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Large lepton asymmetry from Q-balls

M. Kawasaki, Fuminobu Takahashi, Masahide Yamaguchi

TL;DR

This work tackles the tension between a large lepton asymmetry and a small baryon asymmetry by employing Affleck-Dine leptogenesis in the MSSM followed by the formation of long-lived $L$-balls (Q-balls) that trap almost all lepton charge. By choosing the flat direction $e^{c}LL$, the scenario yields a positive electron-type lepton asymmetry $L_e$ while the total lepton number is negative, and a small evaporated fraction before the electroweak transition is converted into baryons via sphalerons, producing $n_B/s$ in the range $\sim 10^{-11}-10^{-10}$. The surviving lepton asymmetry is released after electroweak symmetry breaking but before BBN, giving a sizable electron-neutrino degeneracy parameter $\xi_{\nu_e}$ on the order of $0.01$–$0.1$ for viable $(m_{3/2}, M_F, T_{RH})$ in gauge-mediated SUSY. The authors identify two viable parameter regions and discuss potential effects of neutrino oscillations on equilibration, noting that the timing of $L$-ball decay can preserve the scenario under current bounds from BBN and CMB observations.

Abstract

We propose a scenario which can explain large lepton asymmetry and small baryon asymmetry simultaneously. Large lepton asymmetry is generated through Affleck-Dine (AD) mechanism and almost all the produced lepton numbers are absorbed into Q-balls (L-balls). If the lifetime of the L-balls is longer than the onset of electroweak phase transition but shorter than the epoch of big bang nucleosynthesis (BBN), the large lepton asymmetry in the L-balls is protected from sphaleron effects. On the other hand, small (negative) lepton numbers are evaporated from the L-balls due to thermal effects, which are converted into the observed small baryon asymmetry by virtue of sphaleron effects. Large and positive lepton asymmetry of electron type is often requested from BBN. In our scenario, choosing an appropriate flat direction in the minimal supersymmetric standard model (MSSM), we can produce positive lepton asymmetry of electron type but totally negative lepton asymmetry.

Large lepton asymmetry from Q-balls

TL;DR

This work tackles the tension between a large lepton asymmetry and a small baryon asymmetry by employing Affleck-Dine leptogenesis in the MSSM followed by the formation of long-lived -balls (Q-balls) that trap almost all lepton charge. By choosing the flat direction , the scenario yields a positive electron-type lepton asymmetry while the total lepton number is negative, and a small evaporated fraction before the electroweak transition is converted into baryons via sphalerons, producing in the range . The surviving lepton asymmetry is released after electroweak symmetry breaking but before BBN, giving a sizable electron-neutrino degeneracy parameter on the order of – for viable in gauge-mediated SUSY. The authors identify two viable parameter regions and discuss potential effects of neutrino oscillations on equilibration, noting that the timing of -ball decay can preserve the scenario under current bounds from BBN and CMB observations.

Abstract

We propose a scenario which can explain large lepton asymmetry and small baryon asymmetry simultaneously. Large lepton asymmetry is generated through Affleck-Dine (AD) mechanism and almost all the produced lepton numbers are absorbed into Q-balls (L-balls). If the lifetime of the L-balls is longer than the onset of electroweak phase transition but shorter than the epoch of big bang nucleosynthesis (BBN), the large lepton asymmetry in the L-balls is protected from sphaleron effects. On the other hand, small (negative) lepton numbers are evaporated from the L-balls due to thermal effects, which are converted into the observed small baryon asymmetry by virtue of sphaleron effects. Large and positive lepton asymmetry of electron type is often requested from BBN. In our scenario, choosing an appropriate flat direction in the minimal supersymmetric standard model (MSSM), we can produce positive lepton asymmetry of electron type but totally negative lepton asymmetry.

Paper Structure

This paper contains 4 sections, 28 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Affleck-Dine mechanism and Q-ball formation
  3. Large Lepton Asymmetry from L-ball
  4. Discussion and conclusions

Figures (2)

  • Figure 1: The allowed region for $m_{3/2}$, $M_{F}$ and $T_{RH}$, where our scenario succeeds and the baryon to entropy ratio satisfies the following bounds : $10^{-11} \mathop{}_{ \sim}^{ <} n_B/s \mathop{}_{ \sim}^{ <} 10^{-10}$. Note that there does not exist any upper bound on $T_{RH}$ from the gravitino problem MMYGouvea, since the L-balls dominate the universe and their decay temperature is rather low. The two separate allowed region roughly corresponds to the cases A and B discussed in the text.
  • Figure 2: The contours of the electron neutrino degeneracy are shown. The trapeziform area between two solid lines represents the allowed region where our scenario works and the baryon to entropy ratio satisfies the bounds: $10^{-11} \mathop{}_{ \sim}^{ <} n_B/s \mathop{}_{ \sim}^{ <} 10^{-10}$. The contours represents $\xi_{\nu_e} = 0.005,~0.01,~0.02,~0.06,~0.1$ from top to bottom.