Massive lighter quark corrections to boosted-top cross section

¹ Departamento de Física Teórica, Universidad Autónoma de Madrid, E-28049, Madrid, Spain
² Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca, E-37008 Salamanca, Spain
³ Instituto de Física Teórica UAM-CSIC, E-28049 Madrid, Spain
⁴ Instituto de Física Corpuscular UV-CSIC, E-46980 Valencia, Spain

^* e-mail: alejandro.bris@uam.es
^** e-mail: vmateu@usal.es
^*** e-mail: Fernando.Gil@ific.uv.es

Published online: 22 December 2022

Abstract

In this work we present the computation of the missing pieces to get the bHQET thrust distribution with non-vanishing secondary quark masses at NNLO: the jet and hard functions. The difference with respect to the massless case is encoded in diagrams with massive-quark bubbles. For its computation we use a Mellin Barnes representation of the dispersive integral method that permits expressing the result as an analytic, fast-converging expansion in powers of a small parameter rather than integrals that can only be solved numerically. We also obtain the matching coefficient present when integrating out the quark mass. It is necessary for a continuous top-down running and to verify the consistency check.