon g-2 A very precise test of the Standard Model
Most recent result from the BNLexperiment
Theoretical prediction
Low-energy e^+e^- annihilation cross section data from CMD-2
A new estimation of the light-by-light amplitude (K.Milnikov and A. Vainshtein)
A new evaluation on a^4 QED term (T.Kinoshita and M.Nio)
(e^+e^- data used)
K.Hagiwara, A.D. Martin, D.Nomura, and T.Teubner.

5. Muon EDM The SM contribution is extremely suppressed.
The previous bound of muon EDM is O(10^{-19}) e cm
In fact , the recent BNL experiment is sensitive to both g-2 and EDM.
A new method is proposed to explore the muon EDM at the level of 10^{-24} e cm.
(LoI to J-PARC)
Apply a radial E field to cancel the spin precession due to the anomalous magnetic moment
J.Feng, K.Matchev, and Y.Shadmi, 2003

6. SUSY and g-2, EDM
Slepton-chargino (neutralino) loop diagrams contribute to g-2 and EDM
at the one loop level.
SUSY contribution to g-2: enhanced for a large value of the ratio of
two Higgs VEVs ( ).
SUSY contribution to EDM.
Naively muon EDM is expected as large as 0(10^{-22}) e cm.
In simple cases,
We need source of the lepton-universality violation to enhance muon EDM.

7. Lepton Flavor Violation
No lepton flavor violation (LFV) in the Standard Model.
LFV in charged lepton
processes is negligibly small for a simple seesaw　neutrino model.

8. Three muon LFV processes
Back to back emission of a positron
and a photon with an energy of a half
of the muon mass.
Nucleus
A monochromatic energy electron emission for
the coherent mu-e transition.
Muon in 1s state

9. Experimental bounds Process Current Future
(Ti)
Mu-e conversion search at the level of 10^{-18} is proposed
in the future muon facility at J-PARC (PRIME).

10. Tau LFV processes Many processes. Most of bounds are 10^{-7}
Relation between mu
and tau LFV processes
depends on new physics
model.
Y.Miyazaki ESP 2005

11. LFV and new physics
Many models beyond the Standard Model contain sources of LFV.
Although the simple seesaw or Dirac neutrino model predicts too small generate branching ratios for the charged lepton LFV, other models of neutrino mass generation can induce observable effects.
Generalized Zee model (K.Hasagawa, C.S.Lim, K.Ogure, 2003)
Neutrino mass from the warped extra dimension (R.Kitano,2000)
R-parity violating SUSY model (A.de Gouvea,S.Lola,K.Tobe,2001)
Triplet Higgs model (E.J.Chun, K.Y.Lee,S.C.Park; N.Kakizaki,Y.Ogura, F.Shima, 2003)
Left-right symmetric model (V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004)
SUSY seesaw model (F.Borzumati and A.Masiero 1986)

12. SUSY and LFV g-2: the diagonal term EDM: complex phases
In SUSY models, LFV processes are
induced by the off-diagonal terms
in the slepton mass matrixes
g-2: the diagonal term
EDM: complex phases
LFV: the off-diagonal term
Off-diagonal terms depend on how SUSY breaking is generated and
what kinds of LFV interactions exist at the GUT scale.

13. SUSY GUT and SUSY Seesaw model
L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986
The flavor off-diagonal terms in the slepton mass matrix are induced by renormalization effects
due to GUT and/or neutrino interactions.
@ M_planck
GUT Yukawa
interaction
Neutrino Yukawa
CKM matrix
Neutrino oscillation
LFV

14. m -> e g branching ratio (typical example)
SUSY seesaw model
J.Hisano and D.Nomura,2000
SU(5) and SO(10) SUSY GUT
K.Okumura
SO(10)
SU(5)
Right-handed selectron mass
The branching ratio can be large
in particular for SO(10) SUSY GUT model.
Right-handed neutrino mass

15. Comparison of three processes
If the photon penguin process is dominated, there are simple relations among
these branching ratios.
In many case of SUSY modes, this is true, but there is an important case
In which these relations do not hold.

