Closed-form expressions for tree-level gluon-gluon scattering: a framework for obtaining theoretical systematic uncertainties for jet-medium Monte Carlo simulations

Modern Bayesian theory-to-data comparisons for jet-medium interactions, such as [Phys. Rev. C 111,054913 (2025)], are lacking the careful accounting of theoretical systematic uncertainties included within their uncertainty budget. Tree-level gluon-gluon scattering is revisited to establish a framework capable of quantifying theoretical systematic uncertainties to be used in Bayesian jet-medium constraints. The behavior of tree-level scattering in thermal QCD is examined in detail, finding deviations away from the commonly used approximations. Deviations in the scattering rate affect jet-medium transport coefficients at the partonic level, leading to a more intricate kinematic dependence for $\widehat{q}$ and $\widehat{e}$ than, say, the well-known logarithmic behavior. These deviations away from well-known behavior are used to estimate theoretical systematic uncertainties in Bayesian analysis.