1. Melbourne Neutrino Theory Workshop, June 20081 ROLE OF DENSE MATTER IN COLLECTIVE NEUTRINO TRANSFORMATIONS Sergio Pastor (IFIC Valencia) in collaboration with A. Esteban-Pretel, G. Raffelt, G. Sigl and R. Tomàs Physical Review D 77 (2008) 065024 [arXiv:0712.1137] and arXiv:0806. XXXX MU–TAU NEUTRINO REFRACTION AND COLLECTIVE THREE-FLAVOUR TRANSFORMATIONS IN SUPERNOVAE SN-2008d MU–TAU NEUTRINO REFRACTION AND COLLECTIVE THREE-FLAVOUR TRANSFORMATIONS IN SUPERNOVAE

2. OUTLINE SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20082 INTRODUCTION: COLLECTIVE NEUTRINO TRANSFORMATIONS ROLE OF DENSE MATTER: TWO FLAVOURS ROLE OF DENSE MATTER: THREE FLAVOURS IMPORTANCE OF THE MU-TAU MATTER EFFECT CONCLUSIONS Talks by Dighe, Sawyer, Esteban-Pretel & Dasgupta

3. COLLECTIVE NEUTRINO TRANSFORMATIONS SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20083 There exist some situations where the neutrino refraction index is dominated by neutrinos themselves Early Universe before Neutrino decoupling (T~MeV) If asymmetry non-zero Dense-neutrino region at 50-400 km above the neutrino sphere in a Supernova Non-linear evolution Collective effects: coherent evolution of neutrinos and antineutrinos with different energies

4. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20084 Equations of motion in terms of the matrices of density for (anti)neutrinos and similar for with  COLLECTIVE NEUTRINO TRANSFORMATIONS Matrix of vacuum oscillation frequencies MSW Matter effect, DIAGONAL in the weak- interaction basis Neutrino-neutrino refraction term, NON-DIAGONAL in the weak-interaction basis Pantaleone 1992 Responsible of collective effects, (1-cosθ pq ) can lead to flavour decoherence between different angular modes Talks by Sawyer & Esteban

5. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20085 COLLECTIVE NEUTRINO TRANSFORMATIONS 2 flavours: Spin-precession analogy Magnetic dipole moment associated to P Gyromagnetic ratio for mode p Polarization vector in flavour space Effective magnetic field

6. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20086 COLLECTIVE NEUTRINO TRANSFORMATIONS EOMs for 2 flavours (1) (2) (3) (1): Vacuum, P precesses in “external” magnetic field B with frequency  i (1)+(2): Vacuum+Matter, precession in B with variable frequency (1)+(3)[+(2)]: precession in variable B plus influence of other spins

7. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20087 COLLECTIVE NEUTRINO TRANSFORMATIONS If  dominates, synchronized oscillations with a characteristic frequency (also with antineutrinos) SP, Raffelt & Semikoz 2002 In dense matter, synchronized MSW equilibration of neutrino asymmetries in the Early Universe before BBN Dolgov et al 2002 Wong 2002 Abazajian, Beacom & Bell 2002 Example: evolution of neutrino momenta in a thermal distribution VACUUM LARGE NEUTRINO DENSITY  syn t

8. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20088 COLLECTIVE NEUTRINO TRANSFORMATIONS Particular case: excess of neutrinos AND antineutrinos of one flavour INVERTED HIERARCHY + small θ LARGE flavour transformations: Periodic if  constant SP, Raffelt & Semikoz 2002 Hannestad et al 2006 Non-periodic if  decreases (SUPERNOVA!) Occurs for very small angles Apparently almost independent of the presence of dense normal matter Duan, Fuller & Qian 2005 Duan et al 2006

9. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 20089 ANALOGY OF THE FLAVOUR PENDULUM A certain combination of the global polarization vectors has similar equations to a gyroscopic pendulum (spherical pendulum with radially spinning mass) Hannestad et al 2006 COLLECTIVE NEUTRINO TRANSFORMATIONS Fogli et al 2007

10. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200810 COLLECTIVE NEUTRINO TRANSFORMATIONS ’’ ’’ 1 3 2-flavour limit: the crucial phenomenon is a collective mode of pair transformations driven by and Adiabatic solution (Raffelt & Smirnov 2007)

11. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200811 COLLECTIVE NEUTRINO TRANSFORMATIONS Adding more ingredients MULTIANGLE CALCULATIONS NON- SPHERICAL SN SYMMETRY MULTIENERGY CALCULATIONS Esteban-Pretel et al 2007 Fogli et al 2007 Dasgupta et al 2008

12. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200812 ROLE OF DENSE MATTER: 2 FLAVOURS Hannestad et al 2006  The influence of matter was found to be very small: time scale of conversions depends only logarithmically on the matter density MATTER DOES NOT MATTER ? Larger matter density What happens if the relevant mixing angle is NOT small? Esteban-Pretel et al 2007

13. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200813 ROLE OF DENSE MATTER: 2 FLAVOURS EOMs for monoenergetic neutrinos and antineutrinos If  >>  the fast-rotating transverse part of B averages to zero (but still plays an important role !!) Rotation to eliminate the matter term Duan, Fuller & Qian 2005

14. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200814 ROLE OF DENSE MATTER: 2 FLAVOURS In large matter density: System equivalent (same adiabatic solution) to vacuum case with 1) B aligned with L: projection effect of  m 2 by the large matter effect 2) Vanishing mixing angle and new  θ =  cos2θ Collective transformations between weak-interaction eigenstates  similar to eigenstates of vacuum with m 2 cos2θ Transformation suppressed for maximal mixing ! MATTER SOMETIMES DOES MATTER ! Esteban-Pretel et al, arXiv:0806.XXXX

15. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200815 ROLE OF DENSE MATTER: 3 FLAVOURS Three-flavour system  two of the mixing angles are large: projection effect of  m 2 by a large matter effect can become non-negligible If  and  not distinguishable: diagonalize the 23-subsystem ’’ ’’ Collective pair conversions No effect

16. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200816 MU–TAU NEUTRINO REFRACTION The mu-tau matter effect: second-order difference between the  and  refractive index from radiative corrections to  /  scattering Botella, Lim & Marciano 1987 Total matter effect: Same effect on neutrino dispersion as real  leptons with an abundance

17. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200817 MU–TAU NEUTRINO REFRACTION 3 flavours: 3 possible resonance bands Standard weak potential in matter: H & L Radiative correct. to  / ν  scattering:  SN density profiles Region where collective effects are important Important if original  and  fluxes are not equal Akhmedov, Lunardini & Smirnov, 2002

18. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200818 ROLE OF DENSE MATTER: 3 FLAVOURS When the mu-tau matter potential is large: consider the diagonal elements of M 2 in the weak- interaction basis Changes in lowest effective neutrino eigenstate and effective m 2 Esteban-Pretel et al, arXiv:0806.XXXX No - matter effect similar to θ 23 0 limit (a=1/10 in the fig)

19. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200819 3-FLAVOUR EVOLUTION: NUMERICAL RESULTS Radial evolution of normalized antineutrino fluxes (IH, sin 2 θ 13 =0.01) Delayed onset of bipolar conversions for large - matter effect

20. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200820 3-FLAVOUR EVOLUTION: NUMERICAL RESULTS r (km) Radial evolution of normalized monoenergetic antineutrino fluxes (IH, sin 2 θ 13 =0.01) Vanishing - matter effect Large - matter effect θ 23 <  /4 Esteban-Pretel et al, PRD 77 (2008) 065024

21. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200821 3-FLAVOUR EVOLUTION: NUMERICAL RESULTS r (km) Vanishing - matter effect Large - matter effect θ 23 >  /4 Radial evolution of normalized monoenergetic antineutrino fluxes (IH, sin 2 θ 13 =0.01) Esteban-Pretel et al, PRD 77 (2008) 065024

22. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200822 3-FLAVOUR EVOLUTION: NUMERICAL RESULTS Contours of equal final normalized flux (sin 2 θ 13 =0.01) Dependence with θ 23 for large - matter effect Vanishing - matter effect Large Esteban-Pretel et al, PRD 77 (2008) 065024

23. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200823 LEVEL CROSSING SCHEMES OF NEUTRINO CONVERSION (IH) Vanishing  -  matter effect  and ν  not distinguishable Collective transformations as in the 2-flavour limit any θ 23 ’’ ’’ E ν >E c E <E c

24. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200824 LEVEL CROSSING SCHEMES OF NEUTRINO CONVERSION (IH) Large  -  matter effect Collective transformations depend on the value of θ 23  if θ 23 <  /4  if θ 23 >  /4 Significant changes in spectra! θ 23 >  /4 θ 23 <  /4 E ν >E c E <E c E ν >E c E <E c

25. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200825 3-FLAVOUR EVOLUTION: SUMMARY Esteban-Pretel et al, PRD 77 (2008) 065024

26. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 200826 CONCLUSIONS Collective Neutrino Transformations in SNe: new rich phenomenology Role of Dense Matter: the effective system has to be studied  in vacuum with a vanishing mixing angle  effective mass spectrum given by the projection on the weak-interaction direction Two-flavour case (small mixing angle): no fundamental changes Three-flavours (2 large mixing angles): if  -  matter effect large, the large θ 23 causes an effective mass spectrum very different from vacuum  large modifications in the fluxes  this situation could be typical for early times of iron-core SNe

27. END

28. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 2008 ROLE OF DENSE MATTER: 3 FLAVOURS Diagonal elements of M 2 in the weak-interaction basis (mu-tau large)

29. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 2008 3-FLAVOUR EVOLUTION: NUMERICAL RESULTS

30. SERGIO PASTOR, Melbourne Neutrino Theory Workshop, June 2008 3-FLAVOUR EVOLUTION: NUMERICAL RESULTS