Analytic Calculation of Two Loop Corrections to Heavy Quark Pair Production Vertices Induced by Light Quarks

TL;DR

This work provides analytic non-singlet $\mathcal{O}(\alpha_s^2)$ corrections from light quarks to heavy-quark pair production rates for vector, axial-vector, scalar and pseudoscalar currents, valid above threshold and expressed through moments of the light-quark vacuum polarization. The authors introduce the method of the moments, derive both virtual and real radiation contributions, and show how to translate results into the ${\overline{\mathrm{MS}}}$ scheme and full QCD with proper color factors. They also analyze the near-threshold region, showing that the leading non-relativistic contributions are governed by the static QCD potential and heavy-quark orbital angular momentum, and establish connections to NRQCD matching. The results provide explicit analytic expressions and moments that enable rapid evaluation for other light-particle insertions and offer cross-checks for higher-order approaches.

Abstract

Non-singlet ${\cal{O}}(α_s^2)$ corrections from light quarks are calculated analytically for the massive quark-antiquark pair production rates through the vector, axial-vector, scalar and pseudoscalar currents for all energies above the threshold. The results are presented in terms of the moments of the absorptive part of the vacuum polarization function of the light quarks which allows for an immediate determination of ${\cal{O}}(α_s^2)$ corrections coming from other types of light particles. The kinematic regime close to the threshold is examined.

Figures (2)

• Figure 1: Double bubble diagrams where a pair of heavy quarks of mass $M$ is produced through an external current. The exchanged photon splits into the light quark-antiquark pair of mass $m$.
• Figure 2: Double bubble diagrams, where the massive quark-antiquark pair is produced by the external current and the internal bubble is purely gluonic. The ghost diagrams are not depicted explicitly.