PHYSICAL REVIEW D 92, 125020 (2015) Majorana neutrino magnetic moment and neutrino decoupling in big bang nucleosynthesis † ‡ N. Vassh,1,* E. Grohs,2, A. B. Balantekin,1, and G. M. Fuller3,§ 1Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA 2Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA 3Department of Physics, University of California, San Diego, La Jolla, California 92093, USA (Received 1 October 2015; published 22 December 2015) We examine the physics of the early universe when Majorana neutrinos (νe, νμ, ντ) possess transition magnetic moments. These extra couplings beyond the usual weak interaction couplings alter the way neutrinos decouple from the plasma of electrons/positrons and photons. We calculate how transition magnetic moment couplings modify neutrino decoupling temperatures, and then use a full weak, strong, and electromagnetic reaction network to compute corresponding changes in big bang nucleosynthesis abundance yields. We find that light element abundances and other cosmological parameters are sensitive to −10 magnetic couplings on the order of 10 μB. Given the recent analysis of sub-MeV Borexino data which −11 constrains Majorana moments to the order of 10 μB or less, we find that changes in cosmological parameters from magnetic contributions to neutrino decoupling temperatures are below the level of upcoming precision observations. DOI: 10.1103/PhysRevD.92.125020 PACS numbers: 13.15.+g, 26.35.+c, 14.60.St, 14.60.Lm I. INTRODUCTION Such processes alter the primordial abundance yields which can be used to constrain the allowed sterile neutrino mass In this paper we explore how the early universe, and the and magnetic moment parameter space [4]. weak decoupling/big bang nucleosynthesis (BBN) epochs Since the magnetic moment interaction always changes in particular, respond to new neutrino sector physics in the the helicity of the incoming neutrino, Dirac neutrinos in form of beyond-the-standard model neutrino magnetic particular have been of interest in BBN research due to their moments. Small electromagnetic couplings of neutrinos, ability to populate the “wrong” helicity states. For instance e.g., magnetic moments, may have effects in the early studies of the spin-flip rate in a primordial magnetic field universe, where neutrinos determine much of the energetics [5] and primordial plasmon decay into νν¯ pairs [6] are and composition (e.g., isospin). Examinations of the role centered around the possibility of generating right-handed that neutrino magnetic channels can play in astrophysics neutrino states. If the neutrino is a Dirac particle, magnetic and cosmology began long before laboratory experiments, interactions between the neutrinos and charged leptons such as GEMMA [1], ever attempted to detect beyond-the- could keep the right-handed states in thermal, Fermi-Dirac standard model magnetic moments. Any plasma environ- equilibrium with the left-handed states. The higher energy ment in which neutrinos are produced in copious amounts, ∼3 ∼6 density would increase Neff from to which is in such as the Sun and supernovae, is susceptible to the disagreement with current observations [7]. This has lead possibility of small neutrino magnetic moments having many authors to examine limits on the magnetic moments observable consequences. Since neutrinos are a dominant of Dirac neutrinos by constraining the production of right- constituent of the early universe during the BBN era, this handed states during times earlier than BBN such as the environment is sensitive to the additional interactions that QCD epoch [8–11]. Morgan [8] and Fukugita et al. [9] use the magnetic channels provide. For example, changes in the an approximate neutrino-electron scattering cross section 4 νν¯ primordial He abundance due to annihilation into to quantify the production of these helicity states. Elmfors electron-positron pairs were used to provide limitations et al. [10] and Ayala et al. [11] perform numerical treat- on the mass and magnetic moment of tau neutrinos before ments of the right-handed production rate by considering experiment was able to exclude tau neutrino mass of order the proper photon propagator in an electron-positron MeV [2,3]. Similarly, massive sterile neutrinos have the plasma. These analyses then require that these helicity ability to magnetically decay into a light neutrino while states have decoupled prior to BBN. The connection with injecting a nonthermal photon into the primordial plasma. BBN comes through either comparisons of the expansion rate and right-handed interaction rate or in the case of [9] through constraining the number density of right-handed *[email protected] † [email protected] states. Therefore the limits on the magnetic moment ‡ [email protected] of neutrinos that these works produce are necessarily §[email protected] functions of the right-handed decoupling temperature. 