Three-loop jet function for boosted heavy quarks

A bstract We compute the inclusive jet function for boosted heavy quarks to $$ \mathcal{O}\left({\alpha}_s^3\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> . 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 ≪ 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 $$ \mathcal{O}\left({\alpha}_s^3\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> . We also confirmed that the $$ {n}_{\ell}^2{\alpha}_s^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>n</mml:mi> <mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:math> contribution, where n ℓ 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 ′ 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 ′ , 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 $$ \mathcal{O}\left({\alpha}_s^3\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> . Finally, we estimate the non-logarithmic contribution to the four-loop jet function based on renormalon dominance.