Baryogenesis from Flat Directions of the Supersymmetric Standard Model

TL;DR

This paper shows that baryogenesis via the Affleck-Dine mechanism along MSSM flat directions is robust when two early-universe effects are included: nonrenormalizable superpotential terms lift flat directions at large field values and the finite energy density induces Hubble-scale soft masses that set the dynamics during inflation and the inflaton-dominated era. A negative Hubble-induced mass squared enables large vevs and, with $B$-violating $A$-terms active around $H o m_{3/2}$, generates a substantial baryon number which survives as the universe evolves. The final baryon-to-entropy ratio primarily depends on the dimension $n$ of the lifting operator and the reheating temperature $T_R$, with the LH$_u$ direction offering a link to the lightest neutrino mass. The analysis also discusses the cosmological moduli problem and proposes that enhanced-symmetry points could align early and late-time minima, offering a potential resolution, though the dilaton remains problematic. Overall, the paper argues that flat-direction baryogenesis is a robust and predictive mechanism within SUSY frameworks.

Abstract

Baryogenesis from the coherent production of a scalar condensate along a flat direction of the supersymmetric extension of the standard model (Affleck-Dine mechanism) is investigated. Two important effects are emphasized. First, nonrenormalizable terms in the superpotential can lift standard model flat directions at large field values. Second, the finite energy density in the early universe induces soft potentials with curvature of order the Hubble constant. Both these have important implications for baryogenesis, which requires large squark or slepton expectation values to develop along flat directions. In particular, the induced mass squared must be negative. The resulting baryon to entropy ratio is very insensitive to the details of the couplings and initial conditions, but depends on the dimension of the nonrenormalizable operator in the superpotential which stabilizes the flat direction and the reheat temperature after inflation. Unlike the original scenario, an acceptable baryon asymmetry can result without subsequent entropy releases. In the simplest scenario the baryon asymmetry is generated along the $LH_u$ flat direction, and is related to the mass of the lightest neutrino.