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Analysis of Lepton Flavor Violation in SUSY GUT model

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. Experiment:.

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Analysis of Lepton Flavor Violation in SUSY GUT model

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  1. 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

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

  3. Experiment: 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 !

  4. 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. At first glance, since there are no off-diagonal entries, it seems following LFV diagrams can’t written. 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. If SUSY is broken at low energy, SUSY breaking terms cause large LFV rates generally. • At SUSY breaking mediation scale

  5. In this caseis diagonal, so there is no flavor changing source. However, this adhoc assumption isn’t necessarily needed. 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.

  6. 10: 5: 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. Our Model • We consider following sfermion mass matrix at mediation scale. The reason why is… 1 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.

  7. 10: 5: 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. 2 We can’t release degeneracy between 1 and 2 generation.

  8. 10: 5: 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. 3 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.

  9. 10: 5: Our Model • We consider following sfermion mass matrix at mediation scale. The reason why is… Above sfermion mass matrices are derived inE6 ×Horizontal Symmetry GUT model. 4

  10. 5: 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 λ.

  11. 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! • 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 …

  12. 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.

  13. Right-handed Left-handed 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.

  14. At this point, m=m3 In this reason, the BRs are no longer changed for . There are no source of LFV. BRs don’t decouple as increasing . These behavior are explained qualitatively already. Branching Ratio is independent of unless . dependence

  15. Br(τ→μγ) Br(μ→eγ) (GeV) dependence τ→μγ,μ→eγ strongly depend on . The branching ratio is compatible with current experimental bounds even if we take = 80GeV.

  16. Detectable unless <400GeV Can we discover at the future experiments? (exclude) (exclude) MEG experiment (super-)KEKB τ→μγ Detectable, when tanβ is large and <250GeV μ→eγ

  17. Summary We 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

  18. Superheavy Yukawa hierarchy of is milder than . Mixing of is larger than . 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.

  19. 10: 5: E6×U(2) Horizontal Symmetry • 1,2 generations is identified as U(2) doublet. • SUSY Breaking scalar masses

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