Open issues in
neutrino flavor conversion
in media
Cristina VOLPE
(AstroParticule et Cosmologie–APC, Paris)
Neutrino flavor conversion in media
 solar neutrinos
MSW effect :
resonant flavor
conversion due
to n-e interaction
n e Survival Probability
Important for observations in astrophysical and cosmological context :
 Core-collapse supernovae
pep
pp
7Be
n
MSW solution
8B
n
Borexino , PRL 2012
Neutrino Energy (MeV)
 Early universe - 4He, D, 3H, 7Li primordial abundances
Core-collapse supernovae
Core-collapse supernovae comprise :
 O-Ne-Mg supernovae
 Iron core-collapse supernovae
 Very massive
-> accretion-disk black hole (AD-BH)
O-Ne-Mg
iron
Si
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.
Bruenn et al, arXiv:1002.4909
See MICRA workshop,
september 2013, Trento.
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.
Suzuki, J. of Physics, Conf. (2008)
 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.
SN1987A events
More observations
Neutrino luminosity curves
Time and energy signal of different explosion phases important :
nt
ne
accretion
cooling
accretion
fromcooling
simulations
NS
nm
neutrinosphere
Time after bounce (s)
a sensitive probe of the supernova dynamics
Hüdepohl et al. PRL 104 (2010)
neutronization burst
n flavour conversion in supernovae
ne
n-e
MSW
nm
shock waves
neutrinosphere
Flavour conversion effects arise because of
 the n interaction with n and with matter (MSW effect).
 dynamical aspects - shock waves and turbulence.
Effects
of the conversion
nn interaction
n flavour
in supernovae
Distance in SN
Neutrino Fluxes
spectral split
bippolar
synchronization
n e Survival Probability
Pantaleone, PLB 287 (1992), Samuel,PRD 48 (1993)
at 200 km
characteristic
imprints
Neutrino Energy (MeV)
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
(first 50 ms)
(50-500 ms)
EFFECTS
n-n
cooling
(1-10 s)
?
shock wave
MSW
Dated 12/11/13
The final picture could be simpler than we (might) think.
Open questions
Further work needed to finally assess :
 impact on the shock wave
shock wave n free
streaming
n trapped
nucleosynthesis
Qian et al, PRL 71 (1993)
Dasgupta, o’Connor, Ott, PRD 85 (2012)
 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)
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
76Ge
nuclear collision
76As
76Se
double-beta decay
condensed matter
The exact evolution
Let us consider a system of N-particles described by a Hamiltonian :
n
n
p
e
p
n
e
n
n
n
e
e
p
p p
pe
p ee
n p
p
The system evolution is determined by solving
the Liouville Von-Neumann equation for D :
N-body density matrix
e
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
two-body density
two-body correlations
one-body densities
The first BBGKY equation reduces to :
with
MEAN-FIELD
The n evolution equations in presence of
re (MSW case)
 a matter background
 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
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
mean-field
terms
ne n
t
GF
nm
nm
terms GF2 :
n trapped
Boltzmann
transition
region
extended description
ne
neutrinosphere
Neutrino equations
are non-linear :
novel features can arise.
Further numerical
investigations necessary
for direction-changing term see also,
Cherry et al., PRL108 (2012)
bippolar
synchronization
Appearance of stable or unstable collective
modes studied through linearization.
Sawyer PRD79 (2009),
Banerjee, Dighe, Raffelt, PRD 84 (2011)
n e Probability
Collective stable and unstable modes
Distance in SN
Stability matrix
bippolar
General linearized equations using methods
from many-body approaches
n e Probability
Väänänen, Volpe, PRD88 (2013), arXiv: 1306.6372
synchronization
Collective stable and unstable modes
Distance in SN
w
flavor space
STABILITY MATRIX EIGENVALUES:
real (stable) or imaginary (unstable) modes
n
p
giant resonances
76Ge
76As
76Se
double-beta decay
Current SN observatories
Borexino Baksan
SK (104)
LVD
Daya-Bay
MiniBOONE HALO
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
Two-neutron events
An example :
CC+NC events in HALO-2 (1 kton lead), SN at 10 kpc
Väänänen, Volpe, JCAP 1110 (2011)
n e  208 Pb 
207
ne 
208
Pb 
206
Bi  2n  e -
nx 
208
Pb 
207
Bi  n
nx 
208
Pb 
206
Bi  2n
Bi  n  e -
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)