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

2. Neutrino flavor conversion in media Predictions of primordial elements (BBN epoch). THE EARLY UNIVERSE - NS Core-collapse supernovae (SN) and Accretion disk-black holes SOLAR NEUTRINOS Massive stars (M > 6 M sun ) emit 10 57 neutrinos in 10 seconds, during the gravitational collapse and cooling of the neutron star.  e 

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

4. SN1987A et SN simulations SN1987A events (LMC, 50 kpc) A. Suzuki, J. of Physics, Conf. (2008) see e.g. Pagliaroli et al, Astropart. Phys. 31 (2009)

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

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

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

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

9. 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 np giant resonances nuclear collision metallic clusters phonons 76 Ge 76 As 76 Se  (0 ) double-beta decay condensed matter

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

11. Born-Bogoliubov-Green-Kirkwood-Yvon –BBGKY- hierarchy The s-reduced density matrix : 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) BBGKY : a hierarchy of equations for s-reduced density matrices Solving exactly the many-body problem is equivalent to one-body density two-body density

12. A novel perspective to conversion 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) We have employed the BBGKY for :  a system of particles and anti-particles  particles with mixings anti - occupation number op. decoherence or mixing terms Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374 UNIFIED APPROACH for ASTROPHYSICAL and COSMOLOGICAL APPLICATIONS that allows to go beyond current approximations

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

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

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

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

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

18. terms G F 2 : trapped terms G F mean-field Boltzmann neutrinosphere   e SN : the transition region ?  e transition region transition region extended description Neutrino evolution equations are non-linear, novel features can arise. 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 Väänänen, Volpe, PRD88 (2013), arXiv: 1306.6372 flavor space The appearance of stable or unstable collective modes in flavor space can be studied through linearization. We have applied linearisation methods from many-body microscopic approaches to obtain eigenvalue equations and a stability matrix, valid in the small amplitude approximation  Stability matrix THE STABILITY MATRIX EIGENVALUES: stable or unstable collective modes The eigenvalue equation for the neutrino systems

21. -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

22. Current SN observatories MiniBOONE HALO Borexino LVD Daya-Bay Baksan SK (10 4 ) KamLAND (400) IceCube (10 6 ) Different detection channels available : scattering of anti- e with p, e with nuclei, x with e, p Large scale detectors (LENA, GLACIER, Hyper-K,…) under study

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

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

25. Thank you