neutrino flavor conversion in media Open issues in neutrino flavor conversion in media Cristina VOLPE (AstroParticule et Cosmologie–APC, Paris)

Neutrino flavor conversion in media Important for observations in astrophysical and cosmological context : n e Survival Probability Neutrino Energy (MeV) pep 7Be n Borexino , PRL 2012 MSW solution pp solar neutrinos MSW effect : resonant flavor conversion due to n-e interaction 8B n 8B n Core-collapse supernovae 4He, D, 3H, 7Li primordial abundances Early universe -

Core-collapse supernovae Core-collapse supernovae comprise : O-Ne-Mg O-Ne-Mg supernovae Iron core-collapse supernovae iron Si Very massive -> accretion-disk black hole (AD-BH) H-He Two of the key open questions in astrophysics : - How do very massive stars explode ? - What is the site where heavy elements are made ?

The explosion Current simulations : multidimensional, realistic neutrino transport, convection and turbulence, hydrodynamical instabilities (SASI). Neutrinos play a role in revitalizing the shock. See MICRA workshop, september 2013, Trento. Bruenn et al, arXiv:1002.4909 first 3D : hints for explosion in 3D not enhanced compared to 2D Hanke et al, arXiv:1303.6269

Nucleosynthesis Supernovae, AD-BH, neutron star mergers : sites for heavy elements nucleosynthesis. Neutrinos determine if the site is neutron-rich (r-process elements) or proton-rich (np-process). Beun, McLaughlin, Surman, Hix, PRD73 (2006), 0602012 n flavor conversion in matter impacts the nucleosynthetic outcomes. see Focus Issue on «Nucleosynthesis and Neutrinos» to appear in Journal of Physics G.

More observations ne ne ne SN1987A events Time and energy signal from Suzuki, J. of Physics, Conf. (2008) SN1987A events Time and energy signal from a supernova explosion. In our galaxy, 1-3 events/century; one explosion/3years at 3 Mpc. The Diffuse Supernova Neutrino Background : The SN fluxes integrated over cosmological redshift. Events (10 y) window detector 90 (IH/NH) 9-25 MeV 50 kton scintillator 300 19-30 MeV 440 kton water Cherenkov 30 17-41 MeV 50 kton liquid argon ne ne ne Galais, Kneller, Volpe, Gava, PRD 81(2010) , arXiv :0906.5294.

Neutrino luminosity curves Time and energy signal of different explosion phases important : cooling accretion Time after bounce (s) Hüdepohl et al. PRL 104 (2010) from simulations neutronization burst ne nt nm NS neutrinosphere a sensitive probe of the supernova dynamics

n flavour conversion in supernovae shock waves n-e MSW nm ne neutrinosphere the n interaction with n and with matter (MSW effect). dynamical aspects - shock waves and turbulence. Flavour conversion effects arise because of

Effects of the nn interaction n flavour conversion in supernovae Distance in SN n e Survival Probability Pantaleone, PLB 287 (1992), Samuel,PRD 48 (1993) characteristic imprints Neutrino Fluxes Neutrino Energy (MeV) at 200 km synchronization spectral split bippolar Collective stable and unstable modes in flavor space Duan,Fuller,Qian PRD74 (2006) 76 (2007), Hannestad, al. PRD 74 (2006), Galais, Kneller, Volpe JPG 39 (2012) Duan, Fuller, Qian, PRD76(2007); Meng and Qian, PRD (2011); Raffelt and Smirnov PRD 76, PRL (2007); Esteban-Pretel et al PRD78 (2008) Pehlivan et al, PRD 84 (2011); Galais and Volpe, PRD 84 (2011), Chakraborty, Fischer, Mirizzi, Saviano, Tomas, PRL 107 (2011), Lund and Kneller, PRD 88 (2013), …

n flavour conversion in supernovae Different effects are relevant at different explosion timescales : neutronization burst accretion cooling EFFECTS (first 50 ms) (50-500 ms) (1-10 s) ? n-n shock wave MSW Dated 12/11/13 The final picture could be simpler than we (might) think.

