Analysis of Lepton Flavor Violation in SUSY GUT model

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Analysis of Lepton Flavor Violation in SUSY GUT
model

• S.-G. Kim, N. Maekawa, A. Matsuzaki,
• K. Sakurai, T. Yoshikawa

SI2006 Kazuki Sakurai 8/29
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Contents

• Review of Lepton Flavor Violation
• Our Model
• Estimation and Prediction
• Numerical Results
• Summary

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Review of Lepton Flavor Violation (LFV)
Searching for LFV is one of the most powerful
methods to search for New Physics.

• In the Standard Model, LFV rates is too small to
  be measured, even if neutrino have masses.

The branching ratio is too small due to the
smallness of neutrino masses.
If neutrino have non-degenerate masses, Picking
up off-diagonal entries of their mass matrix, LFV
decay can take place through this diagram.
Current experimental bounds are so far from SM
prediction.
If we will discover LFV decay at the near future
experiments, It means we discover NP beyond the
SM !
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If SUSY is broken at low energy, SUSY breaking
terms cause large LFV rates generally.

• At SUSY breaking mediation scale

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One of the simplest and adhoc solution for this
problem is assuming sfermion mass matrices is
proportional to identity matrix.

• At SUSY breaking mediation scale we assume

In this case, following diagrams cant written
and LFV decays dont take place.
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Our Model

• We consider following sfermion mass matrix at
  mediation scale.

The reason why is
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SU(5) field contains
left-handed quark doublet, So the unitary
rotation of 10 is CKM like small rotation. Thus
even if 10 sfermion mass matrix isnt
degenerate, large off-diagonal entries dont
arise. We can consider non-degenerating form for
10 sfermion mass matrix.
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Our Model

• We consider following sfermion mass matrix at
  mediation scale.

The reason why is
There are sever constraints for FCNC between 1
and 2 generation.
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We cant release degeneracy between 1 and 2
generation.
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Our Model

• We consider following sfermion mass matrix at
  mediation scale.

The reason why is
In the MSSM, up-type higgs mass is receive a
radiative correction from a large top Yukawa
coupling. This correction is proportional to stop
mass.
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Up-type higgs mass is related to Z boson mass.
We can consider naturally and is
in neighborhood of weak scale.
In this context, . As far as
m3 is weak scale, we can raise overall SUSY scale
m with keeping naturalness of the MSSM.
By raising overall SUSY scale m, several
experimental constraints to SUSY (g-2, EDM, 1-2
FCNC) can be relaxed.
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Our Model

• We consider following sfermion mass matrix at
  mediation scale.

The reason why is
Above sfermion mass matrices are derived in E6
Horizontal Symmetry GUT model.
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10
How do LEV decay take place in this model?
flavor violating
No source of flavor violation
We want to consider LeptonFV. We may consider
only right-handed charged slepton sector.
Since 10 contains Q, the form of unitary matrix V
is CKM like. We can parametrize it with Cabibbo
angle ?.
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• By picking up the 3-2 element, the size of t?µ
  transition rate is order .

• For µ?e?, there are two passes to change the
  flavor µ?e. Both they are order .

If we raise overall SUSY scale m
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We can Estimate the BR of the decays.
main diagram

• µ?e? BR can be roughly calculated by use of
  normalization as .

• t?µ? BR can be also calculated by exchanging
  for .

This relation is prediction of this model and
independent of SUSY parameter and tanß.
This model leads large LFV rate within reach of
near future experiments.
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This model suggest thatfinal state lepton tend
to be right-handed.

• Final state lepton has different chirality from
  initial one.

• Intermediate state must be right-handed to pick
  up the .

How can we see this feature experimentally?
spin
spin
We can check this feature experimentally by
measuring the angular distribution of final state
lepton for spin direction of initial lepton.
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dependence
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dependence
t?µ?, µ?e? strongly depend on .
The branching ratio is compatible with current
experimental bounds even if we take
80GeV.
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Can we discover at the future experiments?
(exclude)
(exclude)
MEG experiment
(super-)KEKB
t?µ?
Detectable, when tanß is large and
lt250GeV
µ?e?
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Summary
We analyze t?µ?,µ?e? processes in our model in
which only the third generation sfermions of 10
rep. of SU(5) has different mass from the others.
The branching ratio strongly depend on the
right-handed stau mass.
We may predict the right-handed stau mass, if
t?µ? or µ?e? processes are discovered.
Final state lepton tends to be right-handed in
our model. We can check this feature
experimentally by measuring the angular
distribution of final state lepton for spin
direction of initial lepton.
There are parameter region in which we can
discover LFV at the future experiments.
t?µ? (super)B-factory µ?e? MEG experiment
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E6 GUT

• Symmetry Breaking

• Fundamental rep. is 27

• Superpotential (Yukawa term)

Three among six acquire GUT
scale masses with three and decouple.
corresponds to in low energy.
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E6U(2) Horizontal Symmetry

• 1,2 generations is identified as U(2) doublet.

• SUSY Breaking scalar masses