1550-7998=2015=92(12)=125020(13) 125020-1 © 2015 American Physical Society N. VASSH et al. PHYSICAL REVIEW D 92, 125020 (2015) −11 Fukugita et al. [9] obtain μν < 7 × 10 μB for a right- difficult to solve in the general case, but become simpler in ≃ handed neutrino decoupling temperature of Tdec the homogeneous and isotropic conditions of the early 100 MeV. Elmfors et al. [10] and Ayala et al. [11] obtain universe [24–34]. In contrast to the solar and supernovae −11 −10 μν < 6.2 × 10 μB and μν < 2.9 × 10 μB respectively environments, the literature on the role of Majorana neutrino ≃ 100 (also for Tdec MeV). However, limitations on the transition moments in BBN is sparse. To the best of our magnetic interaction of neutrinos which appeal to the need knowledge the only investigation of Majorana moments in to avoid right-handed states are only applicable to Dirac the early universe appeals to an active-sterile transition neutrinos. A right-handed Majorana neutrino behaves as an moment [35] in the presence of a primordial magnetic field. antineutrino and so would not cause a sizable increase in In this paper, we examine effects of the Majorana the effective number of neutrino species. Since for this neutrino transition moments in the early universe without paper we will consider the case of Majorana neutrinos, invoking sterile neutrinos or primordial magnetic fields. inclusion of the magnetic channels can keep the neutrinos If its transition magnetic moments are large enough, a given interacting with the primordial plasma into the BBN era. active neutrino species can remain coupled to the electro- This allows us to examine explicitly the connection magnetic plasma into the BBN epoch. In the early universe, between neutrino magnetic moment and BBN observables a Majorana neutrino can magnetically interact with elec- such as the primordial abundances and Neff. trons and positrons as well as photons and other neutrinos. In addition to helicity considerations, magnetic inter- However magnetic neutrino-neutrino scattering and inter- actions of Majorana neutrinos differ from the Dirac case in actions between neutrinos and photons (such as neutrino that Majorana dipole moments are necessarily transition Compton scattering) are proportional to the fourth power of moments. Dirac neutrinos can have both diagonal and the magnetic moment [36] and so are suppressed relative to nondiagonal moments, but Majorana neutrino diagonal interactions with electrons and positrons which are propor- moments are identically zero [12]. This implies that for tional to the second power of the magnetic moment. Here we Majorana neutrinos the magnetic channels must occur with explore effects on the primordial abundances when enhanced − − flavor changing currents such as νe þ e → ν¯μ þ e and interactions between electrons/positrons and Majorana neu- þ − νe þ νμ → e þ e . Constraints on the effective magnetic trinos via magnetic scattering and annihilation channels are moment of neutrinos measured by experiments such as taken into account. In Sec. II we demonstrate how magnetic TEXONO [13] and GEMMA are not readily applicable to neutrino-electron scattering can play a significant role in a the transition magnetic moments of Majorana neutrinos. relatively low temperature environment such as the early Experimental upper bounds need to be converted into limits universe. In Sec. III we find the neutrino interaction rate for the case of thermal equilibrium by introducing expressions on transition moments, μxy, where subscripts x and y denote the neutrino states coupling to the photon. Such constraints for the thermally averaged cross section times Moller were first found in [14] using available solar þ reactor velocity which make use of Fermi-Dirac statistics. We use these interaction rates to find neutrino decoupling temper- scattering data from experiments such as SNO, SuperK, μ ROVNO and MUNU. A recent analysis of sub-MeV atures as a function of the transition magnetic moments eμ, μ τ,andμμτ. In Sec. IV we explore the corresponding change Borexino scattering data [15] found constraints on the e in the predicted abundances and N when these decoupling three Majorana transition moments in the mass basis to be eff temperatures are implemented in a modified version of μ ≤ ½3.1–5.6 × 10−11μ [16]. These new limits given by ij B the Wagoner-Kawano (WK)code[37,38]. We conclude in Borexino data are stronger than those found from MUNU Sec. V. Appendix A discusses the inverse Debye screening and TEXONO data, and secondary only to constraints length at all temperatures for an electron-positron plasma from GEMMA data which for Majorana moments are μ ≤ ½2 9–5 0 10−11μ which is used here to demonstrate that the magnetic ij . × B [16]. scattering cross section is finite. Appendix B shows the The most restrictive constraint on Dirac and Majorana derivation of the interaction rate expressions employed here dipole moments comes from astrophysics by considering which are functions of the cross section. All relevant cross how energy loss due to plasmon decay in red giant stars sections are listed in Appendix C. Throughout this paper, we affects the core mass at the helium flash [17].