The Small Observed Baryon Asymmetry from a Large Lepton Asymmetry

TL;DR

The paper investigates whether a large lepton asymmetry can be compatible with the small observed baryon asymmetry. It shows that in the Standard Model, if the electron and muon lepton numbers cancel as $L_e=-L_μ$ (with $L_τ=0$), sphaleron processes naturally generate a baryon asymmetry of the correct order of magnitude (within a factor of two), aided by the small muon Yukawa coupling; for the presence of extra relativistic degrees of freedom, a nonzero electron-neutrino chemical potential $ξ_{ν_e}$ can reconcile the BBN predictions with observations. If the electroweak phase transition is not strongly first order, this mechanism yields $η$ in the ballpark of the observed value, while MSSM enhancements (e.g., large $\tanβ$) can fully account for the discrepancy. The authors also propose an Affleck–Dine–type mechanism to generate $L_e=-L_μ$ with $L_{total}=0$, requiring a high-scale operator and a reheating temperature $T_{RH} \lesssim 10^9$ GeV, and discuss the resulting implications for BBN, cosmology, and potential tests.

Abstract

Primordial Big-Bang Nucleosynthesis (BBN) tightly constrains the existence of any additional relativistic degrees of freedom at that epoch. However a large asymmetry in electron neutrino number shifts the chemical equilibrium between the neutron and proton at neutron freeze-out and allows such additional particle species. Moreover, the BBN itself may also prefer such an asymmetry to reconcile predicted element abundances and observations. However, such a large asymmetry appears to be in conflict with the observed small baryon asymmetry if they are in sphaleron mediated equilibrium. In this paper we point out the surprising fact that in the Standard Model, if the asymmetries in the electron number and the muon number are equal (and opposite) and of the size required to reconcile BBN theory with observations, a baryon asymmetry of the Universe of the correct magnitude and sign is automatically generated within a factor of two. This small remaining discrepancy is naturally remedied in the supersymmetric Standard Model.