Three-loop jet function for boosted top quarks

TL;DR

This paper calculates the three-loop jet function for boosted top quarks using bHQET, enabling precise top mass measurements and improving theoretical predictions for collider experiments.

Contribution

It provides the first three-loop calculation of the boosted heavy-quark jet function, completing ingredients for N$^3$LL$^ extprime$ resummation and relating pole and short-distance mass schemes.

Findings

Results are consistent with non-Abelian exponentiation.

Reproduces known cusp and non-cusp anomalous dimensions at three loops.

Verifies n_l^2 α_s^3 contribution matches renormalon predictions.

Abstract

We present the calculation of the inclusive jet function for highly energetic heavy quarks at order $\mathcal{O}(\alpha_s^3)$ 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 $M^2 - m^2 \ll m^2$, 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 $n_\ell^2 \alpha_s^3$ contribution, with $n_\ell$ denoting the number of light quark flavors, agrees with predictions from renormalon calculus. This calculation completes the list of ingredients required for the N$^3$LL$^\prime$ 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 $\mathcal{O}(\alpha_s^3)$ and provide an estimate of the non-logarithmic part of the four-loop jet function based on renormalon dominance.