Open questions Is the mean-field approximation sufficient ? shock wave n trapped n free streaming Open questions shock wave Further work needed to finally assess : impact on the shock wave impact on (heavy elements) nucleosynthesis, see e.g. Duan, Friedland, McLaughlin, Surman, JPG 38 (2011) merging with realistic supernova simulations (eg. breaking the spherical or azymuthal symmetries) nucleosynthesis Qian et al, PRL 71 (1993) Dasgupta, o’Connor, Ott, PRD 85 (2012) Is the mean-field approximation sufficient ? Balantekin and Pehlivan, JPG 34 (2007)

Looking across fields… Establishing the connection between n flavour conversion in media and other many-body systems such as phonons n p metallic clusters giant resonances nuclear collision 76Ge 76As 76Se bb(0n) condensed matter double-beta decay

Let us consider a system of N-particles described by a Hamiltonian : The exact evolution Let us consider a system of N-particles described by a Hamiltonian : e n p n p p e n e n n e n e p p p The system evolution is determined by solving the Liouville Von-Neumann equation for D : p e p e- e p n N-body density matrix

Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy Kirkwood 1935, Yvon 1935, Born and Green 1946, Bogoliubov 1946 Solving exactly the full many-body problem equivalent to one-body density two-body density BBGKY : a hierarchy of equations for reduced density matrices

A novel perspective to n conversion Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374 We have applied the BBGKY hierarchy to neutrinos and antineutrinos propagating in environments : a rigorous derivation of n evolution equations it allows to test current mean-field approximation UNIFIED APPROACH FOR COSMOLOGICAL and ASTROPHYSICAL applications

First BBGKY equation the mean-field approximation re two-body correlations two-body density one-body densities The first BBGKY equation reduces to : with MEAN-FIELD The n evolution equations in presence of a matter background re (MSW case) a n and n backgrounds for the early Universe, supernovae, AD-BH the mean-field approximation consistent with previous derivations Sigl and Raffelt, Nucl. Phys. B406 (1993), Fuller and Qian PRD 51 (1995)

Beyond mean-field The extended mean-field n equations can be cast as abnormal density n-n pairing correlations PAIRING MEAN-FIELD The extended mean-field n equations can be cast as generalised density generalised Hamiltonian the role of neutrino-antineutrino (and other) correlations? Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374

the transition region in supernovae investigations necessary mean-field terms GF nm nm ne nt transition region extended description Neutrino equations are non-linear : novel features can arise. terms GF2 : n trapped Boltzmann ne Further numerical investigations necessary neutrinosphere for direction-changing term see also, Cherry et al., PRL108 (2012)

Collective stable and unstable modes Distance in SN n e Probability synchronization Appearance of stable or unstable collective modes studied through linearization. Sawyer PRD79 (2009), Banerjee, Dighe, Raffelt, PRD 84 (2011) bippolar

Collective stable and unstable modes Distance in SN n e Probability synchronization Väänänen, Volpe, PRD88 (2013), arXiv: 1306.6372 General linearized equations using methods from many-body approaches Stability matrix flavor space bippolar w STABILITY MATRIX EIGENVALUES: real (stable) or imaginary (unstable) modes n p giant resonances 76Ge 76As 76Se bb(0n) double-beta decay

Current SN observatories Borexino Baksan SK (104) LVD HALO Daya-Bay MiniBOONE KamLAND (400) IceCube (106) Different detection channels available : scattering of anti-ne with p, ne with nuclei, nx with e, p Large scale detectors (LENA, GLACIER, Hyper-K,…) under study

Pinning down information An example : CC+NC events in HALO-2 (1 kton lead), SN at 10 kpc Väänänen, Volpe, JCAP 1110 (2011) Two-neutron events With nn and the n-matter uncertainties in the fluxes, at the neutrinosphere One-neutron events COMBINING DIFFERENT DETECTION CHANNELS

Conclusions and Perspectives Numerous aspects understood but more work needed. An important question : testing the mean field approximation. Establishing connections to other many body systems offers novel perspectives : BBGKY gives extended equations with neutrino-antineutrino correlations (but also collisions). - general eigenvalue equations and a stability matrix to study stable and unstable modes. Studies combining different detection channels to pin down Interesting information. A lot to learn from future observations

Merci

n-properties and supernovae Interesting information on unknown neutrino properties encoded in the supernova neutrino fluxes, in particular the mass hierarchy - earth matter effects (with one or two-detectors) ; - the early time signal ; - the full time and energy signal of the explosion. sterile neutrinos non-standard interactions CP violation – exist but small - Balantekin, Gava, Volpe, PLB662, (2008), arXiv:0710.3112 Gava, Volpe, Phys. Rev. D78 (2008), arXiv:0807.3418

The first BBGKY equation one-body density two-body density two-body correlations The first BBGKY equation reduces to : with MEAN-FIELD the mean-field approximation

The MSW and nn (mean-field) terms The n evolution equations in presence of a matter background re electron mean-field a n and n backgrounds for the early Universe, supernovae, AD-BH n mean-field off-diagonal derived from first principles Consistent with previous derivations Sigl and Raffelt, Nucl. Phys. B406 (1993), Fuller and Qian PRD 51 (1995)