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

2. What we know about the neutrino oscillation parameters Super-K I+II Preliminary 1.9  10 -3 eV 2 <   m 2 31  < 3.1  10 -3 eV 2 sin 2 2  23 > 0.93 at 90% CL Best fit:   m 2 31  = 2.5  10 -3 eV 2 sin 2 2  23 =1 K. Inoue at ICHEP06, Moscow

3. 7.83  10 -5 eV 2 <  m 2 12 < 8.01  10 -5 eV 2 0.164< sin 2  12 < 0.494 Best Fit: 7.92  10 -5 eV 2 sin 2  12 =0.314 sin 2 2  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  m 2 31 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 I.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 r c =11.85 g/cm 3 r m =4.67 g/cm 3 are good approximation. Freund and Ohlsson hep-ph/9909501 A. M. Dziewonski and D. L. Anderson, Phys. Earth Planet Int. 25, 297 (1981)

10. LcLc LmLm LmLm Two density begins at L  2L m +L c =10673 km L

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: 0 th order in the series expansion of  m 2 21 /  m 2 31 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.