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Phase Effects in Neutrinos Conversions at a Supernova Shockwave

Joint Indo-German School And Workshop 2007, Mumbai. Phase Effects in Neutrinos Conversions at a Supernova Shockwave. Basudeb Dasgupta TIFR, Mumbai. Outline of the talk. Neutrinos: Oscillations, resonance etc Multiple MSW and phase effects Understanding the phase effects

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Phase Effects in Neutrinos Conversions at a Supernova Shockwave

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

  2. 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 Basudeb Dasgupta, JIGSAW 2007 Mumbai

  3. Neutrinos • 3 mixed neutrinos: Dm122= 7.92 (1±0.09) x 10-5 eV2 and Dm132 = ±2.6 (1±0.15) x 10-3 eV2 sin2q12 = 0.314 ( 1±0.180.15) , sin2q23 = 0.45 ( 1±0.350.20), sin2q13 = ( 0.8±2.30.8) x 10-2 2s limits from Fogli et al, hep-ph/0506083 • Oscillations, MSW resonance: Oscillations in vacuum Matter Effect: A = 2√2GFNeE Resonant Oscillations: tan2qm = Dm2 sin2q / Dm2 sin2q - A Dm2 cos2q = A at MSW resonance Basudeb Dasgupta, JIGSAW 2007 Mumbai

  4. Adiabaticity and Level Crossings H: (Dmatm2 , q13) 103 – 104 g/cc L: (Dmsol2 , qsol) 101 – 102 g/cc Separation of the resonances Multiple resonances Dighe et al, hep-ph/9907423 Kuo & Pantoleone RMP 1989 Are we justified in working with probabilities and NOT amplitudes? Basudeb Dasgupta, JIGSAW 2007 Mumbai

  5. Adiabaticity and Level Crossings H: (Dmatm2 , q13) 103 – 104 g/cc L: (Dmsol2 , qsol) 101 – 102 g/cc Separation of the resonances • Multiple resonances Dighe et al, hep-ph/9907423 Kuo & Pantoleone RMP 1989 When do phase effects become important? Basudeb Dasgupta, JIGSAW 2007 Mumbai

  6. Adiabaticity and Level Crossings H: (Dmatm2 , q13) 103 – 104 g/cc L: (Dmsol2 , qsol) 101 – 102 g/cc Separation of the resonances • Multiple resonances Dighe et al, hep-ph/9907423 Kuo & Pantoleone RMP 1989 Are such phase effects observable? Basudeb Dasgupta, JIGSAW 2007 Mumbai

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

  8. 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 Basudeb Dasgupta, JIGSAW 2007 Mumbai

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

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

  11. Understanding phase effects • Start with: • After first resonance at x1: • Before second resonance at x2: • Finally: • Survival probability: Basudeb Dasgupta, JIGSAW 2007 Mumbai

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

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

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

  15. Neutrino trail r~10Rsun, r~0.1g/cc r~10Kpc, r~1-10g/cc r~10 km, r~1010g/cc r~Kpc, r~0g/cc Space r~0 km, r~1014g/cc Earth Galactic SN • Take primary spectra, fluxes of neutrinos • Include MSW • Find modified spectra, fluxes at earth • Include detector effects • Predict spectra, fluxes of leptons Basudeb Dasgupta, JIGSAW 2007 Mumbai

  16. Results for a “realistic” SN Tail - Reverse Shock - Forward Shock Lcoherence=103 – 105 km q13 = 0.05, Dm2 = 0.002 eV2 q13 = 0.01, Dm2 = 0.002 eV2 Basudeb Dasgupta, JIGSAW 2007 Mumbai

  17. 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 Basudeb Dasgupta, JIGSAW 2007 Mumbai

  18. 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 Basudeb Dasgupta, JIGSAW 2007 Mumbai

  19. Thank You Basudeb Dasgupta, JIGSAW 2007 Mumbai

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