Thermal production of gravitinos

TL;DR

This work refines the thermal production rate of gravitinos in the early universe by incorporating (i) 1→2 decays enabled by thermal masses, (ii) the top Yukawa coupling, and (iii) a realistic treatment of reheating instead of the instantaneous maximal temperature. By computing the gravitino propagator with resummed finite‑temperature propagators and applying subtraction to avoid double counting, the authors obtain a total rate γ = γ_D + γ_S^{sub} + γ_top that is approximately twice the previous estimates at MSSM couplings. The results tighten the upper bound on the reheating temperature and have significant implications for gravitino dark matter and leptogenesis scenarios, while also offering broader insights into finite‑temperature SUSY theories and gravitino couplings. A central conceptual outcome is the equivalence between the production rates of the spin‑3/2 gravitino and the spin‑1/2 Goldstino at high energies, up to universal prefactors, even after accounting for thermal masses and gauge interactions.

Abstract

We reconsider thermal production of gravitinos in the early universe, adding to previously considered 2 -> 2 gauge scatterings: a) production via 1 -> 2 decays, allowed by thermal masses; b) the effect of the top Yukawa coupling; c) a proper treatment of the reheating process. Our final result behaves physically (larger couplings give a larger rate) and is twice larger than previous results, implying e.g. a twice stronger constraint on the reheating temperature. Accessory results about (supersymmetric) theories at finite temperature and gravitino couplings might have some interest.

Figures (12)

• Figure 1: Functions $f_3$, $f_2$ and $f_1$ that, as summarized in section \ref{['fNsummary']}, describe our result for the gravitino production rate from ${\rm SU}(3)_c$ (upper continuous curve, in red), ${\rm SU}(2)_L$ (middle continuous curve, in blue), ${\rm U}(1)_Y$ (lower continuous curve, in green) gauge interactions. The arrows indicate the MSSM values of the thermal mass at $T\sim 10^{9}\,{\rm GeV}$. The lower dashed curve shows the result from Buch, which agrees with our result in the limit of small gauge coupling, and behaves unphysically for relevant ${\cal O}(1)$ values of the MSSM gauge couplings.
• Figure 2: Some Feynman diagrams that contribute to the imaginary part of the gravitino propagator. Thick lines denote resummed thermal propagators for the gluon $g$ and gluino $\lambda$. We do not plot diagrams involving quarks $q$ and squarks $\tilde{q}$, but they are of course included in our computation.
• Figure 3: Two-loop Feynman diagrams that appear in the expansion of diagram ${\rm D}$, that resums all higher loop diagrams with iterated one-loop corrections to gluon and gluino propagators.
• Figure 4: Feynman diagrams that contribute to $gg\to \lambda\Psi$ scatterings.
• Figure 5: Feynman diagrams that contribute to $g\lambda\to g\Psi$ scatterings.