1. Quark-Lepton Complementarity in light of recent T2K & MINOS experiments November 18, 2011 Yonsei University Sin Kyu Kang ( 서울과학기술대학교 )

2. Outline Introduction - current status of neutrino mixing angles Parameterizations of neutrino mixing matrix Quark mixing angles and Quark-Lepton Complementarity (QLC) QLC parameterizations and Triminimal parametrization Predictions of physical observables Summary

3. Purposes of this work To investigate whether neutrino mixing matrix based on Quark-Lepton Complementarity (QLC) reflecting GUT relations or quark-lepton symmetry is consistent with current neutrino data or not. To investigate how we can achieve large values of mixing angle  13 so as to accommodate recent T2K or MINOS experimental results. To point out that nonzero values of  13 can be related to the deviation of  12 from maximal mixing or tri-bimaximal mixing

4. Neutrino Mixing Matrix Atmospheric angle Reactor angle and Dirac CP phase Solar angleMajorana phases Standard Model states Neutrino mass states

5.  Neutrino mixing anlges before T2K ( Schwetz, Tortola, Valle, New J.Phys.13:063004,2011. )

6.  Neutrino data for neutrino mixing angles is consistent with “Tri-bimaximal mixing” pattern at 2σ It can be derived from some discrete symmetries such as A 4, S 4 etc.

7. Recent T2K experiment The results show For non-maximal 23 mixing More data needed to firmly establish ν e appearance and to better determine θ 13

8. Recent MINOS experiment ( 1.7  excess of e events )

9.  Although TB mixing can be achieved by imposing some flavor symmetries, the current neutrino data indicates that TB is a good zeroth order approximation to reality and there may be deviations from TB in general.  To accommodate deviations from TB, neutrino mixing angles can be parameterized (S.F.King 2008)  The global fit of the neutrino mixing angles can be translated into the 3σ

10.  Alternatively, triminimal parametrization has been proposed (Pakvasa, Rodejohann, Weiler, Phys. Rev. Lett.100,2008 )  The neutrino mixing observables up to 2 nd order in

11. Quark Mixing Angles  Current data for quark mixing angles  The standard parameterization of V CKM

12. Wolfenstein Parameterization of quark mixing matrix L. Wolfenstein, Phys. Rev. Lett. 51 (1983)

13. Quark Lepton Complimentarity Lepton mixingsQuark mixings Present experimental data allows for relations like : Raidal (2004) Smirnov, Minakata (2004) 'Quark-Lepton Complementarity‘ QLC is well in consistent with the current data within 2σ

14.  QLC may serve as a clue to quark-lepton symmetry or unification.  So, QLC motivates measurements of neutrino mixing angles to at least the accuracy of the measured quark mixing angles.  In the light of QLC, neutrino mixing matrix can be composed of CKM mixing matrix and maximal mixing matrix.  Three possible combinations of maximal mixing and CKM as parametrization of neutrino mixing matrix (Cheung, Kang, Kim, Lee (2005), Datta, Everett, Ramond (2005) )

15.  Among three possible combinations,  Mixing angles in powers of λ  consistent with the current experimental data.

16.  Among three possible combinations,  Mixing angles in powers of λ  consistent with the current experimental data, but disfavored by T2K measurement of  13

17.  Among three possible combinations,  Mixing angles in powers of λ  consistent with the current experimental data, but disfavored by only T2K measurement of  13 at 90%CL.

18.  The flavor mixings stem from the mismatch between the LH rotations of the up-type and down-type quarks, and the charged leptons and neutrinos.  In general, the quark Yukawa matrices  For charged lepton sector : How to derive those parameterizations

19. For neutrino sector :  Introducing one RH singlet neutrino per family which leads to the seesaw mechanism  Rewriting neutrino mass,  In SO(10), Taking symmetric Y D, Taking

20.  Realistic neutrino mixing matrix, We need to modify  Then, neutrino mixing angles becomes From the empirical relation,

21.  In GUT framework, At low energies, the Yukawa operators of the SM (MSSM) are generated from integrating out heavy fields X which lead to GUT relations between q and l  In SU(5) GUT,

22.  Then, neutrino mixing angles becomes  In Pati-Salam GUT (Antusch & Sinrath (2009) ),  it is possible to have

23.  What if replacing R 12 (  /4) with tri-bimaximal type ? QLC parameterizations become For realistic GUT relation, we replace U CKM  U( ) It is possible to obtain rather large  13 while keeping small deviation of  12

24.  Lepton Flavor Violation in the SUSY caused by the misalignment of lepton and slepton mass matrices RG induces Taking (cf)

25. Predictions for Physical Observables  Neutrino mixing probabilities for phased averaged propagation (Δm 2 L/4E >>1) (Pakvasa, Rodejohann, Weiler, Phys. Rev. Lett.100,2008 )

26.  Using the previous formulae, we obtain  Using the best fit values for the parameters

27.  The phase-averaged mixing matrix modifies the flavor composition of the neutrino fluxes.  The most common source for atmospheric and astrophysical neutrinos is thought to be pion production and decay.  The pion decay chain generates an initial neutrino flux with a flavor composition given approximately for the neutrino fluxes : (P. Lipari, M. Lusignoli, and D. Meloni (2007))  At the Earth :

28.  Matching with triminimal parametrization

29.  In the light of recent data from T2K, Final Remark more favorable because it predicts

30. Summary We have discussed that neutrino mixing matrix based on Quark-Lepton Complementarity (QLC) reflecting GUT relations or quark-lepton symmetry is consistent with global fit to current neutrino data at 2  but some of QLC parameterizations disfavored by T2K We have shown how we can achieve large values of mixing angle  13 so as to accommodate recent T2K or MINOS experimental results. We have observed that QLC based on GUT relations lead to the relation between nonzero values of  13 and the deviation of  12 from maximal mixing or tri-bimaximal mixing