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NNLO QCD corrections to $pp \to γ^* γ^*$ in the large $N_F$ limit

Charalampos Anastasiou, Julian Cancino, Federico Chavez, Claude Duhr, Achilleas Lazopoulos, Bernhard Mistlberger, Romain Mueller

TL;DR

This work addresses NNLO QCD corrections for hadroproduction of a pair of off-shell photons in the large-$N_F$ limit, providing a gauge-invariant partial NNLO contribution that serves as a stepping stone toward a complete diboson calculation. The authors reduce the two-loop amplitude to master integrals and evaluate them analytically in the Euclidean region, then perform an analytic continuation to the physical region using a basis of classical polylogarithms up to weight three with carefully managed branch cuts. They implement a hierarchical subtraction scheme for real radiation, enabling fully differential results and a Monte Carlo implementation, and demonstrate that the NNLO $N_F$ corrections amount to roughly 1–3% of the cross section depending on photon virtualities, with reduced scale uncertainties in the off-shell regime. Overall, the paper advances analytic and numeric techniques for NNLO diboson processes and provides a concrete framework toward a complete, precise background prediction for Higgs analyses at the LHC.

Abstract

We compute the NNLO QCD corrections for the hadroproduction of a pair of off-shell photons in the limit of a large number of quark flavors. We perform a reduction of the two-loop amplitude to master integrals and calculate the latter analytically as a Laurent series in the dimensional regulator using modern integration methods. Real radiation corrections are evaluated numerically with a direct subtraction of infrared limits which we cast in a simple factorized form. The results presented here constitute a gauge invariant part of the full NNLO corrections but are not necessarily dominant. We view this calculation as a step towards a complete computation. Our partial corrections to the total cross-section are about $1\%-3\%$ and vary with the virtuality of the two off-shell photons.

NNLO QCD corrections to $pp \to γ^* γ^*$ in the large $N_F$ limit

TL;DR

This work addresses NNLO QCD corrections for hadroproduction of a pair of off-shell photons in the large- limit, providing a gauge-invariant partial NNLO contribution that serves as a stepping stone toward a complete diboson calculation. The authors reduce the two-loop amplitude to master integrals and evaluate them analytically in the Euclidean region, then perform an analytic continuation to the physical region using a basis of classical polylogarithms up to weight three with carefully managed branch cuts. They implement a hierarchical subtraction scheme for real radiation, enabling fully differential results and a Monte Carlo implementation, and demonstrate that the NNLO corrections amount to roughly 1–3% of the cross section depending on photon virtualities, with reduced scale uncertainties in the off-shell regime. Overall, the paper advances analytic and numeric techniques for NNLO diboson processes and provides a concrete framework toward a complete, precise background prediction for Higgs analyses at the LHC.

Abstract

We compute the NNLO QCD corrections for the hadroproduction of a pair of off-shell photons in the limit of a large number of quark flavors. We perform a reduction of the two-loop amplitude to master integrals and calculate the latter analytically as a Laurent series in the dimensional regulator using modern integration methods. Real radiation corrections are evaluated numerically with a direct subtraction of infrared limits which we cast in a simple factorized form. The results presented here constitute a gauge invariant part of the full NNLO corrections but are not necessarily dominant. We view this calculation as a step towards a complete computation. Our partial corrections to the total cross-section are about and vary with the virtuality of the two off-shell photons.

Paper Structure

This paper contains 25 sections, 165 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Setup and notation
  3. Virtual corrections
  4. Master Integrals
  5. Analytic results in the Euclidean region
  6. One-loop integrals.
  7. Two-loop integrals.
  8. Analytic continuation into the physical region
  9. Definition of the regions.
  10. Analytic continuation of the functions.
  11. Single-real contributions
  12. Quark-antiquark channels
  13. (Anti-)quark gluon channels
  14. Double-real contributions
  15. Semi differential subtraction
  16. ...and 10 more sections

Figures (7)

  • Figure 1: Sample tree and two-loop diagrams contributing to the NNLO corrections for $q\bar{q}\to\gamma^*\gamma^*$ in the large-$N_F$ limit.
  • Figure 2: Scale variation at LO, NLO and NNLO as a function of the photon virtualities, here taken to be equal.
  • Figure 3: Pseudo-rapidity distribution of the two off-shell photons with virtualities $m_3 = 30$GeV (left) and $m_4 = 15$GeV (right).
  • Figure 4: Transverse momentum distribution of the two off-shell photons with virtualities $m_3 = 30$GeV (left) and $m_4 = 15$GeV (right).
  • Figure 5: The invariant mass distribution of the diphoton pair, with ${m_3}=91.188$GeV and ${m_4}=27$GeV.
  • ...and 2 more figures