Magnetic-moment contributions to the neutrino index of refraction in the early Universe

Abstract

The existence of anomalous magnetic dipole moments for neutrinos can affect neutrino oscillations in the early Universe through previously ignored refractive effects. Using the real-time approach of finite-temperature field theory, we have calculated the effective potential for neutrinos due to their magnetic moments and compared it to the standard model value, in view of the astrophysical and laboratory constraints. PACS number(s): 13.10.+q, 13.15.+g, 98.80.Cq The effect of neutrino oscillations in big-bang nucleosynthesis has recently received much attention [I-61. The constraints on mixings between active (v,, v,, v,) and sterile (v,) neutrinos [2,5] from the present observation of the primordial helium abundance are such that excluded regions include the large angle v,-v, Mikheyev-Smirnov-Wolfenstein (MSW) solution [7] as well as the v,-v, mixing solution [8] to the atmospheric neutrino problem. On the other hand, oscillations between ordinary (active) neutrinos would not have any obvious consequences for the early Universe as the abundances of these states are practically equal [9]. For Dirac neutrinos endowed with anomalous magnetic dipole moments (MDM's) the magnetically induced neutrino oscillations in the early Universe may occur [1,10]. In such oscillations between left-handed (vL) and right-handed (vR) states the nucleosynthesis arguments constrain the product of neutrino MDM's and a present-day intergalactic field strength.In all the above examples of neutrino oscillations in the early Universe the neutrino refractive effects are of crucial importance. In terms of standard electroweak interactions the almost C P symmetry of the medium implies that the lowest order refractive effects, which dominate in stars, nearly cancel. Indeed, previous calculations [11,12] have shown that the only nonzero result arises from higher order effects (such as an expansion of gauge-boson propagators and iadiative corrections). However, the CP-symmetric contributions turn out to be suppressed by a very small factor of order T 2 / M & , where the temperature T in the epoch of interest T N 0.1-10 MeV.For neutrinos with MDM's the vR'S (uL'S) and photons of the heat bath will affect vL7S (vR7S) propagation through the coherent forward-scattering amplitude in the lowest order. In addition to the asymmetry term which is probably at the level of 10-lo, as the baryon to photon ratio is, there is a nonvanishing CP-symmetric contribution in the lowest order, as opposed to the case of standard interactions. This motivates us to study the precise temperature dependence of the effect and to compare new contributions to the standard model value in the temperature range of interest (the central discussion goes with the strongest astrophysical bounds on neutrino MDM's).In the application to the early Universe, we consider an ordinary light neutrino v~ (mu, 5 10 eV) in the radiation-dominated epoch with temperatures T -0.1-10 MeV. So. in the calculation of refractive effects its rest mass can always be neglected. In addition, this al...

Nonstandard neutrino properties and the high-energy cosmic neutrino flux

“…This is due to the fact that now all neutrino flavors are present in the background and that each flavor has two independent contributions from the thermal self-energy graph. It is now straightforward to obtain the lower bound on E ν where matter effects start to dominate, since we only need to replace T ν R → T ν L in (8). In this way we obtain…”

“…The refractive potential can be easily calculated via the real part of the neutrino thermal selfenergy due to photon-magnetic moment interaction [8]. Let us stress that a graph with a cut through the photonic line vanishes because of gauge invariance.…”