Nonequilibrium LPM-resummed graviton emission from hard particles

Derive a complete nonequilibrium LPM-resummed treatment of graviton emission by hard gluons undergoing one or more soft scatterings during the in-medium cascade, in order to establish its contribution relative to the hard-soft process.

Background

The hard-component gravitational-wave calculation retains the leading hard-soft process, in which a non-thermal hard gluon scatters with a thermal gluon and emits a graviton. The paper also identifies a distinct possible contribution in which a hard gluon radiates a graviton while undergoing one or more soft scatterings, requiring a nonequilibrium LPM-resummed treatment.

A parametric estimate suggests that this contribution is suppressed by an additional power of the gauge coupling because the transverse-traceless projection removes the usual collinear enhancement. However, the authors explicitly qualify this as only a parametric argument and leave the complete calculation unresolved.

References

Since this argument is only parametric, we leave a complete nonequilibrium LPM-resummed analysis for future work.

— Gravitational Waves from Reheating beyond Instantaneous Thermalization  (2609.01480 - Mukaida et al., 1 Sep 2026) in Section 4.1, footnote following Eq. (local-hard-conversion-estimate)

A complete Standard-Model treatment would also include hard populations of other particle species and their corresponding scattering channels, and would require solving the coupled kinetic equations for the full Standard-Model cascade. These additional channels can modify the overall normalization of the spectrum. The parametric momentum dependence studied below is already present in the gluonic channel. We leave the full SM calculation for future work.

— Gravitational Waves from Reheating beyond Instantaneous Thermalization  (2609.01480 - Mukaida et al., 1 Sep 2026) in Section 4.1, paragraph following Eq. (hard-soft-process)