Regulating the Baryon Asymmetry in No-Scale Affleck-Dine Baryogenesis
Bruce A. Campbell, Mary K. Gaillard, Hitoshi Murayama, Keith A. Olive
TL;DR
The paper investigates why Affleck-Dine baryogenesis in no-scale supergravity with a Heisenberg symmetry tends to overproduce the baryon asymmetry after inflation and identifies several robust suppression mechanisms. It shows that one-loop corrections generate negative masses for most flat directions, driving large vevs and BAU unless regulated, and analyzes dilution by moduli or inflaton decay, nonrenormalizable gravitational operators, and GUT-scale interactions as viable controls. It demonstrates that gravitationally induced quartic operators in the MSSM can naturally yield the observed BAU, while GUT-induced lifting of flat directions must be carefully arranged (GUT-flat vs GUT-non-flat) to avoid overproduction, and that sphaleron dynamics can further reduce BAU via the Kuzmin-Rubakov-Shaposhnikov effect. The results highlight a set of plausible, interconnected pathways—including higher-dimension operators and GUT structure—that align the AD mechanism with cosmological observations, with implications for string/M-theory realizations of unification. The analysis emphasizes that the BAU outcome is sensitive to the interplay between inflationary dynamics, higher-dimensional operators, and late-time entropy production.
Abstract
In supergravity models (such as standard superstring constructions) that possess a Heisenberg symmetry, supersymmetry breaking by the inflationary vacuum energy does not lift flat directions at tree level. One-loop corrections give small squared masses that are negative (about -g^2 H^2/(4π)^2) for all flat directions that do not involve the stop. After inflation, these flat directions generate a large baryon asymmetry; typically $n_B/s \sim$ O(1). We consider mechanisms for suppressing this asymmetry to the observed level. These include dilution from inflaton or moduli decay, GUT nonflatness of the $vev$ direction, and higher dimensional operators in both GUT models and the MSSM. We find that the observed BAU can easily be generated when one or more of these effects is present.