Heavy-quark production in gluon fusion at two loops in QCD

M Czakon,A Mitov,S Moch

doi:10.1016/j.nuclphysb.2008.02.001

Abstract

We present the two-loop virtual QCD corrections to the production of heavy quarks in gluon fusion. The results are exact in the limit when all kinematical invariants are large compared to the mass of the heavy quark up to terms suppressed by powers of the heavy-quark mass. Our derivation uses a simple relation between massless and massive QCD scattering amplitudes as well as a direct calculation of the massive amplitude at two loops. The results presented here together with those obtained previously for quark–quark scattering form important parts of the next-to-next-to-leading order QCD corrections to heavy-quark production in hadron–hadron collisions.

Highlights

The production of heavy quarks at hadron colliders is an important process for a range of reasons
In the high-energy regime on the other hand, when the heavy quarks are fast, logarithms in the quark mass m appear. These log(m)-terms are of collinear origin and dominate cross sections when m becomes negligible in comparison to other kinematical invariants, such as e.g. for the inclusive b-jet spectrum at large transverse momentum
We present results for the virtual Quantum Chromodynamics (QCD) corrections at two loops for the pair-production of heavy quarks in gluon fusion

Summary

Introduction

The production of heavy quarks at hadron colliders is an important process for a range of reasons. In the high-energy regime on the other hand, when the heavy quarks are fast, logarithms in the quark mass m appear These log(m)-terms are of collinear origin and dominate cross sections when m becomes negligible in comparison to other kinematical invariants, such as e.g. for the inclusive b-jet spectrum at large transverse momentum. In a nut-shell this results in an extremely simple universal multiplicative relation between a massive QCD amplitude in the small-mass limit and its massless version [25] In this way, we can largely use for our derivation the results of the NNLO QCD corrections to massless quark-gluon scattering (i.e. gg → qq). Appendix A gives the explicit result for a massive non-planar scalar integral in the small mass limit

Setting the stage

The massive amplitude from QCD factorization

Direct computation of the massive amplitude

Results

Conclusions