Two-loop QCD corrections for three-photon production at hadron colliders

Abstract

We complete the computation of the two-loop helicity amplitudes for the production of three photons at hadron colliders, including all contributions beyond the leading-color approximation. We reconstruct the analytic form of the amplitudes from numerical finite-field samples obtained with the numerical unitarity method. This method requires as input surface terms for all relevant five-point non-planar integral topologies, which we obtain by solving the associated syzygy problem in embedding space. The numerical samples are used to constrain compact spinor-helicity ansätze, which are optimized by taking advantage of the known one-loop analytic structure. We make our analytic results available in a public C++ library, which is suitable for immediate phenomenological applications. We estimate that the inclusion of the subleading-color contributions will decrease the size of the two-loop corrections by about 30% to 50%, and the NNLO cross sections by a few percent, compared to the results in the leading-color approximation.

Tensor reduction of loop integrals

“…understanding of the integrand structure of gauge theory amplitudes [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] has revolutionised their reduction to master integrals both at a conceptual and at a practical level. An ambitious research programme at two loops has already lead to remarkable breakthroughs [26][27][28][29][30][31][32][33][34]. The aforementioned tensor integral and amplitude reduction methods, not only achieve a reduction to scalar integrals, but they also achieve a reduction to master integrals.…”

Two-loop five-parton leading-colour finite remainders in the spinor-helicity formalism

“…This requires prior knowledge of the integrand decomposition Γ ∪ Γ . For the computation of → at two-loop this decomposition was obtained by extending to higher power counting the decomposition previously obtained for → using the embedding space formalism [5].…”

Two-Loop Five-Particle Scattering Amplitudes

“…Over the last years we have seen important progress in this direction, building upon the campaign which mastered the 2 → 2 processes and a deepened understanding of the polylogarithmic special functions appearing in the amplitudes. In the case of fully massless final states, all partonic processes needed for three-jet (in the leading colour approximation) [1,2], three-photon [3][4][5][6], di-photon + jet [7,8], and photon + di-jet [9] production at the LHC have been computed. More recently, several leading-colour amplitudes involving an external massive vector boson [10][11][12][13][14][15] have also become available, and the first steps have been taken for processes with internal massive propagators [16,17] (see Matteo Becchetti's talk [18]).…”