The Effect of the Sparticle Mass Spectrum on the Conversion of B-L to B

TL;DR

This work shows that the conversion from B-L to B in SUSY frameworks is sensitive to the sparticle mass spectrum, and it provides explicit formulas that incorporate kinematic effects through κ-type quantities. By analyzing cases with and without lepton flavor equilibrium, the authors demonstrate that B/(B-L) can deviate significantly from the standard 8/23 value and even change sign, depending on which sparticles are light. The results imply that leptogenesis/baryogenesis predictions and gravitino bounds can be appreciably altered in MSSM-like models, offering a framework to assess B generation given a SUSY spectrum. Near the electroweak transition temperature, the derived relations help quantify how MSSM particle content influences the final baryon asymmetry.

Abstract

In the context of many leptogenesis and baryogenesis scenarios, B-L (baryon minus the lepton number) is converted into B (baryon number) by non-perturbative B+L violating operators in the SU(2)_L sector. We correct a common misconversion of B-L to B in the literature in the context of supersymmetry. More specifically, kinematic effects associated with the sparticle masses can be generically important (typically a factor of 2/3 correction in mSUGRA scenarios), and in some cases, it may even flip the sign between B-L and B. We give explicit formulae for converting B-L to B for temperatures approaching the electroweak phase transition temperature from above. Enhancements of B are also possible, leading to a mild relaxation of the reheating temperature bounds coming from gravitino constraints.

Figures (4)

• Figure 1: Yukawa rates $R^{(f_1,\widetilde{S},\widetilde{f}_2)}$ over $m_{\widetilde{f}_2}$. We have taken $T=100\,{\rm GeV}$, $m_{f_1}=0\,{\rm GeV}$ and $m_{\widetilde{S}}=100\,{\rm GeV}$ (blue solid), $m_{\widetilde{S}}=400\,{\rm GeV}$ (red dotted).
• Figure 2: Triscalar rates $R^{\widetilde{f}_1,S,\widetilde{X}_2}$ over $m_{\widetilde{f}_2}$. We have taken $T=100\,{\rm GeV}$, $m_{S}=100\,{\rm GeV}$ and $m_{\widetilde{f}_1}=100\,{\rm GeV}$ (blue), $m_{\widetilde{f}_1}=400\,{\rm GeV}$ (red dotted).
• Figure 3: We plot $B/(B-L)$ as a function of $\kappa_{Q}$ with other $\vec{\kappa}$ components chosen at random with a flat distribution between their maximum values. The solid line corresponds to $8/23$, a value which is often cavalierly used in the literature and the dashed line corresponds to the typical mSUGRA value of $38/167$. Clearly, the baryon asymmetry is enhanced as more left handed squarks become lighter.
• Figure 5: We plot $B/(B-L)$ as a function of $B/3-L_1$ with other $\vec{P}$ components chosen at random with a flat distribution between their maximum values, except for $B/3-L_3$ which has been set to zero. The solid line corresponds to the value $0.23$, valid for a typical mSUGRA model, and the dashed line corresponds to Eq. (\ref{['eq:msugralinearcurve']}), the mSUGRA situation with two flavors contributing to $B-L$. Note that $B/(B-L)$ can go negative even when $(B/3-L_1)/(B-L)\sim \mathcal{O}(1)$.