We compute the inclusive jet function for boosted heavy quarks to \( \mathcal{O}\left({\alpha}_s^3\right) \) . 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 – m2 ≪ m2, 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 \( \mathcal{O}\left({\alpha}_s^3\right) \) . We also confirmed that the \( {n}_{\ell}^2{\alpha}_s^3 \) contribution, where nℓ is the number of massless quark flavors, agrees with the prediction from renormalon calculus. Our computation provides the last missing piece to obtain the N3LL′ 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 N3LL′, 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 \( \mathcal{O}\left({\alpha}_s^3\right) \) . Finally, we estimate the non-logarithmic contribution to the four-loop jet function based on renormalon dominance.
