We present the calculation of the inclusive jet function for highly energetic heavy quarks at order O (ₛ³) using boosted Heavy-Quark Effective Theory (bHQET). This jet function describes the effect of collinear radiation emitted by energetic heavy quarks on observables dependent on the jet invariant mass M. In particular, we focus on the regime M² - m² m², which is relevant for boosted top quark production at high-energy colliders in the resonance region. Our results are consistent with non-Abelian exponentiation and reproduce the known cusp and non-cusp anomalous dimensions up to three loops. We also verify that the n_² ₛ³ contribution, with n_ denoting the number of light quark flavors, agrees with predictions from renormalon calculus. This calculation completes the list of ingredients required for the N³LL^ resummed (self-normalized) thrust distribution, an essential component for calibrating the top quark mass parameter in parton-shower Monte Carlo generators. It likewise contributes to the invariant-mass distribution of reconstructed top quarks, enabling precise mass determinations at future lepton colliders. Finally, we determine the relation between the pole and two short-distance jet-mass schemes at O (ₛ³) and provide an estimate of the non-logarithmic part of the four-loop jet function based on renormalon dominance.
Barreda et al. (Thu,) studied this question.