Two-loop leading-color helicity amplitudes for three-photon production at the LHC

Abstract

We calculate all planar contributions to the two-loop massless helicity amplitudes for the process $$ q\overline{q} $$ q q ¯ → γγγ. The results are presented in fully analytic form in terms of the functional basis proposed recently by Chicherin and Sotnikov. With this publication we provide the two-loop contributions already used by us in the NNLO QCD calculation of the LHC process pp → γγγ [Chawdhry et al. (2019)]. Our results agree with a recent calculation of the same amplitude [Abreu et al. (2020)] which was performed using different techniques. We combine several modern computational techniques, notably, analytic solutions for the IBP identities, finite-field reconstruction techniques as well as the recent approach [Chen (2019)] for efficiently projecting helicity amplitudes. Our framework appears well-suited for the calculation of two-loop multileg amplitudes for which complete sets of master integrals exist.

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

“…Just as in our recent 3-photon calculation [43], we have decomposed the amplitudes using the helicity projection method proposed in ref. [50].…”

“…The construction of the JHEP07(2021)164 gluon/photon polarization vector follows closely ref. [43]. The fermion projector in our previous work was designed with the permutation symmetry of the final-state photons in mind.…”

“…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].…”