1. EDMs and Lepton Flavor Violation
Yasuhiro Okada (KEK/Sokendai)
The 4th International Symposium on Lepton Moments
July 20, 2010, Centerville, Cape Cod, MA

2. Now, the LHC has started running…
Why do we believe “new things”?
LHC =TeV physics
=Electroweak symmetry breaking
Something beyond the known three gauge interaction is necessary.
Other puzzles
Origin of the neutrino mass
Baryon number of the Universe
Dark matter ….
Lepton number
violation
Lepton flavor
violation
New CP violation
Relevant scale is unknown.

3. An important role of EDMs and Lepton Flavor Violation
EDM and LFV searches can provide a hint on the relationship between two scales.
If two scales are well separated,
EDMs and LFV are suppressed.
TeV
n, Baryogensis
Seesaw neutrino model
Leptogenesis

4. SUSY If two scales are close, large EDMs and LFV are expected. TeV
n, Baryogensis
TeV
Example:
Neutrino mass from loop.
Electroweak baryogenesis
In supersymmetric models, large EDMs and LFV are expected even if two scales are separated.
SUSY
n, Baryogensis
TeV
Existence /absence of EDMs and LFV is a clue to fundamental problems such as
neutrino mass generation and baryongenesis,

5. 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 and the Dirac neutrino model.

6. Three muon LFV processes
m-e conversion search at 0(10-16) is planned at
COMET(KEK) and Mu2e (Fermilab) experiments

7. Effective interactions
6 additional operators
Various llqq operators

8. Tau LFV processes Various flavor structures and their CP conjugates
Current bounds for tau LFV processes: from Belle and BaBar.
O(10-9) at e+e- Super B factories.
CMS study: B(t->3m) < 3.8x10 -8 at 30 fb-1 (R. Satinelli and M. Biasini 2002)

9. Distinguishing various LFV interactions
Comparison of three muon LFV processes.
(m-> eg, m->eee, m-e conversion)
Angular distribution of polarized muon decays in m-> eg, m->eee.
Atomic number dependence of the mu-e conversion rate.

10. (1) Comparison of three branching ratios
If the photon penguin process is dominant, there are simple relations
among these branching ratios.
In many case of SUSY modes, this is true.
Other cases:
Additional Higgs exchange diagram (SUSY with large tan b)
Dominance of tree exchange diagrams (LR symmetric models)
Loop-induced but Z-penguin dominance (Little Higgs with T-parity)

11. (2) Muon Polarization The SUSY seesaw model
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 discriminate different models.
The SUSY seesaw model
Only LFV coupling for the left-handed slepton mixing
=>

12. m-> 3e P and T-odd asymmetries in minimal SUSY GUT models
Two P-odd and
one T-odd asymmetries
P and T-odd asymmetries in minimal SUSY GUT models

13. (3) Atomic number dependence of the mu-e conversion
rate for various LFV interactions
Atomic number dependences for heavier nuclei are different for
different types of LFV interactions.
“ Finite size effect”, “Relativistic effect”
Main sources of theoretical uncertainty are also different.
Photonic dipole
Vector
Scalar
gluonic

14. Maximal in the intermediate nuclei.
Atomic number dependence of the mu-e conversion rate for various LFV operators
Z-like vector
Photon-like vector
Photonic dipole
Higgs-like scalar Al Ti Pb
Maximal in the intermediate nuclei.
Different Z dependence for heavy nuclei.
Large enhancement in the scalar case
(neutron-rich for heavy nuclei).
V. Cirigliano, R.Kitano, Y.Okada, and P.Tuson, 2009

15. Theoretical uncertainty depends on a type of operators
Photonic dipole case: Almost no uncertainty
The calculation only depends on the charge distribution
in a nucleus, which is precisely known by electron scattering.
(2) Vector case:
The main uncertainty comes from the neutron density.
Little uncertainty for light nuclei.
Uncertainty is 5% level for heavy nuclei if the proton scattering
data is available (ex. Pb).
(3) Scalar case:
An addition source of uncertainty is scalar quark densities
in a nucleon.
The new lattice QCD estimation of strange quark scalar density.
H. Ohki et.al. (JLQCD) PRD 78,
compared with the previous phenomenological
estimate

16. m e s An example: SUSY seesaw model with a large “tanb” Blue band :
Uncertainty from y
V. Cirigliano, R.Kitano, Y.Okada, and P.Tuson, 2009

17. Electric Dipole Moments
An intrinsic electric dipole moment breaks T invariance. s H E
s•H
s•E P + - T
If CPT invariance is assumed , EDM implies a new source of
CP violation. Effect of the Kobayashi-Maskawa phase is small.

18. Various EDMs
EDMs are measured for neutrons, muons, and various atoms and molecules. Extraction of EDMs for elementary particles are not simple except for muons.
We can distinguish models by measuring various EDMs

19. g-2 EDM LFV Naïve scaling of new physics effects in lepton moments
New physics effects can be extracted from
the combination of the electron g-2and the muon g-2.
EDM
LFV
The current bound on the muon EDM (O(10-19))
is not competitive to the electron EDM( O(10-27)).
No apparent lepton mass dependence.
Sensitive to flavor mixing structure.
These relations are not exact and there are always exceptions

20. Muon and electron EDMs in SUSY examples
Minimal supergravity model
Type-II Seesaw model
(Triplet Higgs)
EDM from slepton LFV L L T H H
d(muon)/d(electron)~200
Hisano-Nagai-Paradisi-Shimizu,09
Can be deviated from
the naïve relation (dm/de=mm/me)

21. New physics examples
In order to discriminate theoretical models , comparison of various signals is important.
SUSY Seesaw with/without SU(5) GUT model
The Littlest Higgs Model with T parity

22. SUSY GUT and SUSY Seesaw model
Quark and neutrino Yukawa couplings are sources of squark and slepton flavor mixings.
Flavor univesrality of
SUSY breaking terms
at the cutoff scale
Quark FCNC
LFV
Quark Yukawa coupling
Neutrino Yukawa coupling Yq Yn
Neutrino seesaw model
mSUGRA
GUT
L.J.Hall,V.Kostelecky,S.Raby,1986;A.Masiero, F.Borzumati, 1986

23. m-> eg, t-> eg, t->mg
SUSY Seesaw +SU(5) GUT
SUSY Seesaw model
T.Goto, Y.Okada,T.Shindou,M.Tanaka, 2008

24. Neutron, electron, and Hg EDMs muon EDM vs. electron EDM
T.Goto, Y.Okada,T.Shindou,M.Tanaka, 2008

25. Little Higgs Model with T parity
The Higgs boson is a pseudo Nambu-Goldstone boson of some strong dynamics at ~10 TeV.
New gauge bosons and a top partner to stabilize the Higgs potential against large radiative corrections without fine-tuning.
T-odd heavy qaurks and leptons are introduced. New flavor mixing matrixes. d qH
WH,ZH,AH
VHd l lH
WH,ZH,AH
VHl
New quark and lepton flavor mixing->
Quark FCMNC and LFV

26. Different correlation from SUSY case.
m->3e vs. m-eg
m-e conv vs m->eg
Different correlation from SUSY case.
T.Goto, Y.Okada, Y.Yamamoto, 2010

27. Atomic number dependence for m-e conversion rate
T.Goto, Y.Okada, Y.Yamamoto, 2010

28. Summary
EDMs and LFV are important probes to New Physics at the TeV scale.
Well-motivated models like SUSY and Little Higgs models with T parity predict interesting range of signals.
Correlations between various signals, angular distribution of m-eg and m->3e, atomic number dependence of m-e conversion rate are useful in discriminating different theoretical models.