The Q_t and Δϕ_tt̅ Spectra in Top-Antitop Hadroproduction at NNLL+NNLO: the Interplay of Soft-Collinear Resummation and Coulomb Singularities

In this paper, we calculate the differential transverse momentum and azimuthal decorrelation cross sections, dσ_tt̅/dq_T and dσ_tt̅/dΔϕ_tt̅, in top-antitop pair production at the LHC up to NNLL+NNLO accuracy. Due to the emergence of Coulomb singularities in both the hard sector and the corresponding anomalous dimension as the relative tt̅ pair velocity, β_tt̅, approaches zero, extrapolating the soft-collinear resummation that is derived in the domain where the top and antitop quarks are kinematically well-separated into the full phase space is not trivial. Focussing on two observables that are insensitive to azimuthal asymmetric divergences, q_T and Δϕ_tt̅, we will demonstrate that a literal application of a SCET+HQET based resummation onto dσ_tt̅/dq_T and dσ_tt̅/dΔϕ_tt̅ is only possible up to NLL accuracy. Starting at NNLL, however, such a naïve procedure will develop power-like divergences in β_tt̅ in the threshold regime. To this end, two prescriptions, dubbed the D- and R-schemes, are introduced to facilitate the extrapolation of the resummation framework from the well-separated region where β_tt̅∼𝒪(1) to the threshold regime β_tt̅→0, enabling us to compute dσ_tt̅/dq_T and dσ_tt̅/dΔϕ_tt̅ at NNLL+NNLO accuracy throughout. Further, by comparing the results of both formulations, we can assess the theoretical uncertainty caused by the truncation of the Coulomb-enhanced terms in the perturbative series.