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Lepton Flavor Violation as a Probe of Quark-Lepton Unification

Lepton Flavor Violation as a Probe of Quark-Lepton Unification

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Lepton Flavor Violation as a Probe of Quark-Lepton Unification

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  1. Lepton Flavor Violation as a Probe of Quark-Lepton Unification ICFP 2005 NCU, Taiwan 3-8 October 2005 Jake Lee (Yonsei University, Korea)

  2. Outlines • Quark-Lepton Complementarity (QLC) • Interpretations of QLC in GUT context and Possible Quark-Lepton Unifications • Lepton Flavor Violation: How to Probe Quark-Lepton Unification • Conclusion In collaboration with K. Cheung, S.K. Kang and C.S.Kim, PRD72 (2005) "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  3. Quark-Lepton Complementarity • It has been claimed that the relation may indicate quark-lepton symmetry or Grand Unification. (Minakata & Smirnov ’04, Raidal, Frampton & Mohapatra ’04, Kang, Kim, Lee ’05) "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  4. How to obtain QLC from GUT ? "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  5. link "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  6. Realistic GUT Relations for Quarks and Leptons Considering a well known empirical relation, More realistic unification leads to (Ferrandis, Pakvasa ’04) This mixing can be obtained by introducing Higgs sector transforming under 45 of SU(5) or 126 of SO(10) (Georgi, Jarlskog ’79; Babu, Barr ’00) "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  7. Lepton Flavor Violation and Quark-Lepton Unification • QLC motivated possible parameterizations of UMNS (a) U+CKMUbimax Left (b) UbimaxU+CKM Right Cabibbo shifts (c) U23m U+CKMU12m Middle up to some corrections, maybe compensated by renormalization effects as discussed earlier. • Different parameterizations may imply different fundamental flavor structures. • How to Probe these different structures? link Maybe through LFV radiative decaysin SUSY context "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  8. LFV radiative decays in SSM • Tiny in minimal extensions of SM • Sizable effects in supersymmetric extensions of SM due to new sources of LFV • Caused by the misalignment of lepton and slepton mass matrices (Masiero, Borzumatti ’86) • Depends on the neutrino Dirac Yukawa matrix • And so reflects some fundamental flavor structures (like QLC) • Br depends on unknown SUSY parameters and so consider relative size of "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  9. RG running induces off-diagonal terms in the slepton mass matrix even for the case of universal slepton masses at GUT scale (Casas, Ibarra ’01) : where is defined in heavy Majorana mass diagonal basis. • This can be a source of LFV decays, : • Then, the Br is given by "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  10. Case(a) Left Cabibbo shift U+CKMUbimax Here VR is the rotation matrix of MR, and is diagonal neutrino Dirac Yukawa matrix, parameterized by "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  11. For the case of realistic quark-lepton unification satisfying "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  12. Other Cases (b) Right shift (c) Middle shift For the quark-lepton unification, "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)

  13. Conclusion • Interpreting the interesting empirical relation , as a support of the quark-lepton unification, we find that the MNS mixing matrix can be parameterized by a CKM-like matrix and maximal mixing matrices in various way. • Each parameterization may imply very different fundamental flavor structure. • In the context of SSM, measurements of the relative size of the LFV radiative decays, may used to pin down the UMNS parameterization, assuming the quark-lepton unification. "Lepton Flavor Violation as a Probe of Quark-Lepton Unification" by Jake Lee (Yonsei Univ.)