Collective Neutrino Oscillations in Supernovae. Huaiyu Duan

Transcription

1 Collective Neutrino Oscillations in Supernovae Huaiyu Duan INFO Santa Fe, July, 2011

2 Outline Neutrino mixing and self-coupling Why do collective oscillations occur? Where do collective oscillations occur?

3 Neutrino Oscillations in SNe i d dλ ψ ν,p = Ĥ ψ ν,p mass matrix electron density H = M2 2E + 2G F diag[n e, 0, 0] + H νν neutrino energy!-! forward scattering (self-coupling)

4 Neutrino Oscillations H νν in SNe αβ = 2G F (1 ˆp ˆp )n ν ν β ψ ν ψ ν ν α ν ν (1 ˆp ˆp )n ν ν β ψ ν ψ ν ν α Fuller et al, Astrophys. J 322:795, 1987 Nötzold & Raffelt, Nucl. Phys. B307:924, 1988 Pantaleone, Phys. Rev. D46:510, 1992 Sigl & Raffelt, Nucl. Phys. B406:423, 1993 Qian & Fuller, Phys. Rev. D51:1479, 1995

5 Neutrino Oscillations H νν in SNe αβ = 2G F (1 ˆp ˆp )n ν ν β ψ ν ψ ν ν α ν ν (1 ˆp ˆp )n ν ν β ψ ν ψ ν ν α neutrinosphere!k!p!q

6 δm 2 = ev 2, θ v 1, L ν = erg/s E νe = 11 MeV, E νe = 16 MeV, E νx, ν x = 25MeV

7 Why?

8 Neutrino Flavor Isospin i d dλ ψ ν = Hψ ν = H σ 2 ψ ν e µ/τ ν e ν µ /ν τ Weak Isospin d dλ s = s H Flavor Isospin e-flavor τ -flavor maximally mixed s ν ψ ν σ 2 ψ ν s ν (σ y ψ ν ) σ 2 (σ yψ ν )

9 Vacuum Oscillations H = ω H vac H vac ê f x sin 2θ v +ê f z cos 2θ v ê f z ω ± δm2 2E H vac s ν 2θ v s f z = P νe ν e 1 2

10 MSW Mechanism H = ω H vac + H matt Hmatt ê f z 2GF n e ω H vac ê f z ω H vac ê f z s ν n e 0 H ω = δm2 2E, δm2 > 0 neutrino, normal hierarchy s ν H matt

11 MSW Mechanism δm 2 < 0 inverted hierarchy antineutrino neutrino

12 Collective Oscillations δm 2 < 0 inverted hierarchy antineutrino neutrino

13 Collective Oscillations δm 2 < 0 inverted hierarchy antineutrino neutrino

14 Collective Oscillations P!! E (MeV)

15 Collective Oscillations d dt s ω = s ω H ω homogeneous, isotropic neutrino gas = s ω (ω H vac + H matt + H νν ) cause collective oscillations neutral (HD et al, PRD, 2005) special axis H νν = µ dω f(ω ) s ω disrupt collective oscillations distribution function coupling strength,! neutrino density

16 Collective Oscillations if collective precession exists until nν 0: Pνν E ν neutrino ω =+ δm2 2E -! " 0 0 EC 1 inverted mass hierarchy antineutrino ω = δm2 2E 0 +!! 0 E ν HD et al, PRD (2006)

17 Collective Oscillations ω =+ δm2 2E -! E ν 0 ω = δm2 2E -! E ν neutrino " 0 EC antineutrino 1 1 Pνν inverted mass hierarchy antineutrino ω = δm2 2E 0 +! neutrino 0 E ν normal mass hierarchy ω =+ δm2 2E 0 +! " 0 EC 0! 0 E ν HD et al, PRD (2006)

18 Where?

19 Neutrino Oscillations H = M2 2E + 2G F diag[n e, 0, 0] + H νν vacuum term: Λvac=Δm 2 /2E matter (electron) density: Λmat= 2 GFne neutrino density: Λν= 2 GF(nν-nν )

20 Collective Oscillations Λvac depends on neutrino energy ΔΛvac: dispersion in energies ΔΛ vac (~ Λvac) Λν 1-cosΘ : neutrinos with different energies oscillate in phase &!k " vac =#m 2 /2E "! =$2%GF(n! -n!% )!q

21 Collective Oscillations Λvac depends on neutrino energy ΔΛvac: dispersion in energies ΔΛ vac (~ Λvac) Λν 1-cosΘ : neutrinos with different energies oscillate in phase "! 1-cos& ' r -2 r -2 = r -4 " vac =#m 2 /2E "! =$2%GF(n! -n!% )

22 Self-Suppression ΔΛ vac (~ Λvac) Λν 1-cosΘ : synchronization; no significant oscillations unless experiencing MSW resonance (Pastor et al 2001, 2002) Criterion for significant collective oscillations: ΔΛvac (~ Λvac) ~ Λν 1-cosΘ (Duan, Fuller & Qian, 2005) " vac =#m 2 /2E "! =$2%GF(n! -n!% )

23 Matter Suppression Λ mat Λν 1-cosΘ : suppression of collective oscillations? No. Uniform matter distribution does not suppress collective oscillations in the homogeneous and isotropic neutrino gas. (Duan, Fuller & Qian, 2005) " mat =$2%G F n e "! =$2%GF(n! -n!% )

24 Matter Suppression i d dλ ψ ν,p = Ĥ ψ ν,p ( (+)( (cos&) -1 )r )r & wavefronts of coll. osc.

25 Matter Suppression Dispersion in Λmatdλ/dr: ΔΛmat Criterion for significant collective oscillations: ΔΛvac + ΔΛmat ~ Λν 1-cosΘ ΔΛ mat Λν 1-cosΘ suppression of collective oscillations (Esteban-Pretel et al, 2008) ΔΛmat r -2 ρ(r) suppression only at earlytime and/or very close to NS " vac =#m 2 /2E " mat =$2%G F n e "! =$2%GF(n! -n!% )

26 Multiangle Suppression Λ ν 1-cosΘ depends on neutrino emission angle dispersion in angles ΔΛν (~Λν 1- cosθ ) Criterion for significant collective oscillations: ΔΛvac +ΔΛmat + ΔΛν ~ Λν 1-cosΘ or ΔΛvac ~ ΔΛν for low matter density (Duan & Friedland, 2010; Banerjee, Dighe & Raffelt, 2011) " vac =#m 2 /2E "! =$2%GF(n! -n!% )

27 Multiangle Suppression Spectral Distortion single-angle Using late-time spectra from Monte Carlo simulations (Keil et al 2002) r [km] Duan & Friedland, PRL 106, (2011)

28 Multiangle Suppression Spectral Distortion *+0.2 Using late-time spectra from Monte Carlo simulations (Keil et al 2002) 10-4 * r [km] Duan & Friedland, PRL 106, (2011)

29 Multiangle Suppression Spectral Distortion L! +0.2 L! +5.0 #"! 'L! r -4 Using late-time spectra from Monte Carlo simulations (Keil et al 2002) r [km] Duan & Friedland, PRL 106, (2011)

30 L νe =4.1foe, L νe =4.3foe, L νx, ν x =7.9foe E νe =9.4 MeV, E νe = 13.0 MeV, E νx, ν x = 15.8MeV

31 Summaries Collective neutrino oscillations can occur in dense neutrino media a result of intrinsic symmetry. Significant collective oscillations occur when neutrino densities are moderate. Be careful with the single-angle approximation. More than one collective modes exist phase transition?