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Melbourne Neutrino Theory Workshop , June 2008 1
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
OUTLINE
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 2
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
COLLECTIVE NEUTRINO TRANSFORMATIONS
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 3
There exist some situations where the neutrino refraction index is dominated by neutrinos themselves
Early Universe beforeNeutrino 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
p
mnGF 2
22
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 4
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-cosθpq) can lead to flavour decoherence between different angular modes Talks by Sawyer & Esteban
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 5
COLLECTIVE NEUTRINO TRANSFORMATIONS2 flavours: Spin-precession analogy
MBPBp
m
dt
Pd
2
2
),,( zyx PPPP
zyx
yxz
PiPP
iPPPPp
1
1)1()( 2
121
PpmM
)2/( 2 Magnetic dipole moment associated to P
2/2 pm Gyromagnetic ratio for mode p
Polarization vector in flavour space
Effective magnetic field )2cos,0,2(sin B
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 6
COLLECTIVE NEUTRINO TRANSFORMATIONS
EOMs for 2 flavours
ii
F
eF
ii
PP
nG
nGL
pm
2
)1,0,0(2
2/2
(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
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 7
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
VACUUMLARGE NEUTRINO DENSITY
synt
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 8
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 2002Hannestad 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 2005Duan et al 2006
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 9
ANALOGY OF THE FLAVOUR PENDULUM
A certain combination of the global polarization vectors has similar equations to agyroscopic pendulum (spherical pendulum with radially spinning mass)
Hannestad et al 2006
COLLECTIVE NEUTRINO TRANSFORMATIONS
Fogli et al 2007
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 10
COLLECTIVE NEUTRINO TRANSFORMATIONS
’ ’
13 02 atmm
2m1
3
2-flavour limit: the crucial phenomenon is a collective mode of pair transformations driven by and
Adiabatic solution (Raffelt & Smirnov 2007)
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 11
COLLECTIVE NEUTRINO TRANSFORMATIONS
Adding more ingredients
MULTIANGLECALCULATIONS
NON-SPHERICAL SN SYMMETRY
MULTIENERGY CALCULATIONS
Esteban-Pretel et al 2007 Fogli et al 2007
Dasgupta et al 2008
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 12
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 densityMATTER DOES NOT MATTER ?
Larger matter density
What happens if the relevant mixing angle is NOT small?
Esteban-Pretel et al 2007
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 13
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 termDuan, Fuller & Qian 2005
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 14
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 m2 by the large matter effect2) Vanishing mixing angle and new θ= cos2θ
2cos2m
Collective transformations between weak-interaction eigenstates similar to eigenstates of vacuum with m2cos2θ
Transformation suppressed for maximal mixing !
MATTER SOMETIMES DOES MATTER !
Esteban-Pretel et al, arXiv:0806.XXXX
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 15
ROLE OF DENSE MATTER: 3 FLAVOURS
Three-flavour system two of the mixing angles are large: projection effect of m2 by a large matter effect can become non-negligible
If and not distinguishable: diagonalize the 23-subsystem
’ ’
Collective pair conversions No effect
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 16
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 asreal leptons with an abundance
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 17
MU–TAU NEUTRINO REFRACTION
3 flavours: 3 possible resonance bands
Standard weak potential in matter: H & L
Radiative correct. to / ν scattering:
SN densityprofiles
Region wherecollective effectsare important
Important iforiginal and
fluxes are not equalAkhmedov, Lunardini & Smirnov, 2002
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 18
ROLE OF DENSE MATTER: 3 FLAVOURS
When the mu-tau matter potential is large: consider the diagonal elements of M2 in the weak-interaction basis
Changes in lowest effective neutrino eigenstate
and effective m2
Esteban-Pretel et al, arXiv:0806.XXXX
No - matter effect similar to θ230 limit
30/1/
16/22
1312
solatm mma
,
(a=1/10 in the fig)
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 19
3-FLAVOUR EVOLUTION: NUMERICAL RESULTS
Radial evolution of normalized antineutrino fluxes (IH, sin2θ13=0.01)
Delayed onset of bipolar conversions for large - matter effect
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 20
3-FLAVOUR EVOLUTION: NUMERICAL RESULTS
r (km) r (km)
Radial evolution of normalized monoenergetic antineutrino fluxes (IH, sin2θ13=0.01)
Vanishing - matter effect Large - matter effect
θ23 < /4
Esteban-Pretel et al, PRD 77 (2008) 065024
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 21
3-FLAVOUR EVOLUTION: NUMERICAL RESULTS
r (km) r (km)
Vanishing - matter effect Large - matter effect
θ23 > /4
Radial evolution of normalized monoenergetic antineutrino fluxes (IH, sin2θ13=0.01)
Esteban-Pretel et al, PRD 77 (2008) 065024
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 22
3-FLAVOUR EVOLUTION: NUMERICAL RESULTS
Contours of equal final normalized flux (sin2θ13=0.01)
Dependence with θ23 for large - matter effect
Vanishing - matter effect Large
Esteban-Pretel et al, PRD 77 (2008) 065024
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 23
LEVEL CROSSING SCHEMES OF NEUTRINO CONVERSION (IH)
Vanishing - matter effect
and ν not distinguishable
Collective transformations as in the 2-flavour limit
any θ23
’ ’
Eν>Ec
E<Ec
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 24
LEVEL CROSSING SCHEMES OF NEUTRINO CONVERSION (IH)
Large - matter effect
Collective transformations depend on the value of θ23
if θ23 < /4
if θ23 > /4
Significant changes in spectra!ee /
θ23 > /4
θ23 < /4
Eν>Ec
E<Ec
Eν>Ec
E<Ec
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 25
3-FLAVOUR EVOLUTION: SUMMARY
Esteban-Pretel et al, PRD 77 (2008) 065024
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008 26
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 θ23 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
ee /
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008
ROLE OF DENSE MATTER: 3 FLAVOURS
Diagonal elements of M2 in the weak-interaction basis (mu-tau large)
SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008
3-FLAVOUR EVOLUTION: NUMERICAL RESULTS