Cristina VOLPE (AstroParticule et Cosmologie -APC)

1. Open issues in neutrino flavor conversion in media Cristina VOLPE (AstroParticule et Cosmologie -APC)

2. Neutrino flavor conversion in media SOLAR NEUTRINOS ne Core-collapse supernovae (SN) and Accretion disk-black holes Massive stars (M > 6 Msun) emit 1057 neutrinos in 10 seconds, during the gravitational collapse and cooling of the neutron star. NS nt nm NS Predictions of primordial elements (BBN epoch). THE EARLY UNIVERSE -

3. TheMikheev-Smirnov-Wolfenstein effect established Hmatter GF re Wolfenstein PRD (1978) Mikheev and Smirnov, Sov. J. Nucl. Phys. (1985) ne ne Neutrino interaction with matter induces resonant flavour conversion. e e pep ne Survival Probability pp 7Be n MSW solution Borexino coll, PRL 108 (2012) 8B n Neutrino Energy (MeV) The solar neutrino deficit problem solved

4. SN1987A et SN simulations A. Suzuki, J. of Physics, Conf. (2008) SN1987A events (LMC, 50 kpc) see e.g. Pagliaroli et al, Astropart. Phys. 31 (2009) Marek & Janka, ApJ (2009) SN simulations have reached a high degree of complexity : 2D-3D, convection, realistic neutrino transport, SASI. Star radius (km) Time (ms)

5. Supernova observations • 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. Solar abundance of heavy elements • Element nucleosynthesis • r-process, np-process, • n-nucleosynthesis. log Y(A) see Focus Issue on «Neutrinos and Nucleosynthesis » to appear in Journal of Physics G. with n-n A Duan, Friedland, McLaughlin, Surman JPG 38 (2010)

6. n flavour conversion in supernovae n-e MSW effect neutrinosphere ne nm shock waves (multiple MSW) Numerous aspects are being investigated. The situation differs from the case of the sun. Conversion phenomena appear because of • the n interaction with matter – MSW effect – and with n. • dynamical aspects - shock waves and turbulence. Novel conversion phenomena discovered in the last years.

7. The effects of the nninteraction Pantaleone, PLB 287 (1992), Samuel,PRD 48 (1993), Sigl and Raffelt, NPB 406 (1993), n-fluxes at 200 km • synchronization mode : no flavor conversion occurs characteristic imprints • bipolar regime : occurrence of an instability in flavour space Duan,Fuller,Qian PRD74 (2006) 76 (2007), Hannestad, et al. PRD 74 (2006), Galais, Kneller, Volpe JPG 39 (2012) ne Survival Probability • spectral split : full or no conversion depending on energy Neutrino Fluxes Duan, Fuller, Qian, PRD76(2007); Meng and Qian, PRD (2011); Raffelt and Smirnov PRD 76, PRL (2007); Pehlivan et al, PRD 84 (2011); Galais and Volpe, PRD 84 (2011) Collective flavor conversion modes appear Distance in SN Neutrino Energy (MeV)

8. nt ne nm Is the mean-field approximation sufficient ? SOLAR NEUTRINOS Yes ? Supernovae and AD-BH New flavour conversion phenomena (nn-interaction, shock-waves and turbulence) being uncovered Beyond the mean-field, Balantekin and Pehlivan, JPG 34 (2007) NS Collisions recently discussed in Cherry et al., PRL108 (2012) The Boltzmann approximation for particles with mixings is used. The role of other two-body correlations? THE EARLY UNIVERSE -

9. 76As 76Ge bb(0n) 76Se Theoretical frameworks across fields… General theoretical frameworks allow to establish the connection between neutrino flavour conversion phenomena in media and stable and unstable modes in other many-body systems, such as phonons n p metallic clusters giant resonances nuclear collision condensed matter double-beta decay

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

11. Born-Bogoliubov-Green-Kirkwood-Yvon –BBGKY- hierarchy Kirkwood, J. Chem. Phys. 3 (1935), Yvon, Actual. Sci. Ind. 203 (1935), Born and Green Proc. R. Soc. A 188 (1946), Bogoliubov, J. Phys. 10 (1946) The s-reduced density matrix : two-body density one-body density Solving exactly the many-body problem is equivalent to BBGKY : a hierarchy of equations for s-reduced density matrices

