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Application of Jacobi method to Long Baseline Neutrino Oscillations

Application of Jacobi method to Long Baseline Neutrino Oscillations

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Application of Jacobi method to Long Baseline Neutrino Oscillations

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  1. Application of Jacobi method toLong Baseline Neutrino Oscillations Yee Kao (Virginia Tech) University of Wisconsin-Madison, 2007.5.7 Based on talk prepared and presented by Minako Honda (Ochanomizu) @DPF2006, Hawaii, 2006.10.31 Tatsu Takeuchi (Virginia Tech) University of Cincinnati, 2007.4.9

  2. Preprints: hep-ph/0602115 hep-ph/0603268 hep-ph/0610281 arXiv:0704.0369 [hep-ph] Collaborators: Minako Honda (OchanomizuWashington) Naotoshi Okamura (YITPKEK) Alexey Pronin (Virginia Tech) Tatsu Takeuchi (Virginia Tech)

  3. In many models beyond the SM,the universality of the couplingscan be violated through radiative corrections. beam (a) charged current interaction processes ex) MSSM with etc... lead to the NC universalityviolation Universality Violation in NC Matter effect (b) neutral current interaction

  4. Z couplings to neutrinos cf ) Z couplings to charged leptons 0.9-1.2 PLB180,303(1986), PLB320,203(1994) LEP/ OPAL, DELPHI, L3, ALEPH, SLD LEP invisible decay width (total width is constrained.) The experimental constraints~individual~ CHARM, CHARM II @ CERN (’80s)

  5. CHARM, CHARM II PLB180,303(1986), PLB320,203(1994) • The theoretical possibility of universality violation in many models • The weakness of the current experimental bounds It would be interesting to analyze the effect of such a violation on neutrino oscillations.

  6. Universality Violation U:MNS matrix CC effect derived from universality violationin Neutral Current interaction Step by step:1.Neutrino Oscillation2.CC effect3.Universality Violation

  7. Neutrino Oscillation:

  8. Evolution of a neutrino flavor eigenstate:

  9. The neutrino oscillation probability in vacuum:

  10. Matter effect: No effect on neutrino oscillation

  11. Effective Masses and Mixing Angles:

  12. Vacuum-mass basis: Use Jacobi Method to obtain approximate diagonalization

  13. Effective mixing angles:

  14. Universality Violation U:MNS matrix NC CC derived from universality violationin Neutral Current interaction central valueof CHARM : measure of universality violation in NC : effective mixing matrix : effective mass-squares

  15. Using Jacobi method, after two rotations… Another (1,2) or (1,3) rotation is necessary at high energies If (1,2) rotation shifts 12 If (1,3) rotation shifts 23

  16. effective mixing angles(normal hierarchy) : violation factor in NC (details in our paper)

  17. effective mixing angles(inverted hierarchy) : violation factor in NC (details in our paper)

  18. Survival Probabilities ( )

  19. Summary • Jacobi Method:Obtain approximate analytic solution to matter effect of Neutrino Oscillation • Can also be used to calculate the effect of NC universality violation • Can the effect be measured?-> please listen to next speaker