GGI Firenze Sept

1
GGI Firenze
Sept06Neutrino spectrum distortion due to
active-sterile neutrino oscillations and its
effect on BBN

• Daniela Kirilova
• Institute of Astronomy, BAS, Sofia
• D.K.,M.Panayotova, astro-ph/0608103
• D.K., astro-ph/0511231 I.J.M.P.D 2004,13,831

2
Motivation

• Active-sterile neutrino oscillations?
• Spectrum distortion?
• BBN?

• Though solar and atmospheric neutrino anomalies
  are well described in terms of flavor neutrino
  oscillations, sub-leading sterile oscillations
  may provide better fit
• Neutrino oscillations may influence
  considerably the neutrino involved processes in
  the early Universe.
• The major effect of non-equilibrium neutrino
  oscillations
• One of the most precision probes
• for new neutrino physics, like decays,
• oscillations, species, etc.

3
Observational evidences for ? oscillations

• Solar neutrino anomaly
• Homestake, Kamiokande, SuperKamioKa, Gallex,
  SAGE, SNO
• ?? ? ?? (LMA)
  recent global
  analyses
• 
  Fogli
  et.al, 2006
• ?m2? 7.9.10-5eV2 sin22? 0.31
  Strumia, Vissani, 2006
• Atmospheric neutrino anomaly
  alternative models with ?s
• Super-KamioKa, Macro, Soudan 2, IMB
  Holanda, Smirnov, 2004
• ?? ? ??, ?m2? 2.6.10-3eV2 maximal ?
  better agreement with
  Homestake
• Terrestrial experiments
  Chauhan, Pulido, 2004
• LSND, KamLAND, K2K
  Caldwell D, Sturrock
  P.,2005
  
• ?? ? ?e, ?m2? O(1eV2) ? sin22?O(0,003)
  variation of the flux with B
• 
  

4
Oscillations in the early Universe

• Explore the cosmological influence of
  oscillations
• Neutrino oscillations may
• excite additional light particles into
  equilibrium
• distort the neutrino energy spectrum and
• affect neutrino-antineutrino asymmetry of
  the medium (suppress / enhance).
• All these may play crucial role for neutrino
  involved processes in the
• early Universe.
• Obtain cosmological constraints on oscillations
• From the allowed range of the observables of the
  early Universe, like
• baryonic density, light elements abundances,
  expansion rate, CMB
• spectrum, structure characteristics of the
  Universe, etc.,
• it is possible to constrain the parameters of
  neutrino oscillations.

5

• OUTLINE
• Effects of neutrino oscillations
• type of oscillations oscillation channels,
• the degree of equilibrium of oscillating
  neutrinos,
• plasma characteristics ( in vacuum in
  matter)
• Spectrum distortion of electron neutrino
• depletion, asymmetry, approximations, exact
  solutions
• role of initial population, role of flavor
  mixing
• BBN with oscillations (distortion accounted)
• He-4 overproduction, maximal
  overproduction, general case
• BBN constraints on oscillations parameters
• role of initial population, He-4
  uncertainty
• possible relaxations LA, even higher He
  systematics

6
Neutrino oscillations

• The basic idea of oscillations is that mass
  eigenstates are distinct from
• the flavor eigenstates.
• ?m Umf ?f, (f e, ?, ?)
• Transitions b/n different flavors are possible.
• Neutrino oscillations imply non-zero mass
  differences and mixing
• ?m2 ? 0, at least 2 neutrino have mn ? 0
• two-neutrino case ?? ? ?s
• vacuum oscillations ?1 ?ecos? ?ssin?
• ?2 - ?esin? ?scos?
• The probability to find at a time t (distance l)
  a given neutrino type in an initially
• homogeneous neutrino beam of the same type is
• Pff 1- sin22?sin2(?m2t/4E) flavor composition
  changes with time

7
Matter oscillations

• The medium distinguishes between different
  neutrino types due to their different
  interactions
• with fermions of the hot plasma at BBN epoch.
  This leads to different potentials for different
  
• neutrino types
• V Q L, Q-bE2T4/?m2
  L-aET3Lf/ ?m2
• Matter oscillations parameters depend on the
  values of the vacuum oscillations parameters and
• on the characteristics of the medium, like
  density, temperatute, leptonic asymmetry.
• sin22?m sin22? /sin22? (Q
  L -cos2?)
• In general medium suppresses oscillations
  decreasing their amplitude.
• A possibility of enhanced oscillation exists,
  however, in case
• 
  Wolfenstein,
  1978
• Q L cos2?
  Miheev,Smirnov 1985
• 
  

8
Oscillations effects

• Mixing b/n active neutrinos influence neutrino
  spectra and Dolgov ,1981
• BBN negligibly.
• Active sterile mixings of neutrinos
• Dynamical effect production of additional
  neutrino species.
• Additional degree of freedom enhances the energy
  density
• and drives expansion faster.
• Tf geff1/6 ? 4?? overproduction
• 
  Shvartsman, 1969
  