12. A novel perspective to n conversion Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374 • We have employed the BBGKY for : • a system of particles and anti-particles • particleswithmixings anti-n n occupation number op. • The BBGKY is a rigorous theoretical framework : • to go from the N-body to the 1-body description • that is very general, equivalent the Green’s • function formalism (equal-time limit) UNIFIED APPROACH for ASTROPHYSICAL and COSMOLOGICAL APPLICATIONS that allows to go beyond current approximations decoherence or mixing terms

13. The first BBGKY equation one-body density two-body density The two-body density matrix can be written as : two-body correlation function The first BBGKY equations gives for the mean-field evolution equations with MEAN-FIELD the mean-field approximation

14. BBGKY applied to neutrinos Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374 • We have derived the n evolution equations in presence of • a matter background - MSW effect re electron mean-field • a n and n backgrounds for the early Universe, supernovae, AD-BH n mean-field off-diagonal contribution diagonal contribution MEAN-FIELD EQUATIONS - MSW and nn– reDERIVED Sigl and Raffelt, Nucl. Phys. B406 (1993), Fuller and Qian PRD 51 (1995) Consistent with previous derivations

15. Beyondthe mean-field approximation Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374 two-body correlations The evolution equation for the two-body correlation function : Including the collision term one obtains the Boltzmann equation for n. different approach in Sigl and Raffelt, Nucl. Phys. B406 (1993)

16. Beyondthe mean-field approximation Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374 We have included another contribution to the two-body correlations : abnormal density The evolution equation for the two-body correlation function : n-n pairing correlations nn pairing correlations : new contributions at mean-field level

17. Extended equations in media Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374 They include a pairing mean-field associated with abnormal densities : PAIRING MEAN-FIELD n-n pairing correlations The extended mean-field n equations can be cast as generalised density generalised Hamiltonian the role of neutrino-antineutrino correlations?

18. nm nm ne ne nt SN : the transition region ? mean-field terms GF transition region terms GF2 : n trapped extended description Boltzmann Neutrino evolution equations are non-linear, novel features can arise. neutrinosphere Further numerical investigations necessary

19. Linearization methods The appearance of stable or unstable collective modes in flavor space can be studied through linearization. Sawyer PRD79 (2009), Banerjee , Dighe, Raffelt, PRD 84 (2011)

20. Linearization methods The appearance of stable or unstable collective modes in flavor space can be studied through linearization. Väänänen, Volpe, PRD88 (2013), arXiv: 1306.6372 We have applied linearisation methods from many-body microscopic approaches to obtain eigenvalue equations and a stability matrix, valid in the small amplitude approximation flavor space The eigenvalue equation for the neutrino systems THE STABILITY MATRIX EIGENVALUES: stable or unstable collective modes w Stability matrix

21. n-properties and supernovae Balantekin, Gava, Volpe, PLB662, (2008), arXiv:0710.3112 Gava, Volpe, Phys. Rev. D78 (2008), arXiv:0807.3418 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 -

22. Current SN observatories Borexino Baksan SK (104) LVD Daya-Bay HALO 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

23. Mass hierarchy from late SN signal Imprint of the mass hierarchy in a water Cherenkov and scintillator detector, if a supernova at 10 kpc explodes. Prediction including the nn interaction and shock wave effects. ne+ p n + e+ inverted hierarchy 29 MeV e+ flux (/MeV/s/ton) Gava, Kneller, Volpe, McLaughlin, PRL 103(2009) 15 MeV Time signal (s) Bump (dip) at 3.5 (1) sigma in Super-Kamiokande

24. Reducing the degeneracies Vaeaenaenen, Volpe, JCAP 1110 (2011) . (CC+NC) events in HALO-2 (1 kton lead) for a SN at 10 kpc Predictions include nn the n-matter interaction and the uncertainties in the fluxes, at the neutrinosphere Two-neutron events One-neutron events Detection channels with different energy thresholds help identifying solutions.

25. Thank you