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

Contents

Review of Lepton Flavor Violation

Our Model

Estimation and Prediction

Numerical Results

Summary

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.

Experiment:

If neutrino have non-degenerate masses, Picking up off-diagonal entries of their mass matrix, LFV decay can take place through this diagram.

The branching ratio is too small due to the smallness of neutrino masses.

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 !

At first glance, since there are no off-diagonal entries, it seems following LFV diagrams can’t written.

If SUSY is broken at low energy, SUSY breaking terms cause large LFV rates generally.

At SUSY breaking mediation scale

When we rotate the bases in order to carry initial and final fermions to mass eigenstates, above slepton mass matrix receive a unitary transformation and off-diagonal entries (It is expected they are O(100GeV)2 naturally.) arise.

Although these off-diagonal entries are expected to be O(100GeV)2, current experiments constrain them to be very smaller than it. It is called SUSY Flavor Problem.

In this case　　　 is diagonal, so there is no flavor changing source.　　　

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 can’t written and LFV decays don’t take place.

However, this adhoc assumption isn’t necessarily needed.

Our Model

10: 5:

We consider following sfermion mass matrix at mediation scale.

The reason why is…

1 SU(5) 　　 field contains left-handed lepton doublet, so the unitary rotation of 5 is MNS like large rotation. Thus we can’t release 5 sfermion mass matrix from degenerate form, otherwise large off-diagonal entries are generated with this rotation.

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 isn’t degenerate, large off-diagonal entries don’t arise. We can consider non-degenerating form for 10 sfermion mass matrix.

Our Model

10: 5:

We consider following sfermion mass matrix at mediation scale.

The reason why is…

2 There are sever constraints for FCNC between 1 and 2 generation.

We can’t release degeneracy between 1 and 2 generation.

Our Model

10: 5:

We consider following sfermion mass matrix at mediation scale.

The reason why is…

3 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.

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.

Our Model

10: 5:

We consider following sfermion mass matrix at mediation scale.

The reason why is…

4 Above sfermion mass matrices are derived in E6 ×Horizontal Symmetry GUT model.

How do LEV decay take place in this model?

10: 5:

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 λ.

By picking up the 3-2 element, the size of τ→μ transition rate is order .

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

If we raise overall SUSY scale m …

Propagator suppression from 1 or 2 generation is stronger, but mass difference is increase.

As a result, both transition rate remain finite, and don’t decouple!

We can Estimate the BR of the decays.main diagram :

μ→eγ BR can be roughly calculated by use of normalization as 　　　　 .

τ→μγ BR can be also calculated by exchanging for 　　　 .

This relation is prediction of this model and independent of SUSY parameter and tanβ.

This model leads large LFV rate within reach of near future experiments.

This model suggest thatfinal state lepton tend to be right-handed.

ie jep

ppq

p

Final state lepton has different chirality from initial one.

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

Right-handed

e

e

Left-handed

spin

spin

How can we see this feature experimentally?

We can check this feature experimentally by measuring the angular distribution of final state lepton for spin direction of initial lepton.

dependence

Branching Ratio is independent of unless .

At this point, m=m3

There are no sourceof LFV.

In this reason, the BRs are no longer changed for . BRs don’t decouple as increasing .

These behavior are explained qualitatively already.

dependence

Br(τ→μγ) Br(μ→eγ)

3m (GeV)

τ→μγ, 　 μ→eγ strongly depend on .

The branching ratio is compatible with current experimental bounds even if we take = 80GeV.

11100.1 (exclude)

Can we discover at the future experiments?

9100.7

(exclude)

8100.7

14100.1

MEG experiment

τ→μγ

μ→eγ Detectable unless <400GeV

(super-)KEKB

Detectable, when tanβ is large and 　　 <250GeV

SummaryWe analyze τ→μγ,μ→eγ 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 τ→μγ or μ→eγ 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.

τ→μγ : (super)B-factory

μ→eγ : MEG experiment

E6 GUT

Fundamental rep. is 27

Symmetry Breaking

Superpotential (Yukawa term)

Superheavy

　　　　　　　　　 corresponds to

in low energy.

　 Yukawa hierarchy of is milder than .

　Mixing of is larger than .

Three among six acquire GUT scale masses with three and decouple.

E6×U(2) Horizontal Symmetry

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

SUSY Breaking scalar masses

10: 5: