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 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.

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 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 q q → γγγ [40,42,43], which in turn has enabled, for the first time, the computation of the Nextto-Next-to-Leading-Order (NNLO) QCD corrections for a 2 → 3 process [40,47].…”

NNLO QCD corrections to diphoton production with an additional jet at the LHC

“…[40] with the help of refs. [41][42][43] (an equivalent expression for the spin-averaged two-loop squared amplitude has also been derived in ref. [44]).…”

Bootstrapping a Two-Loop Four-Point Form Factor

“…These developments not only reveal rich mathematical structures in the formal aspects of QFTs, but also have important phenomenological applications such as in the Large Hadron Collider (LHC). At the moment, two-loop corrections for 2 → 3 processes have been at the frontier of amplitude computations which are under intense studies in last couple of years: based on the advancements of integral computations [3][4][5][6][7][8], a number of amplitudes have been obtained in compact analytic form, including all massless cases [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and a two-loop five-point amplitude with one massive vector boson [25].…”