The q T and ∆ ϕ t t ¯ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities

In this paper, we present the resummation-improved differential transverse momentum and azimuthal decorrelation cross sections, dσtt¯/dqT and dσtt¯/d∆ϕtt¯, in top-antitop pair production at the LHC. Our calculation is based on the observation that both cross sections are dominated by topologies where the top-quark pair is well separated, expressed in their relative velocity βtt¯∼O1, at colliding energies of s = 13 TeV or higher. Therefore, the asymptotic behaviour in the limits qT → 0 and ∆ϕtt¯ → 0 can mostly be captured by the soft and collinear resummation in the HQET+SCET framework. Nevertheless, starting at N2LL, Coulomb singularities emerge in the threshold regime, βtt¯ → 0, in both the hard sector and its evolution kernels, leading to unphysical results upon integration over the entire βtt¯ range. To this end, two prescriptions, dubbed the D- and R-prescription, are introduced to regularise these Coulomb singularities. They embody two fundamentally different methods to truncate the threshold enhanced terms, rendering their contribution finite. In the absence of a combined threshold and small-transverse-momentum resummation, we present a quantitative assessment of the ambiguity introduced by the choice of prescription, itself a test of the sensitivity of our calculation to such threshold enhancements, for both the dσtt¯/dqT and dσtt¯/d∆ϕtt¯ spectra.