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/0608103 D.K., astro-ph/0511231 ; I.J.M.P.D 2004,13,831

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.

Observational evidences for  oscillations Solar neutrino anomaly Homestake, Kamiokande, SuperKamioKa, Gallex, SAGE, SNO е   (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) и sin22=O(0,003) variation of the flux with B

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.

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

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

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

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

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

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 !

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

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

Evolution of the distortion The spectrum distortion of the active neutrino for a wide range of oscillation parameters persists during the nucleons freezing period.

Energy spectrum distortion evolution

The depletion of active neutrinos (an integral effect of the distortion) DK, Chizhov 1997, 2004

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 .

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).

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

BBN WITH OSCILLATIONS

SBBN production of 4Не Т > 1 MeV Т < 1 MeV Т < 80 KeV

4Не – the preferred element Observed in НІІ low metalicity regions of dwarf galaxies Extrapolated towards zero metalicity Recent observational data: Yp=0,2421 0,0021 Izotov, Thuan 2000 Yp=0,2429 0,009 Izotov, Thuan 2004 dispersion of the determinations Yp=0,245 0,013 Olive, Skillman 2004 Yp=0,2491 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.

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

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

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

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

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

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

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, 2003 - spectrum distortion

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.

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

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=0,5. DK, Panayotova, 2006

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.