Transverse-momentum resummation fo top-quark pair production at the LHC

TL;DR

This paper develops a transverse-momentum resummation formalism for top-quark pair production at the LHC, extending the framework to include the unique color- and angle-dependent soft wide-angle radiation inherent to heavy-quark final states. The authors implement the resummation in impact-parameter space up to next-to-leading logarithmic accuracy (NLL) and match it with fixed-order results up to NLO, enabling reliable predictions for the q_T spectrum across small to intermediate q_T. They demonstrate that NLL+NLO yields physically meaningful distributions, with controlled perturbative uncertainties and good agreement with ATLAS and CMS data at 8 TeV, while fixed-order NNLO improves the high-q_T region but struggles at small q_T without resummation. The work also quantifies the impact of soft radiation color-coherence and non-perturbative effects, and compares with NLO+PS Monte Carlo approaches, highlighting the complementarity of resummation and parton-shower techniques. Future improvements await the NNLO hard-virtual coefficient H^(2) to enable NNLL+NNLO predictions.

Abstract

We consider transverse-momentum resummation for top-quark pair production in hadron collisions. At small transverse momenta of the top-quark pair, the logarithmically-enhanced QCD contributions are resummed to all orders up to next-to-leading logarithmic accuracy. At intermediate and large values of transverse momenta, the resummation is consistently combined with the complete result at fixed perturbative order. We present numerical results for the transverse-momentum distribution of top-quark pairs at LHC energies. We perform a detailed study of the scale dependence of the results to estimate their perturbative uncertainty. We comment on the comparison with ATLAS and CMS data.

Figures (10)

• Figure 1: The $q_T$ cross section $d\sigma/dq_T$ of the $t\bar{t}$ pair produced in $pp$ collisions at ${\sqrt s}=8$ TeV: NLO (red dashed) and NNLO (blue solid) theoretical predictions at central scales and including scale dependence. The lower panel shows the ratio $K$ of the NNLO and NLO results (blue solid), and the relative scale dependence at NLO (red dashed).
• Figure 2: Same as in Fig. \ref{['fig:NLO_LO']} for the normalized $q_T$ distribution $1/\sigma\,(d\sigma/dq_T)$.
• Figure 3: Fractional difference of NLO predictions (red dashed), NNLO predictions (blue solid) and LHC data Aaboud:2016iotKhachatryan:2015oqa with respect to the NNLO result at $\mu_F=\mu_R=m_t$. The results refer to the normalized $q_T$ distribution $1/\sigma\,(d\sigma/dq_T)$ of $t{\bar{t}}$ pairs at ${\sqrt s}=8$ TeV. The two panels highlight (a) the intermediate and large $q_T$ region and (b) the small-$q_T$ region.
• Figure 4: The transverse-momentum cross section $d\sigma/dq_T$ of the $t\bar{t}$ pair at the LHC ($\sqrt{s}=8~\mathrm{TeV}$) computed through resummation at NLL+NLO accuracy (blue solid). The resummed result at central scales ($\mu_R=\mu_F=Q=m_t$) is compared to the corresponding NLO result (red dashed). The contribution of the regular component (black dotted) to the NLL+NLO result is also shown.
• Figure 5: The transverse-momentum cross section $d\sigma/dq_T$ of the $t\bar{t}$ pair at the LHC ($\sqrt{s}=8~\mathrm{TeV}$) computed at NLL+NLO accuracy. The bands (blue and red lines) are obtained by varying $\mu_F$ and $\mu_R$ (left) and $Q$ (right) as described in the text. The lower panels present the scale variation bands relative to the result at central scales ($\mu_R=\mu_F=Q=m_t$).