• 
  BBN constraints on ?Ns
  
• ?Yd 0.013 ?Ns
  Dolgov ,1981
• ( 1 additional ? ? ?Yp/Yp 5 )
  oscillations dynamical effect

9
Effects of nonequilibrium ?e ? ?s

• Kinetic effect ? ?e energy
  spectrum distortion,
  
• ? ?e depletion,
  D.K.,1988
  Barbieri,Dolgov, 1990
• 
  
  Enqvist et.al., 92 DK M.Chizhov, PLB
  ,1997
• ? energy threshold effect
  ? pre-BBN kinetics
• ? neutrino-antineutrino asymmetry growth
  Foot, Volkas,1996 DK M.Chizhov,1997
• 
  
  Dolgov et al., 2002
• In case of oscillations effective after ?
  decoupling and
• provided that the sterile state is not in
  equilibrium (?Nslt1),
• the spectrum distortion effect is the major one.
• Expressed in terms of effective number of
  neutrinos
• ?Nk,0 ?6 for resonant oscillations
• ?Nk,0 ?3 for non-resonant oscillations
  DK , Astrop.Phys.,2003

10
Oscillations medium influence

• Medium suppresses the oscillations amplitude
• Medium may enhance them
• great spectrum distortion in the resonant
  case
• Negligible spectrum distortion ?
• (work with particle densities and T shift one
  momentum approximations.)

• -Fast oscillations equilize pre-existing
  asymmetries
• - Oscillations cause great spectrum
  distortion, asymmetry growth
• Persists, and is often the leading effect ,
  hence it
• should be precisely described !

11
Evolution of neutrinos in the presence of
oscillations Approach follow the evolution of
neutrino for each momentum account for
oscillations, expansion and interactions with the
medium simultaneously
Dolgov,81DK 1988,
Chizhov, DK, 1997
12
The evolution of spectrum distortion

• The distortion concerns first the low energetic
  part of the spectrum because the oscillations
  become effective first to low energy neutrinos
• Soon after, the whole spectrum is
• distorted from its equilibrium FD form
• The non-equilibrium initial condition
• leads to considerable and continuous
• deviations from the equilibrium

13
Evolution of the distortionThe spectrum
distortion of the active neutrino for a wide
range of oscillation parameters persists during
the nucleons freezing period.
14
Energy spectrum distortion evolution
15
The depletion of active neutrinos(an integral
effect of the distortion) DK,
Chizhov 1997, 2004
16
Role of the initial population of ?s

• Sterile neutrinos may be present at the onset
  of BBN epoch -- they may be
• produced in GUT models, in models with
  large extra dimensions, Manyfold
• Universe models, mirror matter models, or
  by oscillations in 4-neutrino mixing
• schemes, etc.
• The degree of population and
  the initial energy spectrum may
• be different depending on the production
  model.
• The distortion of the neutrino spectrum
  due to active-sterile
• oscillations depends on the degree of
  initial population of ?s.
• The biggest effect is at ?Ns0, the
  effect decreases with ?Ns .
• 
  
• 
  

17
Distortion dependence on ?Ns
Spectrum distortion for different initial
population of ?s. ?Ns0 the lowest curve,
?Ns0,5 and ?Ns0,8 the upper curve. The
dashed curve shows the equilibrium spectrum (DK ,
IJMPD2004).
18
Role of flavor mixing(preliminary)

• 2 neutrino mixing
• N 0.5 Neq
• 4 neutrino mixing
• N0.75 Neq
• ?Nk,4 lt ?Nk,2

• Sterile state is filled for
• the sake of ?e
• Sterile state filles from . ?e
• ?e is partially re-filled for the sake of muon
  and tau neutrino
• Flavor mixing decreases the depletion and
  spectrum distortion

19
BBN WITH OSCILLATIONS
20
SBBN production of 4??

• ? gt 1 MeV
• ? lt 1 MeV
• ? lt 80 KeV

21
4?? the preferred element

• Observed in ??? low metalicity regions of dwarf
  galaxies
• Extrapolated towards zero metalicity
• Recent observational data
• Yp0,2421? 0,0021 Izotov, Thuan 2000
• Yp0,2429? 0,009 Izotov, Thuan 2004
• 
  dispersion of the determinations
• Yp0,245? 0,013 Olive, Skillman 2004
• Yp0,2491? 0,0091 Olive, Skillman 2004
• Determinations indicate 3-5 uncertainty
  (systematic errors). Sasselov, 95
• Possibly it is related with the evaluation of
  ionization level, stellar absorption, ..
  Luridiana, 2002
• For a precise analysis of the oscillations effect
  on BBN, He-4 is used because the most
• reliable and abundant data now available are for
  that element.
• The primordial abundance Yp, predicted from SBBN,
  is calculated with
• great precision the theoretical uncertainty is
  less than 0.1 within a wide
• range of baryon density.

