Three-loop jet function for boosted heavy quarks

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.

28 pages + appendices, 7 figures. v2: Few typos fixed, included extra sentences to clarify some technical points, missing references added. Journal version

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