Muon Physics

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Muon Physics

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

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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.

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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

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Muon g-2
A very precise test of the Standard Model
Most recent result from the BNLexperiment
Theoretical prediction
Low-energy ee- 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 a4 QED term (T.Kinoshita and
M.Nio)
(ee- data used)
K.Hagiwara, A.D. Martin, D.Nomura, and
T.Teubner.
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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
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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.
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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.

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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
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Experimental bounds
(Ti)
Mu-e conversion search at the level of 10-18
is proposed in the future muon facility at J-PARC
(PRIME).
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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
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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)

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SUSY and LFV
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.
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SUSY GUT and SUSY Seesaw model
L.J.Hall,V.Kostelecky,S.Raby,1986A.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.
LFV
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m -gt 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
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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.
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Muon polarization
m-gt eg

• If the muon is polarized, we can define
• a P-odd asymmetry for m -gt e g
• and T-odd and P-odd asymmetries for
• m-gt3e. These asymmetries are useful
• to distinguish different models.
• Polarized muon is also useful to reduce
• physics and accidental background for the
• m -gt eg search (Y. Kuno, A.Maki, Y.Okada,1997)

m-gt 3e
Two P-odd and one T-odd asymmetries
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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
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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
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mu-e conversion rate normalized at Al.
The branching ratio is largest for the atomic
number of Z30 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.
vector
Another way to discriminate different models
dipole
scalar
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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

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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)
The heavy Higgs-boson exchange provides a new
contribution of a scalar type.
Higgs-exchange contribution
Photon-exchange contribution
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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.
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Triplet Higgs model
N.Kakizaki,Y.Ogura, F.Shima, 2003

• Neutrino mass is generated by a triplet Higgs
  VEV.
• Connection between LFV and neutrino mixing
  matrix.
• m -gt 3e processes are enhanced because of
• the tree-level charged Higgs excahnge.

m -gteg
m-gt3e
m-e conv
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Three branching ratios depends on neutrino mass
pattern.
B(m-gteg)B(mA-eA)
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LFV in LR symmetric model
V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf,
P.Vogel, 2004
(Non-SUSY) left-right symmetric model
Llt-gtR parity
Higgs fields, (bi-doublet, two triplets)
Low energy (TeV region ) seesaw mechanism for
neutrino masses
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Four lepton interactions are dominant among
various LFV processes.
In general,
(kfa 0(1) number)
V.Cirigliano, A.Kurylov, M.J.Ramsey-Musolf,
P.Vogel, 2004
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A1 asymmetry in polarized mu -gt3e
Asymmetry in mu-gt3e and tau-gt3mu
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
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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.
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Comparison of three muon processes in various
new physics models
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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.