Soft radiation in heavy-particle pair production: All-order colour structure and two-loop anomalous dimension

Abstract

We consider the total production cross section of heavy coloured particle pairs in hadronic collisions at the production threshold. We construct a basis in colour space that diagonalizes to all orders in perturbation theory the soft function, which appears in a new factorization formula for the combined resummation of soft gluon and Coulomb gluon effects. This extends recent results on the structure of soft anomalous dimensions and allows us to determine an analytic expression for the two-loop soft anomalous dimension at threshold for all production processes of interest.

From webs to polylogarithms

“…In recent years we have seen significant progress towards determining the singularities of multi-leg amplitudes with general kinematics beyond the planar limit and beyond one loop [4,19,20,[25][26][27][28][29][30][31][32][33][34]41]. Complete two-loop results are now available for the soft anomalous dimension in both the massless and massive cases.…”

NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels

“…Broadly speaking, one can identify two such approaches, usually referred to in the literature as resummed and approximate NNLO, the latter simply being the truncation of the former to order O(α 4 S ). The improved-NLO approximation to the NNLO cross-section is based on the nextto-next-to-leading log (NNLL) threshold approximation [2,3] and also includes Coulombic terms [4] through NNLO. This approach is valid close to absolute threshold and the approximate results are added to the well known NLO [5][6][7] and NLL [8] results.…”

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

“…Most of the observables related to the top-quark pair production have been calculated up to NLO [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In several cases, the next-to-leading (NLO) corrections have been supplemented by the resummation of large logarithmic corrections at leading (LL, [25][26][27][28][29][30][31]), next-to-leading (NLL, [32][33][34][35][36][37][38]) and next-to-next-to-leading logarithmic (NNLL, [39][40][41][42][43]) accuracy. However, to match the precision of the forthcoming experimental data, full next-to-next-to-leading order (NNLO) calculations are required for at least some of the observables, such as the top-quark pair production total cross section [44][45][46][47][48].…”