phase effects in neutrinos conversions at a supernova shockwave

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


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


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


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?




H: (matm2 , 13)

103 – 104 g/ccL: (msol

2 , sol)


Multiple resonances


When do phase effects become important?




H: (matm2 , 13)

103 – 104 g/ccL: (msol

2 , sol)


Multiple resonances


Are such phase effects observable?


Neutrinos through inhomogeneous matter

EOM in flavor basis

On decoupling

Initial conditions

Need to solve for survival probability for an arbitrary density profile


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


Perturbation theory result• Perturbation parameter:

• Ansatz:

• Solution:

• Important quantity:

• Survival probability:

• Multiple resonances:

Dasgupta, Dighe hep-ph/0510219


Phase effects for multiple MSW• Survival probability:

• Simple model:


Understanding phase effects

• Start with:

• After first resonance at x1:

• Before second resonance at x2:

• Finally:

• Survival probability:


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


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


SN density profile

• Density range over 10 Orders of magnitude

• Non-Adiabaticity at shocks, tail region• Time dependence

Tomas et al, astro-ph/0407132


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


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


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


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


Thank You

phase effects in neutrinos conversions at a supernova shockwave

Documents

resonancesdighe et

hepph0304056kneller

keil et

phase effects observable

phase effects sum

fluxes of neutrinos

supernova neutrinosfogli

hepph0506083 oscillations