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

2. 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 -

3. 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 ?

4. 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:
first 3D : hints for explosion in 3D not enhanced compared to 2D
Hanke et al, arXiv:

5. 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),
n flavor conversion in matter impacts the nucleosynthetic outcomes.
see Focus Issue on «Nucleosynthesis and Neutrinos» to appear in Journal of Physics G.

6. 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) MeV 50 kton scintillator
MeV 440 kton water Cherenkov
MeV 50 kton liquid argon ne ne ne
Galais, Kneller, Volpe, Gava, PRD 81(2010) , arXiv :

7. 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

8. 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

9. 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), …

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

11. 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)

12. 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

13. 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

14. 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

15. A novel perspective to n conversion
Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv:
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

16. 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)

17. 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:

18. 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)

19. 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

20. Collective stable and unstable modes
Distance in SN
n e Probability
synchronization
Väänänen, Volpe, PRD88 (2013), arXiv:
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

21. 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

22. 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

23. 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

24. Merci

25. 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:
Gava, Volpe, Phys. Rev. D78 (2008), arXiv:

26. 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

27. 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)