22
BBN with oscillations

• He-4 mass fraction is a strong function of the
  effective number of light stable particles at
  BBN epoch
• It depends also on the ?e characteristics
• decrease ? n/p freezes earlier ? 4?? is
  overproduced
• BBN with fast ?a ? ?s
  increase
• effective before ?a decoupling
• BBN with ?a ? ?s ?e
  spectrum distortions
• effective after ?a decoupling and ?Nslt1

23
Evolution of nucleons in the presence of ?? ?
?sthe numerical approach
24
The interplay b/n effects
?Nk,0 gt1
?N ?Nk,0- ?Nk,0 ?Ns ?Ns
?Nk,0 ?Ns gt?Ns
?m2 10-7 eV2 sin22? 1
25
The role of additional light ?s
?Nk,0 lt 1
?N ?Nk,0- ?Nk,0 ?Ns ?Ns
?Nk,0 ?Ns lt ?Ns
26
Maximum He-4 overproduction in BBN with
oscillations due to spectrum distortion

• Dependence of maximum
• overproduction on the mixing
• 0??Y/Y ?32 for resonant oscillations
• 0??Y/Y ?14 for non-resonant oscillations
• DK , Astrop.Phys.,2003

27
Maximum He-4 overproduction in BBN with
oscillations due to spectrum distortion

• Maximal overproduction
• dependence on mass difference
• BBN constraints do exist
• if He-4 uncertainty is over 5 but
• for non-equilibrium oscillations.
• BBN with nonequilibrium ?e??s
• allows to constrain ? oscillation
• parameters for He-4 uncertainty
• up to32 (14) in resonant
• (non-resonant) case.
• DK , Astrop.Phys.,2003

28
Role of spectrum distortion account for BBN
constraints on oscillationsBBN with neutrino
oscillations between initially empty ns and
ne
Observational data on primordial He- 4 was
used to put stringent limits on the allowed
oscillation parameters. BBN constraints on ?? ?
?s Barbieri, Dolgov 91 depletion
account Dolgov 2000 dashed curve DK, Enqvist
et al. 92 one p approx. DK.,Chizhov 2001
distortion and asymmetry growth account Dolgov,
Villante, 2003 - spectrum distortion
29
Spectrum distortion reflected in neutrino
oscillations constraints

• The distortion leads to a decrease of the
  weak rates and, hence to an increase of the n/p
  freezing T and He-4 overproduction.
• Correspondingly the account of
• spectrum distortion leads to strengthening
  of BBN constraints.
• The account of the asymmetry growth in
  resonant oscillations leads to relaxation of the
  constraints for small mixings.

30
Spectrum distortion and BBN constraintsFor
nonequilibrium oscillations the constraints are
strengthened by orders of magnitude
Dolgov A., F.Villante ,2003 ?m2gt10-6 eV2, i.e.
kinetic equilibrium constraints for non-resonant
case
At smaller ?m2 re-population of active neutrino
becomes slow, spectrum distortion is
considerable. Chizhov M., DK, 2001 D.K. 2005

31
Role of the initial population of ?s BBN
constraints relaxed or strengthened?Additional
?s population may lead to stonger or weaker
BBN constraints on oscillation parameters.
There exist an interplay b/n the effects of
non-zero initial population of ?s on BBN in
case the dynamical effect dominates, He-4
overproduction is enhanced and BBN constraints
strengthen, in case the kinetic effect
dominates He-4 overproduction decreases and BBN
constraints relax. The dotted blue (red) contour
presents ?Yp/Yp3 (?Yp/Yp5.2 ) for ?Ns0,
the solid blue (red) contour presents ?Yp/Yp3
(?Yp/Yp5) for ?Ns0,5.
DK, Panayotova, 2006
32
Conclusions

• Spectrum distortion plays a major role in
  evaluating the influence of
• neutrino oscillations on BBN for oscillations
  effective after neutrino
• decoupling. It leads to overproduction of
  helium. Precise numerical
• account of the distortion caused by oscillations
  reveals the possibility
• for 6 times higher helium overproduction than
  accepted before.
• (But requires orders of magnitude more CPU
  timeand not only CPU)
• Distortion decreases with the increase of the
  initial population of the
• sterile neutrino, the kinetic effect decreases
  correspondingly.
• Helium may be both overproduced or underproduced
  in comparison with
• the case of zero initial population due the
  interplay b/n dynamical and
• kinetic effect of non-zero sterile neutrino
  population.
• BBN with nonequilibrium ?e ? ?s oscillations
  allows to put constraints
• on ? oscillation parameters for He-4 uncertainty
  up to 32(14) in resonant
• (non-resonant) case, provided ?s was not in
  equilibrium, which corresponds
• to Nlt9 (not Nlt4 which is valid only for fast
  oscillations).
• BBN constraints strengthen by orders of magnitude
  when distortion effect of