1. Basudeb Dasgupta, JIGSAW 2007 Mumbai Phase Effects in Neutrinos Conversions at a Supernova Shockwave Basudeb Dasgupta TIFR, Mumbai Joint Indo-German School And Workshop 2007, Mumbai

2. Basudeb Dasgupta, JIGSAW 2007 Mumbai Outline of the talk Neutrinos: Oscillations, resonance etc Multiple MSW and phase effects Understanding the phase effects Neutrinos from a galactic supernova Phase effects for SN neutrinos ? Summary

3. Basudeb Dasgupta, JIGSAW 2007 Mumbai Neutrinos 3 mixed neutrinos:  m 12 2  = 7.92 (1±0.09) x 10 -5 eV 2 and  m 13 2 = ±2.6 (1±0.15) x 10 -3 eV 2 sin 2  12 = 0.314 ( 1± 0.18 0.15 ), sin 2  23 = 0.45 ( 1± 0.35 0.20 ), sin 2  13 = ( 0.8± 2.3 0.8 ) x 10 -2 2  limits from Fogli et al, hep-ph/0506083 Oscillations, MSW resonance: Oscillations in vacuum Matter Effect: A = 2√2G F N e E Resonant Oscillations: tan2  m =  m 2 sin2  m 2 sin2  A  m 2 cos2  = A at MSW resonance

4. Basudeb Dasgupta, JIGSAW 2007 Mumbai Adiabaticity and Level Crossings Dighe et al, hep-ph/9907423 H: (  m atm 2,  13 ) 10 3 – 10 4 g/cc L: (  m sol 2,  sol ) 10 1 – 10 2 g/cc Separation of the resonances Multiple resonances Kuo & Pantoleone RMP 1989 Are we justified in working with probabilities and NOT amplitudes?

5. Basudeb Dasgupta, JIGSAW 2007 Mumbai Adiabaticity and Level Crossings Dighe et al, hep-ph/9907423 H: (  m atm 2,  13 ) 10 3 – 10 4 g/cc L: (  m sol 2,  sol ) 10 1 – 10 2 g/cc Separation of the resonances Multiple resonances Kuo & Pantoleone RMP 1989 When do phase effects become important?

6. Basudeb Dasgupta, JIGSAW 2007 Mumbai Adiabaticity and Level Crossings Dighe et al, hep-ph/9907423 H: (  m atm 2,  13 ) 10 3 – 10 4 g/cc L: (  m sol 2,  sol ) 10 1 – 10 2 g/cc Separation of the resonances Multiple resonances Kuo & Pantoleone RMP 1989 Are such phase effects observable?

7. Basudeb Dasgupta, JIGSAW 2007 Mumbai Neutrinos through inhomogeneous matter EOM in flavor basis On decoupling Initial conditions Need to solve for survival probability for an arbitrary density profile

8. Basudeb Dasgupta, JIGSAW 2007 Mumbai Neutrinos through inhomogeneous matter EOM in flavor basis On decoupling Initial conditions We employ logarithmic perturbation in the mixing angle Balantekin et al, PRD 1988

9. Basudeb Dasgupta, JIGSAW 2007 Mumbai Perturbation theory result Perturbation parameter: Ansatz: Solution: Important quantity: Survival probability: Multiple resonances: Dasgupta, Dighe hep-ph/0510219

10. Basudeb Dasgupta, JIGSAW 2007 Mumbai Phase effects for multiple MSW Survival probability: Simple model:

11. Basudeb Dasgupta, JIGSAW 2007 Mumbai Understanding phase effects Start with: After first resonance at x 1: Before second resonance at x 2: Finally: Survival probability:

12. Basudeb Dasgupta, JIGSAW 2007 Mumbai Where can such effects be present? Solar Neutrinos Haxton, PRD 1987 Supernova Neutrinos Fogli et al, hep-ph/0304056Kneller et al, hep-ph/0509356

13. Basudeb Dasgupta, JIGSAW 2007 Mumbai Supernova Neutrinos Spectral shape Garching: Livermore: Keil et al, astro-ph/0208035 Time dependence: Falling luminosity, rising E avg over 10 secs Garching group, astro-ph/0303226 Plots taken from Raffelt’s ISAPP’04 lectures

14. Basudeb Dasgupta, JIGSAW 2007 Mumbai SN density profile Density range over 10 Orders of magnitude Non-Adiabaticity at shocks, tail region Time dependence Tomas et al, astro-ph/0407132

15. Basudeb Dasgupta, JIGSAW 2007 Mumbai Neutrino trail r~10 km,  ~10 10 g/cc r~0 km,  ~10 14 g/cc r~10R sun,  ~0.1g/cc r~Kpc,  ~0g/cc r~10Kpc,  ~1-10g/cc Galactic SN Space Earth Take primary spectra, fluxes of neutrinos Include MSW Find modified spectra, fluxes at earth Include detector effects Predict spectra, fluxes of leptons

16. Basudeb Dasgupta, JIGSAW 2007 Mumbai Results for a “realistic” SN Tail - Reverse Shock - Forward Shock L coherence =10 3 – 10 5 km  13 = 0.01,  m 2 = 0.002 eV 2  13 = 0.05,  m 2 = 0.002 eV 2

17. Basudeb Dasgupta, JIGSAW 2007 Mumbai Results for a “realistic” SN Phase effect survives in the neutrino spectrum Almost wiped out in the lepton spectrum Observation is quite unlikely Severely limited by energy resolution and also detector sizes Upshot: Can ignore phase effects

18. Basudeb Dasgupta, JIGSAW 2007 Mumbai Summary Analytic understanding of multiple resonances, phase effects Perturbation theory based solution Physical manifestation: Energy dependent spectrum modulation Realistic SN treated to some extent Effects in the standard scenario are very small Collective effects, fluctuations, time variation not included in the analysis

19. Basudeb Dasgupta, JIGSAW 2007 Mumbai Thank You