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Antenna subtraction with massive fermions at NNLO: Double real initial-final configurations

Gabriel Abelof, Aude Gehrmann-De Ridder, Oliver Dekkers

TL;DR

The paper advances NNLO QCD predictions for top-quark pair production by deriving and integrating three initial-final four-parton antenna functions with a massless initial-state parton and a massive final-state fermion. By reducing the problem to four master integrals and employing IBP and differential-equation techniques, it provides explicit pole structures and all-order master-integral representations (with new calculations) needed for the integrated subtraction terms. These integrated antennae enable consistent cancellation of infrared poles in double-real contributions and specifically address the N_F-dependent piece of tt̄ hadroproduction at NNLO. The work thus completes a critical piece of the antenna-subtraction toolkit for processes involving massive fermions at NNLO and facilitates accurate, infrared-safe predictions for tt̄ observables.

Abstract

We derive the integrated forms of specific initial-final tree-level four-parton antenna functions involving a massless initial-state parton and a massive final-state fermion as hard radiators. These antennae are needed in the subtraction terms required to evaluate the double real corrections to $t\bar{t}$ hadronic production at the NNLO level stemming from the partonic processes $q\bar{q}\to t\bar{t}q'\bar{q}'$ and $gg\to t\bar{t}q\bar{q}$.

Antenna subtraction with massive fermions at NNLO: Double real initial-final configurations

TL;DR

The paper advances NNLO QCD predictions for top-quark pair production by deriving and integrating three initial-final four-parton antenna functions with a massless initial-state parton and a massive final-state fermion. By reducing the problem to four master integrals and employing IBP and differential-equation techniques, it provides explicit pole structures and all-order master-integral representations (with new calculations) needed for the integrated subtraction terms. These integrated antennae enable consistent cancellation of infrared poles in double-real contributions and specifically address the N_F-dependent piece of tt̄ hadroproduction at NNLO. The work thus completes a critical piece of the antenna-subtraction toolkit for processes involving massive fermions at NNLO and facilitates accurate, infrared-safe predictions for tt̄ observables.

Abstract

We derive the integrated forms of specific initial-final tree-level four-parton antenna functions involving a massless initial-state parton and a massive final-state fermion as hard radiators. These antennae are needed in the subtraction terms required to evaluate the double real corrections to hadronic production at the NNLO level stemming from the partonic processes and .

Paper Structure

This paper contains 12 sections, 32 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Initial-final antenna subtraction with massive fermions at NNLO
  3. Antenna functions for double real radiation
  4. Integration of initial-final antenna functions at NNLO
  5. General structure of the integrated antennae
  6. Master integrals
  7. The master integrals $I_{[0]}$ and $I_{[-8]}$
  8. The master integrals $I_{[4]}$ and $I_{[4,9]}$
  9. Integrated antennae
  10. Conclusions
  11. Acknowledgments
  12. Four-parton antennae

Figures (1)

  • Figure 1: The topologies and mass distributions of the four master integrals encountered in the calculation of the integrated NNLO four-parton antennae ${\cal B}^0_{q',Qq\bar{q}}$, ${\cal E}^0_{g,Qq\bar{q}}$ and ${\cal\tilde{E}}^0_{g,Qq\bar{q}}$. Bold (thin) lines refer to massive (massless) scalar propagators. The double line in the external states represents the off-shell momentum $q$, with $q^2 = -Q^2$. The cut propagators are the ones intersected by the dashed line.