1. Lepton Flavor Violation
Yasuhiro Okada (KEK/Sokendai)
2nd International Neutrino Summer School
August 27, 2010, Yokohama

2. Lepton Flavor Violation (LFV)
muon number
electron number
total lepton number
Lepton numbers of each generation is not conserved although
the total lepton number is a conserved quantity.

3. LFV in the LHC era
LHC experiments start to explore the physics at the TeV scale. Something new must exist behind the electroweak symmetry breaking.
Lepton Flavor Violation (LFV) in the charged lepton sector is one way to look for effects from new physics at the TeV scale.
Connection to neutrino mass generation is important. Large LFV is expected for neutrino masses from low scale or supersymmetric models.

4. Contests History of LFV Phenomenology of LFV processes
LFV in new physics models

5. Moun: an unexpected particle
Discovery of neutrons (J. Chadwick, 1932)
Prediction of Yukawa meson( H.Yukawa,1935)
Discovery of muons in cosmic rays (S.H.Neddermeyer and C.D. Anderson, 1937)
Muons turned out to be different from the Yukawa meson intermediating the nuclear force.
Discovery of pions (C.Powell, et.al. 1947)

6. n e g m n p Particle physics in late 1940’s
“Strong” e g m
“Electromagnetic”
“Who ordered that?” (I.I.Rabi) n
“Weak”

7. LFV searches
Muon LFV search started from early days of muon experiments.
Absence of m->eg indicates that the muon is not an excited state of the electron, but rather a new elementary particle.

8. m->eg in the intermediate boson model
G.Feinberg, “1957”
If the weak interaction is mediated
by the W boson, m->e g should be
0(10-4) for the model with
one species of neutrinos.

9. Two neutrino experiment at BNL
A neutrino beam from pion decays only produces muons. O X
The muon neutrino and the electron neutrino are different particles

10. The news from the BNL experiment gave an impact to the Japanese
theory community.
Baryon-lepton
correspondence
=>
four quark model
The Kobayashi-Maskawa paper
on CP violation
in 1973
Neutrino mixing

11. In the Standard Model of the elementary particle physics
formulated in early 1970’s, lepton flavor conservation is a
natural consequence of massless neutrinos.
V: Cabbibo-Kobayashi-Maskawa matrix
V can be rotated away if all three
neutrinos are massless.

12. Neutrino oscillation has established since 1990’s, which leads
to renewed interest to LFV in charged lepton sector.
The separate conservation of the lepton number for each generation
seems to be violated.
In the Dirac neutrino,
~10-47
A large suppression in seesaw neutrino models with
the Majorana neutrino scale beyond the TeV scale.
This suggests that the LFV in the charged lepton sector is a probe
to neutrino mass generation mechanism beyond the simple Dirac
or seesaw model.

13. Phenomenology of LFV processes
(MEGA)
(SINDRUM)
(SINDRUMII)
m-e conversion search at 0(10-16) is planned at
COMET(KEK) and Mu2e (Fermilab) experiments

14. Effective interactions
6 additional operators
Various llqq operators

15. 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)

16. K.Hayasaka, ICHEP 2010

17. 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.

18. (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)

19. (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
=>

20. 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

21. (3) Atomic number dependence of the mu-e conversion
rate for various LFV interactions
O.U.Shanker,1979
A.Czarnecki, W.J.Marciano, K.Melnikov, 1998
R.Kitano, M.Koike, Y.Okada, 2002
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

22. 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 Z-like vector case
(neutron-rich for heavy nuclei).
V. Cirigliano, R.Kitano, Y.Okada, and P.Tuson, 2009

23. 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

24. LFV and New Phyiscs
New physics at the TeV scale can induce sizable LFVs in the charged lepton sector if there is a source of flavor transition in the lepton sector.
Relationship between physics of neutrino mass generation is important.
Scale of the Electorweak
symmetry breaking
Scale of the origin of neutrino mass
TeV n
If two scales are well separated, LFVs are suppressed.
Seesaw neutrino model

25. n n SUSY If two scales are close, large LFVs are expected. TeV
Example:
Neutrino mass from loop.
In supersymmetric models, LFV are expected even if two scales are separated.
SUSY n
TeV
Existence /absence of LFV is a clue to fundamental
problems such as　neutrino mass generation 。

26. 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
Neutrino mass from TeV physics and LFV

27. SUSY is special
SUSY is an extension of relativity (Super- Poincare algebra)
A flame work connecting the electroweak and the Planck scales.
Relativity
particle anti-particle
CPV possible
SUSY
ordinary particle  SUSY partner
SUSY breaking possible
If SUSY exist, existence of elementary scalar particles is a built-in
property of the theory.
The electroweak scale is derived from the SUSY breaking scale.

