The real radiation antenna function for $S \to Q {\bar Q} q {\bar q}$ at NNLO QCD

TL;DR

This work advances NNLO QCD by constructing the real radiation antenna function for $S \to Q{\bar Q} q{\bar q}$ with a massive quark and its analytic integration, a crucial building block for antenna subtraction with massive final-state quarks. It achieves a complete IBP-based reduction to five master integrals, which are computed analytically and expressed in harmonic polylogarithms, enabling a compact final form for the integrated antenna $\mathcal{B}^0_{Q q \bar q \bar Q}$. As a cross-check, the authors evaluate the $\alpha_s^2 e_Q^2 N_f$ contribution to the inclusive $e^+e^- \to Q{\bar Q} + X$ cross section, verify IR pole cancellation, and reproduce known massless-limit results. The results provide essential building blocks for NNLO calculations involving massive quarks and point toward analytic handling of other final-state channels like $S \to Q{\bar Q} g g$.

Abstract

As a first step towards the application of the antenna subtraction formalism to NNLO QCD reactions with massive quarks, we determine the real radiation antenna function and its integrated counterpart for reactions of the type $S \to Q{\bar Q} q {\bar q}$, where $S$ denotes an uncolored initial state and $Q$, $q$ a massive and massless quark, respectively. We compute the corresponding integrated antenna function in terms of harmonic polylogarithms. As an application and check of our results we calculate the contribution proportional to $α_s^2 e^2_Q N_f$ to the inclusive heavy-quark pair production cross ection in $e^+e^-$ annihilation.

Figures (1)

• Figure 1: Feynman diagrams contributing to $\gamma^\ast \to Q \bar{Q} q \bar{q}$ at tree-level. Bold (thin) lines refer to massive (massless) quarks.