NNLO QCD corrections to $γγ\rightarrow Q\bar{Q}$ from Local Unitarity combined with Coulomb resummation and NLO EW effects

Abstract

The Local Unitarity (LU) formalism provides a constructive, integrand-level realisation of the Kinoshita-Lee-Nauenberg (KLN) theorem, by combining loop and phase-space integrals appearing in scattering cross-sections in such a way that their final-state infrared singularities cancel before integration. Supplemented with localised ultraviolet renormalisation, it enables the direct Monte Carlo integration of cross sections at arbitrary perturbative order in four-dimensional spacetime. In this paper, we present its application to the next-to-next-to-leading order (NNLO) QCD total cross sections for heavy-quark pair production in direct photon fusion, involving the contribution from 138 distinct forward-scattering diagrams where external photons couple only to heavy quarks. By combining NNLO QCD with next-to-leading order (NLO) electroweak (EW) corrections and next-to-leading power (NLP) Coulomb resummation, we obtain state-of-the-art predictions for top-, bottom-, and charm-quark production in ultraperipheral hadron collisions and at $e^+ e^-$ colliders.

Figures (19)

• Figure 1: The two graphs contributing to the process $\gamma\gamma \to Q\bar{Q}$. Note that these graphs only involve a single Cutkosky cut each, and are assigned a multiplicity factor of $2$ stemming from the symmetrisation of the initial states.
• Figure 2: The ten graphs contributing to the correction to the process $\gamma\gamma \to Q\bar{Q}$. Multiplicity factors arise from the combination of isomorphic graphs when accounting for the symmetry stemming from swapping initial states as well as complex conjugation symmetry.
• Figure 3: Two example diagrams contributing to the classes A and B of section \ref{['sec:FSGenumerate']}. Pink-coloured fermion lines denote massless quarks.
• Figure 4: The four singlet graph contributions. Multiplicity factors arise from the combination of isomorphic graphs when accounting for the symmetry stemming from swapping initial states as well as complex conjugation symmetry.
• Figure 5: Selection of the 18 (amongst 138) diagrams highlighted in figure \ref{['fig:SupergraphHierarchy']}, sorted according to the absolute value of their contribution for $\gamma\gamma \to t\bar{t}$ at $\sqrt{s}=500\;\text{GeV}$. All of them belong to class D in the classification of section \ref{['sec:FSGenumerate']}. Multiplicity factors arise from the combination of isomorphic graphs when accounting for the symmetry stemming from swapping initial states as well as complex conjugation symmetry.