1. Osamu Yasuda Tokyo Metropolitan University Model independent analysis of New Physics interactions and implications for long baseline experiments INTERNATIONAL NEUTRINO FACTORY AND SUPERBEAM SCOPING STUDY MEETING 26 April 2006 @RAL

2. Based on a work with Hiroaki Sugiyama (KEK) & Noriaki Kitazawa (TMU) Without referring to specific models, assuming the maximum values of the New Physics parameters which are currently allowed by all the experimental data, the values of oscillation probabilities are estimated for future long baseline experiments.

3.   f f NP effects in propagation (NP matter effect) SMNP the same f (f=e, u, d) potential due to CC int additional potential A  

4.  ll f’ f NP effects at source and detector (Charged Current) SM NP (source) NP (detector)

5. j propagation in energy eigenstate energy eigenstate to flavor eigenstate flavor eigenstate to energy eigenstate SM+m   ll ll ff’F F’

6. NP ll j ll   ff’F F’

7. For simplicity, here we discuss the case where U s =U d = 1, i.e., NP exists only in propagation. For simplicity, we’ll also neglect all complex phases. 1 1 Present talk

8.  Davidson et al (’03): Constraints from various experiments Our starting point: two constraints on  

9. With some modifications:  Friedland-Lunardini (’05): Constraints from atmospheric neutrinos 95%CL 99%CL 3  CL

10. : Points used as reference values Large values, if any, come from,  ee,  e ,   :

11. Phenomenology with  ee,  e ,   ~ O(1) ~10MeV~a few 10GeV E In high energy limit (|  E jk |<< A), it reduces to N =2 case analytical result In low energy limit (|  E jk |>> A), reduces to vacuum oscillation analytical result In between ( |  E jk |~ A ), analytical treatment is difficult numerical result

12.  In high energy limit |  E jk | a few 10 GeV), it reduces to N =2 case: if this factor~1, P e  ~ O(1) !! AL/2~ L/4000km

13.  In low energy limit |  E jk |>> A (E< 10 MeV), it reduces to vacuum oscillations reactors have no sensitivity to NP (because AL<<1) (reactor) indistinguishable

14.  In between 10 MeV <E< a few 10 GeV ( |  E jk |~ A ), analytical treatment is difficult.  numerically calculated MINOS (   e ) (L=730km, 0<E<25GeV) T2K(K) (   e ) (L=295km, 0<E<1GeV) (L=1050km, 0<E<5GeV)  factory ( e  ,  e   ) (L=3000km, 0<E<50GeV) (L=730km, 0<E<25GeV) Plot for SM+m has  30% uncertainty because 0.9<sin 2 2  23 <1.0. Nevertheless NP effects can be distinguishable even with this uncertainty, except for T2K. NB

15. MINOS may see NP! MINOS ( e appearance)

16. T2K(K) ( e appearance)

17.  factory ( channel)

18. Amazing!!!  factory ( channel)

19. Summary There is a chance that MINOS (   e ), T2K(K) (   e ),  factory ( e  ,  e   ) see a signal of NP which could be larger than what is expected from the CHOOZ limit on  13 in SM+m. Assuming the maximum values of the NP parameters which are currently allowed by all the experimental data, the values of oscillation probabilities are estimated (taking into account NP in propagation only) for future long baseline experiments.

20. The (for NF) ( e   ) and e appearance (for SB) (   e ) channels are also powerful to detect the effects of New Physics (because of large  23 mixing   ). The probability to see the effects of New Physics depends both on the baseline and E, and combination of a reactor, T2K, NF is necessary to identify the source of the oscillation. The channel ( e   ) is the most powerful to detect the effects of New Physics for larger value of  e  allowed by atm.

21. Future work (in progress) Inclusion of NP at source (U s ) & detector (U d ) U s and U d only change the magnitudes of P (the oscillation lengths are not modified). The best way to measure U s and U d is to take the limit L  0. For SB/BB, processes of production and detection are both hadronic, so U d = U s SB/BB with L  0 is useless. For NF, production process is leptonic while detection process is hadronic, so U d  U s NF with L  0 is useful! Analytical treatment of probabilities NP

22. At detector (hadronic) At source NF (leptonic) SB/BB (hadronic) In case of N =2 using Grossman’s notation

23. Backup slides