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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 - PowerPoint PPT Presentation
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Basudeb Dasgupta, JIGSAW 2007 Mumbai
Phase Effects in Neutrinos Conversions at a Supernova Shockwave
Basudeb DasguptaTIFR, Mumbai
Joint Indo-German School And Workshop 2007, Mumbai
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
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Neutrinos
• 3 mixed neutrinos:m12
2= 7.92 (1±0.09) x 10-5 eV2 and m132 = ±2.6 (1±0.15) x 10-3 eV2
sin212 = 0.314 ( 1±0.180.15) ,
sin223 = 0.45 ( 1±0.350.20),
sin213 = ( 0.8±2.30.8) x 10-2
2 limits from Fogli et al, hep-ph/0506083
• Oscillations, MSW resonance:Oscillations in vacuum
Matter Effect: A = 2√2GFNeE
Resonant Oscillations: tan2m = m2 sin2m2 sin2A m2 cos2 = A at MSW resonance
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Adiabaticity and Level Crossings
Dighe et al, hep-ph/9907423
H: (matm2 , 13)
103 – 104 g/ccL: (msol
2 , sol)
101 – 102 g/ccSeparation of the resonances
Multiple resonances
Kuo & Pantoleone RMP 1989
Are we justified in working with probabilities and NOT amplitudes?
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Adiabaticity and Level Crossings
Dighe et al, hep-ph/9907423
H: (matm2 , 13)
103 – 104 g/ccL: (msol
2 , sol)
101 – 102 g/ccSeparation of the resonances
Multiple resonances
Kuo & Pantoleone RMP 1989
When do phase effects become important?
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Adiabaticity and Level Crossings
Dighe et al, hep-ph/9907423
H: (matm2 , 13)
103 – 104 g/ccL: (msol
2 , sol)
101 – 102 g/ccSeparation of the resonances
Multiple resonances
Kuo & Pantoleone RMP 1989
Are such phase effects observable?
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
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
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Perturbation theory result• Perturbation parameter:
• Ansatz:
• Solution:
• Important quantity:
• Survival probability:
• Multiple resonances:
Dasgupta, Dighe hep-ph/0510219
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Phase effects for multiple MSW• Survival probability:
• Simple model:
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Understanding phase effects
• Start with:
• After first resonance at x1:
• Before second resonance at x2:
• Finally:
• Survival probability:
Basudeb Dasgupta, JIGSAW 2007 Mumbai
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
Supernova Neutrinos
• Spectral shape
Garching:
Livermore:
Keil et al, astro-ph/0208035
• 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
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
Neutrino trail
r~10 km, ~1010g/cc
r~0 km, ~1014g/cc
r~10Rsun, ~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
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Results for a “realistic” SN
Tail - Reverse Shock - Forward Shock
Lcoherence=103 – 105 km
13 = 0.01, m2 = 0.002 eV2
13 = 0.05, m2 = 0.002 eV2
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
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
Basudeb Dasgupta, JIGSAW 2007 Mumbai
Thank You
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