Three-loop jet function for boosted heavy quarks

TL;DR

This paper calculates the three-loop jet function for boosted heavy quarks within bHQET, enabling precise predictions for top quark mass measurements at colliders and advancing theoretical understanding of jet radiation effects.

Contribution

It provides the first complete three-loop calculation of the boosted heavy-quark jet function, verifying key theoretical properties and supporting high-precision top quark mass determinations.

Findings

Verified non-Abelian exponentiation at three loops.

Confirmed known anomalous dimensions at $ ext{O}( ext{α}_s^3)$.

Estimated non-logarithmic contributions to four-loop jet function.

Abstract

We compute the inclusive jet function for boosted heavy quarks to $\mathcal{O}(\alpha_s^3)$. The jet function is defined and calculated in the framework of boosted Heavy-Quark Effective Theory (bHQET). It describes the effect of radiation collimated in narrow jets arising from energetic heavy quarks on observables probing the jet invariant mass $M$ in the region where $M^2 - m^2 \ll m^2$, with $m$ the heavy quark mass. This kinematic situation is relevant e.g. in boosted top (pair) production at high-energy colliders. We have verified that our result satisfies non-Abelian exponentiation and checked that our calculation reproduces the known cusp and non-cusp anomalous dimensions of the jet function to $\mathcal{O}(\alpha_s^3)$. We also confirmed that the $n_\ell^2\alpha_s^3$ contribution, where $n_\ell$ is the number of massless quark flavors, agrees with the prediction from renormalon calculus. Our computation provides the last missing piece to obtain the N$^3$LL$^\prime$ resummed (self-normalized) thrust distribution used for the calibration of the top quark mass parameter in parton-shower Monte Carlo generators. Our result also contributes to the invariant mass distribution of reconstructed top quarks at N$^3$LL$^\prime$, which can be employed for a precise top mass determination at future lepton colliders. As a by-product, we obtain the relation between the pole and short-distance jet-mass schemes at $\mathcal{O}(\alpha_s^3)$. Finally, we estimate the non-logarithmic contribution to the four-loop jet function based on renormalon dominance.