| Summary: | Abstract In this paper, we present the resummation-improved differential transverse momentum and azimuthal decorrelation cross sections, d σ t t ¯ / d q T $$ {\textrm{d}\sigma}_{t\overline{t}}/{\textrm{d}q}_{\textrm{T}} $$ and d σ t t ¯ / d ∆ ϕ t t ¯ $$ {\textrm{d}\sigma}_{t\overline{t}}/\textrm{d}\Delta {\phi}_{t\overline{t}} $$ , 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 β t t ¯ ∼ O 1 $$ {\beta}_{t\overline{t}}\sim \mathcal{O}(1) $$ , at colliding energies of s $$ \sqrt{s} $$ = 13 TeV or higher. Therefore, the asymptotic behaviour in the limits q T → 0 and ∆ ϕ t t ¯ $$ \Delta {\phi}_{t\overline{t}} $$ → 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, β t t ¯ $$ {\beta}_{t\overline{t}} $$ → 0, in both the hard sector and its evolution kernels, leading to unphysical results upon integration over the entire β t t ¯ $$ {\beta}_{t\overline{t}} $$ 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 d σ t t ¯ / d q T $$ {\textrm{d}\sigma}_{t\overline{t}}/{\textrm{d}q}_{\textrm{T}} $$ and d σ t t ¯ / d ∆ ϕ t t ¯ $$ {\textrm{d}\sigma}_{t\overline{t}}/\textrm{d}\Delta {\phi}_{t\overline{t}} $$ spectra.
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