Open issues in neutrino
flavor conversion in media
Cristina VOLPE
(AstroParticule et Cosmologie -APC)
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.
THE EARLY UNIVERSE -
nt
NS
nm
Predictions of primordial
elements (BBN epoch).
The Mikheev-Smirnov-Wolfenstein effect established
Wolfenstein PRD (1978)
Mikheev and Smirnov, Sov. J. Nucl. Phys. (1985)
ne
e
e
GF r e
Hmatter
pep
pp
7Be
n
MSW solution
8B
Neutrino Energy (MeV)
n
Borexino coll, PRL 108 (2012)
The solar neutrino
deficit problem
solved
n e Survival Probability
Neutrino interaction with matter
induces resonant flavour conversion.
ne
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)
Star radius (km)
Marek & Janka, ApJ (2009)
SN simulations have reached a
high degree of complexity :
2D-3D, convection, realistic
neutrino transport, SASI.
Time (ms)
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.
log Y(A)
Solar abundance of heavy elements
 Element nucleosynthesis
r-process, np-process,
n-nucleosynthesis.
with n-n
see Focus Issue on
«Neutrinos and Nucleosynthesis »
to appear in Journal of Physics G.
A
Duan, Friedland, McLaughlin, Surman JPG 38 (2010)
n flavour conversion in supernovae
neutrinosphere
ne
n-e
MSW effect
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.
The effects of the nn interaction
Neutrino Fluxes
n e Survival Probability
Pantaleone, PLB 287 (1992), Samuel,PRD 48 (1993), Sigl and Raffelt, NPB 406 (1993),
Distance in SN
n-fluxes at 200 km
characteristic
imprints
Neutrino Energy (MeV)
 synchronization mode : no flavor conversion occurs
 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)
 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
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)
Collisions recently discussed in
Cherry et al., PRL108 (2012)
nt
ne
NS
nm
THE EARLY UNIVERSE - The Boltzmann approximation
for particles with mixings is used.
The role of other two-body correlations?
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
76Ge
nuclear collision
76As
76Se
double-beta decay
condensed matter
A many-body system perspective
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 –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 :
one-body density
two-body density
Solving exactly the many-body problem is equivalent to
BBGKY : a hierarchy of equations for s-reduced density matrices
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
occupation number op.
 particles with mixings
anti-n
n
decoherence or mixing terms
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
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
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
diagonal
contribution
off-diagonal
contribution
MEAN-FIELD EQUATIONS - MSW and nn – reDERIVED
Consistent with previous derivations
Sigl and Raffelt, Nucl. Phys. B406 (1993),
Fuller and Qian PRD 51 (1995)
Beyond the 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)
Beyond the 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
Extended equations in media
Volpe, Väänänen, Espinoza, PRD87 (2013), arXiv: 1302.2374
They include a pairing mean-field associated with abnormal densities :
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 correlations?
SN : the transition region ?
mean-field
terms
ne n
t
nm
nm
terms GF
n trapped
GF
2:
Boltzmann
transition
region
extended description
ne
neutrinosphere
Neutrino evolution equations are
non-linear, novel features can arise.
Further numerical
investigations necessary
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)
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
flavor space
We have applied linearisation methods from
many-body microscopic approaches to obtain
eigenvalue equations and a stability matrix,
valid in the small amplitude approximation
The eigenvalue equation for the neutrino systems
Stability
matrix
w
THE STABILITY
MATRIX
EIGENVALUES:
stable or unstable
collective modes
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
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
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.
e+ flux (/MeV/s/ton)
Prediction including the nn interaction and shock wave effects.
ne + p
n + e+
inverted hierarchy
29 MeV
Gava, Kneller,
Volpe, McLaughlin,
PRL 103(2009)
15 MeV
Time signal (s)
Bump (dip) at 3.5 (1) sigma in Super-Kamiokande
Two-neutron events
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
One-neutron events
Detection channels with different energy
thresholds help identifying solutions.
Thank you