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Q-Balls and Baryogenesis in the MSSM

Kari Enqvist, John McDonald

TL;DR

This work demonstrates that Q-balls arise naturally in the MSSM with gravity-mediated SUSY breaking, occupying distinct roles along flat directions: L-balls with TeV-scale minima and small charges along $H_uL$, and large-charge B-balls along squark directions ($u^c d^c d^c$, $u^c u^c d^c e^c$). It shows that large B-balls can form during Affleck-Dine baryogenesis and decay after the electroweak transition, providing a novel route to the baryon asymmetry that remains viable even with L-violating processes or $B-L$ conservation. The paper analyzes Q-ball solutions, their radii and charges (thick- vs thin-wall regimes), the impact of radiative corrections, and the inflationary seed perturbations that trigger fragmentation, then discusses cosmological consequences including bounds on the reheating temperature and potential links to dark matter or inhomogeneous nucleosynthesis. Overall, it presents Q-ball decay as a robust alternative to condensate decay for baryogenesis in MSSM cosmology, motivating further study of formation dynamics, thermalization, and observational implications.

Abstract

We show that Q-balls naturally exist in the Minimal Supersymmetric Standard Model (MSSM) with soft SUSY breaking terms of the minimal N=1 SUGRA type. These are associated with the F- and D-flat directions of the scalar potential once radiative corrections are taken into account. We consider two distinct cases, corresponding to the "H_u L" (slepton) direction with L-balls and the "udd" and "uude" (squark) directions with B-balls. The L-ball always has a small charge, typically of the order of 1000, whilst the B-ball can have an arbitrarily large charge, which, when created cosmologically by the collapse of an unstable Affleck-Dine condensate, is likely to be greater that 10^14. The B-balls typically decay at temperatures less than that of the electroweak phase transition, leading to a novel version of Affleck-Dine baryogenesis, in which the B asymmetry comes from Q-ball decay rather than condensate decay. This mechanism can work even in the presence of additional L violating interactions or B-L conservation, which would rule out conventional Affleck-Dine baryogenesis.

Q-Balls and Baryogenesis in the MSSM

TL;DR

This work demonstrates that Q-balls arise naturally in the MSSM with gravity-mediated SUSY breaking, occupying distinct roles along flat directions: L-balls with TeV-scale minima and small charges along , and large-charge B-balls along squark directions (, ). It shows that large B-balls can form during Affleck-Dine baryogenesis and decay after the electroweak transition, providing a novel route to the baryon asymmetry that remains viable even with L-violating processes or conservation. The paper analyzes Q-ball solutions, their radii and charges (thick- vs thin-wall regimes), the impact of radiative corrections, and the inflationary seed perturbations that trigger fragmentation, then discusses cosmological consequences including bounds on the reheating temperature and potential links to dark matter or inhomogeneous nucleosynthesis. Overall, it presents Q-ball decay as a robust alternative to condensate decay for baryogenesis in MSSM cosmology, motivating further study of formation dynamics, thermalization, and observational implications.

Abstract

We show that Q-balls naturally exist in the Minimal Supersymmetric Standard Model (MSSM) with soft SUSY breaking terms of the minimal N=1 SUGRA type. These are associated with the F- and D-flat directions of the scalar potential once radiative corrections are taken into account. We consider two distinct cases, corresponding to the "H_u L" (slepton) direction with L-balls and the "udd" and "uude" (squark) directions with B-balls. The L-ball always has a small charge, typically of the order of 1000, whilst the B-ball can have an arbitrarily large charge, which, when created cosmologically by the collapse of an unstable Affleck-Dine condensate, is likely to be greater that 10^14. The B-balls typically decay at temperatures less than that of the electroweak phase transition, leading to a novel version of Affleck-Dine baryogenesis, in which the B asymmetry comes from Q-ball decay rather than condensate decay. This mechanism can work even in the presence of additional L violating interactions or B-L conservation, which would rule out conventional Affleck-Dine baryogenesis.

Paper Structure

This paper contains 16 sections, 43 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Q-balls and radiatively corrected flat directions in the MSSM
  3. Flat directions in the MSSM
  4. $H_{u}L$ direction
  5. $u^{c}d^{c}d^{c}$ direction
  6. $u^{c}u^{c}d^{c}e^{c}$ direction
  7. Q-ball solutions
  8. Q-ball equation of motion
  9. $H_{u}L$ direction
  10. $u^{c}d^{c}d^{c}$ and $u^{c}u^{c}d^{c}e^{c}$ directions
  11. Q-Ball Cosmology
  12. AD baryogenesis and Q-ball formation
  13. Seed perturbations from quantum fluctuations during inflation
  14. Negative pressure and Q-Ball formation
  15. Cosmological consequences of Q-balls in the MSSM
  16. ...and 1 more sections

Figures (2)

  • Figure 1: a) The running of the mass in the $H_uL$ direction (lower set of curves) for the susy parameters (a) $m_0=0,~A(M_X)=0,~\mu_H=2.55$, (b) $m_0=0,~A(M_X)=-3,~\mu_H=2.4$ and (c) $m_0=1,~A(M_X)=-1,~\mu_H=2.5$, all in units of the common gaugino mass; for comparision, the running of the physical Higgs mass is also shown (upper set of curves). b) The Q-ball potential for the case (a).
  • Figure 2: Q-ball decay temperature $T$ vs. the charge $Q$. The regions where L-balls and B-balls exist are also indicated.