16. Muon polarization m-> eg m-> 3e
If the muon is polarized, we can define
a P-odd asymmetry for m -> e g
and T-odd and P-odd asymmetries for
m->3e. These asymmetries are useful
to distinguish different models.
Polarized muon is also useful to reduce
physics and accidental background for the
m -> eg search (Y. Kuno, A.Maki, Y.Okada,1997)
m-> 3e
Two P-odd and one T-odd asymmetries

17. P and T-odd asymmetries in SUSY GUT models
The T-odd asymmetry
can be 10 % level for
some parameter space
of the SU(5) SUSY GUT
and the SUSY seesaw
model.
Information on lepton
sector CP violation
Y.Okada,K.Okumura,and Y.Shimizu, 2000
T-odd asymmetry in the SUSY seesaw model
J.Ellis,J.Hisano,S.Lola, and M.Raidal, 2001

18. Z dependence of mu-e conversion branching ratio
R.Kitano, M.Koike and Y.Okada. 2002
We have calculated the coherent mu-e conversion branching ratios in various nuclei for general LFV interactions to see:
(1) which nucleus is the most sensitive to mu-e conversion searches,
(2) whether we can distinguish various theoretical models by the Z dependence.
Relevant quark level interactions
Dipole
Scalar
Vector

19. mu-e conversion rate normalized at Al.
The branching ratio is largest
for the atomic number of Z=30 – 60.
For light nuclei, Z dependences
are similar for different operator forms.
Sizable difference of Z dependences for dipole, scalar and vector interactions. This is due to a relativistic effect of the muon wave function.
Another way to discriminate different models
vector
dipole
scalar

20. Examples of new physics models
Several examples with specific features
in ratios of branching ratios in three processes, asymmetries in polarized muon decay, Z-dependence of the mu-e conversion.
SUSY seesaw model with large tan beta
Triplet Higgs model
Left-right symmetric model
R-parity violating SUSY model

21. SUSY seesaw with a large tan b
R.Kitano,M.Koike,S.Komine, and Y.Okada, 2003
SUSY loop diagrams can generate
a LFV Higgs-boson coupling
for large tan b cases. (K.Babu, C.Kolda,2002) s m e
The heavy Higgs-boson exchange provides
a new contribution of a scalar type.
Higgs-exchange contribution
Photon-exchange contribution

22. Ratio of the branching ratios and Z-dependence of mu-e conversion rates
mu-e conversion is enhanced.
Z-dependence indicates the scalar exchange contribution.

23. Triplet Higgs model Neutrino mass is generated by a triplet Higgs VEV.
N.Kakizaki,Y.Ogura, F.Shima, 2003
Neutrino mass is generated by a triplet Higgs VEV.
Connection between LFV and neutrino mixing matrix.
m -> 3e processes are enhanced because of
the tree-level charged Higgs excahnge.
m ->eg
m->3e
m-e conv

24. Three branching ratios
depends on neutrino
mass pattern.
B(m->eg)~B(mA-eA)

25. LFV in LR symmetric model
V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004
(Non-SUSY) left-right symmetric model
L<->R parity
Higgs fields, (bi-doublet, two triplets)
Low energy (TeV region ) seesaw mechanism for neutrino masses

26. Four lepton interactions are dominant among various LFV processes.
In general,
(kf~a 0(1) number)
V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004

27. A1 asymmetry in polarized mu ->3e
Asymmetry in mu->3e and tau->3mu
Since the flavor mixing in
left and right handed doubly charged
Higgs interaction is the same in this
Model, the parity-odd asymmetry in
mu to 3e and tau to 3mu processes
are only a function of two Higgs boson
masses.
A.Akeroyd, M.Aoki and Y.Okada, 2005

28. SUSY with R parity violation
A.de Gouvea,S.Lola,K.Tobe,2001
Depending on assumption of coupling combination, various pattern
can arise for ratios of the three branching ratios and asymmetry.

29. Comparison of three muon processes in various new physics models
SUSY GUT/Seesaw
B( m->e g ) >> B(m->3e) ~B(mA-eA)
Various asymmetries in polarized m decays.
SUSY with large tan b
m-e conv. can be enhanced. Z-dependence in m-e conv. branching ratio.
Triplet Higgs for neutrino
B(m->3e) > or ~ B(m->eg) ~B(mA-eA)
RL model
B(m->3e) >> B(m->eg) ~B(mA-eA)
Asymmetry in m->3e
RPV SUSY
Various patterns of branching ratios and asymmetries

30. Summary
Muon LFV experiments provide various opportunities to search for new physics effects.
Large effects are expected in well-motivated models of SUSY for LFV processes.
If there are new particles at the TeV region related to the lepton flavor mixing, the neutrino oscillation may have some connection to the charged lepton LFV processes.
There are various observable quantities in muon LFV processes. Different neutrino mass generation mechanism predicts different characteristic signals in LFV processes.
Comparison of muon g-2, EDM, and various LFV processes is important to distinguish different models.