Probing the Octant of  23 with very long baseline neutrino oscillation experiments

1. CYCU Oct. 17 2006 Probing the Octant of 23 with very long baseline neutrino oscillation experiments G.-L. Lin National Chiao-Tung U. Taiwan Work done with Y. Umeda

2. What we know about the neutrino oscillation parameters Super-K I+II Preliminary 1.910-3 eV2 < m231 < 3.110-3 eV2 sin2223 > 0.93 at 90% CL Best fit:  m231 = 2.510-3 eV2 sin2223=1 K. Inoue at ICHEP06, Moscow

3. 7.8310-5 eV2 < m212< 8.0110-5 eV2 0.164< sin212< 0.494 Best Fit: 7.9210-5 eV2 sin212=0.314 sin2213< 0.124 @2 G.L. Fogli, E. Lisi, A. Marrone and A. Palazzo Progress in Particle and Nuclear Physics 2006

4. What we don’t know about the neutrino mixing parameter (a)The sign of m231 LBL+ATM(magnetized iron calorimeter), Very Long Baseline Experiment (matter effect) (b)The octant of mixing angle 23 LBL+ATM, Very Long Baseline Experiment (matter effect) (c)The value of mixing angle 13 Reactors, T2K, NOA (d) The value of CP violation phase

5. For references on parameter degeneracy in LBL • experiments and 3 flavor effects in atmospheric • neutrinos, see T. Schwetz in ICHEP06, Moscow • For proposals of very long baseline experiments, see • Mocioiu and R. Shrock, Phys. Rev. D 62, 053017 (2000); V. D. Barger, • S. Geer, R. Raja and K. Whisnant, Phys. Lett. B485, 379 (2000); • V. D. Barger, S. Geer, R. Raja and K. Whisnant, Phys. Rev. D 62, 013004 • (2000); F. DeJongh, arXiv:hep-ph/0203005 • For relating matter effects in  survival probability to 23 , see • Antusch et al., hep-ph/0404268; D. Choudhury and A. Datta, JHEP07, • 058 (2005). • For experiments probing 13 and CP violation phase,see • K. Inoue and R. Rameika at ICHEP06, Moscow

6. What I am going to show Given a known mass hierarchy (with the help of magnetized iron calorimeter), and the knowledge on 13, how the mixing angle 23 can be best extracted in the very long baseline neutrino experiments ?

7. Solid and dashed test 23-min Solid and dotted test 13-max

8. Solid and dashed test 23 Solid and dotted test 13

9. The step functions with rc=11.85 g/cm3 rm=4.67 g/cm3 are good approximation. Freund and Ohlsson hep-ph/9909501 A. M. Dziewonski and D. L. Anderson, Phys. Earth Planet Int. 25, 297 (1981)

10.   Lm L Lc Lm Two density begins at L2Lm+Lc=10673 km

11. Max2 emerges at 7000 km Y. Ashie et al., Phys. Rev. Lett 93, 101801 (2004) J. N. Bahcall, M. C. Gonzalez-Garcia and C. Pena-Garay, JHEP 0408 (2004)

12. </4 >/4 Chooz bound +<<- for inverted hierarchy min max

13. ->> + +-

14. An insight from analytic approximations For a constant medium density: 0th order inthe series expansion of m221/m231 E. K. Akhmedov et al., JHEP 0404, 078 (2004)

15. The above forms for oscillation probabilities can be generalized to the two-density case: J. Bernabeu, S. Palomares-Ruiz, A. Perez and S.T. Pecov, Phys. Lett. B 531, 90 (2002)

17. Implications • The sensitivity of muon neutrino survival probability on 23: • For measurement at the local maximum, no 23 degeneracy in principle. The sensitivity on 23 is completely determined by +. Reasonable sensitivities at L=7000 km and 11000 km.

18. For measurement at the local minimum, min1, - determines the sensitivity on 23 . Sensitivity increases linearly with cos223. Very small sensitivity at 23=/4. For measurement along min2, - determines the sensitivity on 23 until L=6000 km. Longer than this baseline, both - and + are equally important. For 9000 km <L<10500 km, there are good sensitivities on 23 even for 23=/4. More importantly, 23 degeneracy is partially lifted.