28. In SUSY GUT, for example, many area of particle physics is related
to each other 　
Energy frontier
LHC, LC
Quark flavor physics
Bd 　Bs　K　charm
Neutrino physics
LFV
Muon g-2
e, mu, n EDM
Proton decay
SUSY GUT
squark search
slepton search
squark CPV
muon physics
Combining all information we may be able to answer
questions like Unification, Neutrino mass, Baryogenesis,
and Dark matter.

29. SUSY and Flavor Physics
SUSY modes introduce SUSY partners.
Squark/sleption mass matrixes are new sources of flavor mixing and CP violation.
LHC can find squrks/gluino up to 2-3 TeV.
W,Z,g, H
gluon
lepton
quark
neutralino,
chargino
gluino
slepton
squark
SM particles
Super partners
Spin 1/2
Spin 0
Spin 1
Quark mass
Squark mass
SUSY breaking

30. Slepton flavor mixing 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.

31. SUSY GUT and SUSY Seesaw model
Quark and neutrino Yukawa couplings are sources of squark and slepton flavor mixings.
There are many new sources of new CP violation.
(Universal SUSY breaking terms, GUT and/or neutrino Yukawa coupling constants)
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

32. 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

33. m-> eg, t-> eg, t->mg
SUSY Seesaw model
SUSY Seesaw +SU(5) GUT
t->mg
m-> eg
t-> eg
Slepton mass
Neutrino inversed hierarchy
=> t->mg is also large
Neutrino normal hierarchy
=> Large m->eg
T.Goto, Y.Okada,T.Shindou,M.Tanaka, 2008

34. m e s Higgs exchange contribution in SUSY seesaw model
with a large “tanb” s m e
Blue band :
Uncertainty from “y”
Light: 0<y<0.4
Dark:0<y<0.05
V. Cirigliano, R.Kitano, Y.Okada, and P.Tuson, 2009

35. 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 quarks and leptons are introduced. New flavor mixing matrixes.
J.Hubisz,S.J.Lee,G.Paz, 2005 d qH
WH,ZH,AH
VHd l lH
WH,ZH,AH
VHl
New quark and lepton flavor mixing->
Quark FCNC and LFV

36. FCNC and LFV in the Littlest Higgs Model with T-parity
M.Blanke,et al
S.Rai Choudhury, et al. 2007
T.Goto, Y.Okada, Y.Yamamoto, 2009
F.del Aguila, J.I.Illana, M.D.Jenkins,2009,2010
“Z-penguin dominated”
m->3e vs. m-eg
m-e conv vs m->eg
Different correlation from SUSY case.
T.Goto, Y.Okada, Y.Yamamoto, 2010

37. Neutrino mass from TeV physics and LFV
If the origin of neutrino mass comes from TeV physics, a large LFV is expected.
Each model shows a characteristic feature in branching ratios, angular distributions, etc.
Examples
Radiative neutrino mass generation (Zee model, etc)
Neutrino mass in the warped extra dimension
R-parity violating SUSY model
Triplet Higgs model
Left-right symmetric model
m->3e
m ->eg
m-e conv
H++

38. Left-Right symmetric model m->eg and m->3e asymmetries
Triplet Higgs model
N.Kakizaki,Y.Ogura, F.Shima, 2003
Left-Right symmetric model
m->eg and m->3e asymmetries
A(m->eee)
V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf, P.Vogel, 2004
A.Akeroyd, M.Aoki and Y.Okada,2006

39. Summary
LFV processes are important probes to New Physics at the TeV scale.
Well-motivated models like SUSY, Little Higgs models, and neutrino mass generation from TeV physics predict interesting range of signals.
Correlations among various signals including angular distribution of m->eg and m->3e and atomic number dependence of m-e conversion rates are useful in discriminating different theoretical models.