Thermal Production of Gravitinos

TL;DR

This paper derives the leading-order thermal production rate of gravitinos in supersymmetric QCD using hard thermal loop resummation, revealing a crucial logarithmic dependence on the gluon plasma mass and resolving cutoff ambiguities. By parallel analysis of axion production in a QED plasma, it also provides a byproduct rate for axions. The authors propagate the gravitino production rate into cosmology, showing that, for reheating temperatures around $T_R \sim 10^8$–$10^{10}$ GeV, gravitinos could constitute a significant portion of cold dark matter in certain mass ranges, while respecting BBN and NSP constraints. The study highlights the potential need for higher-order corrections due to the relatively large QCD coupling at these temperatures and emphasizes the central role of the thermal production rate in constraining SUSY cosmology and dark matter scenarios.

Abstract

We evaluate the gravitino production rate in supersymmetric QCD at high temperature to leading order in the gauge coupling. The result, which is obtained by using the resummed gluon propagator, depends logarithmically on the gluon plasma mass. As a byproduct, a new result for the axion production rate in a QED plasma is obtained. The implicatons for the cosmological dark matter problem are briefly discussed, in particular the intriguing possibility that gravitinos are the dominant part of cold dark matter.

Figures (6)

• Figure 1: Axion self energy; the blob denotes the resummed photon propagator.
• Figure 2: Axion production in electron-photon scattering.
• Figure 3: Gluon-gluino loop diagram, the leading contribution to the imaginary part of the gravitino self energy. The blob denotes a resummed gluon propagator.
• Figure 4: The density parameter $\Omega_{\tilde{G}} h^2$ for different gravitino masses $m_{\tilde{G}}$ as function of the reheating temperature $T_R$. The gluino mass has been set to $m_{\tilde{g}}=700$ GeV.
• Figure 5: Upper and lower bounds on the gluino mass and the NSP mass as functions of the gravitino mass. The full lines represent the upper bound on the gluino mass $m_{\tilde{g}} > m_{NSP}$ for different reheating temperatures from the closure limit constraint. The dashed line is the lower bound on $m_{NSP}$ which follows from the NSP lifetime.