1. GGI Firenze Sept’06 Neutrino 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/
D.K., astro-ph/ ; 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
е   (LMA) recent global analyses
Fogli et.al, 2006
m2 eV2 sin22 = Strumia, Vissani, 2006
Atmospheric neutrino anomaly alternative models with s
Super-KamioKa, Macro, Soudan 2, IMB Holanda, Smirnov, 2004
  , m2 eV2 maximal  better agreement with Homestake
Terrestrial experiments Chauhan, Pulido, 2004
LSND, KamLAND, K2K Caldwell D, Sturrock P.,2005
  e, m2 O(1eV2) и 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. Effects of neutrino oscillations
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 е  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 V = Q L, Q=-bE2T4/m2 L=-aET3Lf/ m2
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 Shvartsman, 1969
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  4Не 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 (Ns<1),
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,81;DK 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 distortion The 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 Ns=0, the effect decreases with Ns .

17. Distortion dependence on Ns
Spectrum distortion for different initial population of s.
Ns=0 – the lowest curve, Ns=0,5 and Ns=0,8 – 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:
N=0.75 Neq
Nk,4 < 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 4Не
Т > 1 MeV
Т < 1 MeV
Т < 80 KeV

21. 4Не – the preferred element
Observed in НІІ low metalicity regions of dwarf galaxies
Extrapolated towards zero metalicity
Recent observational data:
Yp=0,2421 0, Izotov, Thuan 2000
Yp=0,2429 0, Izotov, Thuan 2004
dispersion of the determinations
Yp=0,245 0, Olive, Skillman 2004
Yp=0,2491 0, 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 BBN with fast a  s : increase
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  4Не is overproduced
BBN with fast a  s : increase
effective before a decoupling
BBN with a  s e spectrum distortions
effective after a decoupling and Ns<1

23. Evolution of nucleons in the presence of е  s the numerical approach

24. The interplay b/n effects
Nk,0 >1
N= Nk,0- Nk,0 Ns +Ns
Nk,0 Ns >Ns
total effect decreases
kinetic effect decreases
dynamic effect increases
m2 = 10-7 eV2 sin22 = 1

25. The role of additional light s
Nk,0 < 1
N= Nk,0- Nk,0 Ns +Ns
Nk,0 Ns < Ns
total effect increases
dynamic effect increases
kinetic effect decreases

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 oscillations BBN 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 е  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, 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 constraints For nonequilibrium oscillations the constraints are strengthened by orders of magnitude:
Dolgov A., F.Villante ,2003
m2>10-6 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/Yp=3% (Yp/Yp=5.2% ) for Ns=0,
the solid blue (red) contour presents
Yp/Yp=3% (Yp/Yp=5%) for Ns=0, 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 time…and 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 N<9 (not N<4 which is valid only for fast oscillations).
BBN constraints strengthen by orders of magnitude when distortion effect of
oscillations is accounted for.
Introducing additional partially filled sterile state may lead to strengthening
as well as to relaxation of the BBN constraints!
Flavor mixing will cause decrease of the spectrum distortion effect and relaxation
of the constraints.