On the Thermal Regeneration Rate for Light Gravitinos in the Early Universe

TL;DR

This work reassesses the thermal regeneration rate of light gravitinos in the early Universe within N=1 supergravity. Using the Goldstino effective Lagrangian and Braaten–Pisarski resummation, the authors show that finite-temperature corrections to the gravitino mass and Goldstino coupling are negligible for the relevant temperature range, validating the helicity-1/2 gravitino–Goldstino equivalence in a hot plasma. They derive a leading-regime regeneration rate Γ_G that scales as $T^3$ with a logarithmic enhancement: Γ_G ≈ $\frac{1}{16} (1 + N_f/6) \left|\frac{m_{\rm soft}}{F}\right|^2 T^3 α_s(T) \log(1/α_s(T)) [1 + α_s(T) \log(1/α_s(T)) + T^2/|F|]$, and discuss subleading corrections. The cosmological implications indicate that gravitino regeneration does not force severely low reheating temperatures and remains compatible with baryogenesis mechanisms such as Affleck–Dine or leptogenesis, resolving tensions with Fischler’s earlier claim.

Abstract

We investigate the light gravitino regeneration rate in the early Universe in models based on $N=1$ supergravity. Motivated by a recent claim by Fischler, we evaluate finite-temperature effects on the gravitino regeneration rate due to the hot primordial plasma for a wide range of the supersymmetry-breaking scale $F$. We find that thermal corrections to the gravitino pole mass and to the Goldstino coupling are negligible for a wide range of temperatures, thereby justifying the extension of the equivalence theorem for the helicity-1/2 gravitino and Goldstino to a hot primordial plasma background. Utilizing the Braaten-Pisarski resummation method, the helicity-1/2 gravitino regeneration rate is found to be $0.25 α_s(T) \log(1/α_s(T))|{m_{\rm soft}/F}|^2 T^3(1 + α_s(T) \log(1/α_s(T)) + T^2 / |F|)$ up to a calculable, model-dependent ${\cal O}(1)$ numerical factor. We review the implications of this regeneration rate for supergravity cosmology, focusing in particular on scenaria for baryogenesis.

Figures (4)

• Figure 1: Thermal mass correction to the gravitino mass. Crosses denote insertions of the soft masses for the matter and gluino fields. The dashed line represents a matter scalar field, the solid lines matter fermion and gluino fields.
• Figure 2: Thermal Goldstino vertex correction. The blobs denote thermal corrections to the gluino-gluon-Goldstino and to the matter fermion-scalar-Goldstino couplings.
• Figure 3: Thermal correction to the Goldstino self-energy. The blobs in the propagators are thermal self-energies for the gluon and gluino respectively. The blob is at the gluino-gluon-Goldstino vertex, which is the same as the zero-temperature vertex, as argued in Section 2.
• Figure 4: Two contributions to the Goldstino self energy. (a) For hard thermal loops, the resummed gluon propagator is the dominant effect. (b) For soft thermal loops, thermal corrections to the gluino and to the vertex are the dominant effects.