Melbourne Neutrino Theory Workshop, June 20081 ROLE OF DENSE MATTER IN COLLECTIVE NEUTRINO TRANSFORMATIONS Sergio Pastor (IFIC Valencia) in collaboration

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


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


Equations of motion in terms of the matrices of density for (anti)neutrinos

and similar for with


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


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



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



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



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


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


Fogli et al 2007



’ ’

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)



Adding more ingredients

MULTIANGLECALCULATIONS

NON-SPHERICAL SN SYMMETRY

MULTIENERGY CALCULATIONS

Esteban-Pretel et al 2007 Fogli et al 2007

Dasgupta et al 2008


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



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



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



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


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


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



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)


3-FLAVOUR EVOLUTION: NUMERICAL RESULTS

Radial evolution of normalized antineutrino fluxes (IH, sin2θ13=0.01)

Delayed onset of bipolar conversions for large - matter effect



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



r (km) r (km)

Vanishing - matter effect Large - matter effect

θ23 > /4

Radial evolution of normalized monoenergetic antineutrino fluxes (IH, sin2θ13=0.01)




Contours of equal final normalized flux (sin2θ13=0.01)

Dependence with θ23 for large - matter effect

Vanishing - matter effect Large



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


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


3-FLAVOUR EVOLUTION: SUMMARY



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 /

END

SERGIO PASTOR, Melbourne Neutrino Theory Workshop , June 2008


Diagonal elements of M2 in the weak-interaction basis (mu-tau large)





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Melbourne Neutrino Theory Workshop, June 20081 ROLE OF DENSE MATTER IN COLLECTIVE NEUTRINO TRANSFORMATIONS Sergio Pastor (IFIC Valencia) in collaboration