Alberto M. Clavero | Searcharxiv

arXiv2026

Three-loop jet function for boosted top quarks

We present the calculation of the inclusive jet function for highly energetic heavy quarks at order $\mathcal{O}(α_s^3)$ 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 $n_\ell^2 α_s^3$ 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 $\mathcal{O}(α_s^3)$ and provide an estimate of the non-logarithmic part of the four-loop jet function based on renormalon dominance.

hep-ph↗

arXiv2025

Three-loop jet function for boosted heavy quarks

We compute the inclusive jet function for boosted heavy quarks to $\mathcal{O}(α_s^3)$. 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 $\mathcal{O}(α_s^3)$. We also confirmed that the $n_\ell^2α_s^3$ 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 $\mathcal{O}(α_s^3)$. Finally, we estimate the non-logarithmic contribution to the four-loop jet function based on renormalon dominance.

hep-ph↗