Two-loop leading colour QCD corrections to $$ q\overline{q} $$ → γγg and qg → γγq

Abstract

We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

Leading-color two-loop QCD corrections for three-jet production at hadron colliders

“…[24], our current results are written in terms of a JHEP07(2021)095 different basis of transcendental functions [41] which have also undergone several direct checks (e.g., comparison with the functions of ref. [40]) and indirect checks [32,33,35,36]. Furthermore, we have verified that we reproduce the results independently obtained in ref.…”

“…Furthermore, we implement our expressions in a publicly available C++ library that allows one to evaluate these contributions efficiently and in a stable manner, making our results readily available for a future full calculation of the corresponding NNLO QCD corrections. 1 Our work builds on a number of recent technical advances that have paved the way to the calculation of two-loop scattering amplitudes for 2 → 3 processes with phenomenological applications [32][33][34][35][36][37]. We employ the known pure two-loop master integrals [21,26,38,39], which can be written in terms of a special set of multi-valued transcendental functions -the so-called pentagon functions [40,41].…”

Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC

“…Recently, the spin-averaged amplitudes for the two processes (2.1) were calculated in ref. [44]. We have found complete agreement for all terms except for those containing ε 5 .…”

“…The number of (independent) rational functions for each colour/charge structure can be found in table 1. The appearance of these simpler rational structures has already been discussed in the literature [37,[43][44][45][46] and they have been utilized for expressing the amplitudes in a more compact from. On the other hand, it seems to us that the possible JHEP07(2021)164 true structure behind these independent rational functions has not yet been fully explored and we hope to return to this in a future publication.…”

“…The last few years have seen many advances in the calculation of multi-loop integrals and amplitudes . Two-loop 5-point amplitudes are at the frontier of current amplitude calculations and have been the subject of particularly intense research [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. That research has notably led to the calculation of the 2-loop QCD leading-colour amplitude for qq → γγγ [40,42,43], which in turn has enabled, for the first time, the computation of the Next-to-Next-to-Leading-Order (NNLO) QCD corrections for a 2 → 3 process [40,47].…”