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.
Highlights
Corrections [29,30,31,32,33,34,35,36] and resummation [37,38,39,40]
The gluon initiated partonic cross-section which emerges for the first time at next-to-next-to-leading-order (NNLO) from the square of one-loop amplitudes has been singled out due to its numerical importance and it was computed in refs. [41,42,43,44,45]
In appendix A we present a way to construct a set of basis functions up to weight four with the correct physical branch cuts contributing to the large NF limit of the the q q → γ∗ γ∗ amplitude at two loops
Summary
We compute the fully differential cross-section at the LHC for the process of producing two idealized off-shell photons,. With σij→γ∗γ∗X [J ] denoting the differential cross section for the process i(p1) + j(p2) → γ∗(p3) + γ∗(p4) + X, where i and j run over the parton flavors g, u, u, d, d, . The partonic cross sections are computed as a perturbative expansion in the bare strong coupling constant αsb, σij→γ∗γ∗X [J ] = σi(j0→) γ∗γ∗ [J ]. At NNLO, the partonic processes which contribute to the correction are qq → γ∗γ∗q qand qq → γ∗γ∗qq In the latter process, we retain only the interference terms with two spin lines. That in the numerical evaluation of the PDFs and the strong coupling from their values at their initial scales we use the complete β-function and Altarelli-Parisi kernels and not just their NF parts.
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