Resummed Differential Cross Sections for Top-Quark Pairs at the LHC

We present state of the art resummation predictions for differential cross sections in top-quark pair production at the LHC. They are derived from a formalism which allows the simultaneous resummation of both soft and small-mass logarithms, which endanger the convergence of fixed-order perturbative series in the boosted regime, where the partonic center-of-mass energy is much larger than the mass to the top quark. We combine such a double resummation at next-to-next-to-leading logarithmic${}^{\prime }$ (${\mathrm{NNLL}}^{\prime }$) accuracy with standard soft-gluon resummation at next-to-next-to-leading logarithmic accuracy and with next-to-leading-order calculations, so that our results are applicable throughout the whole phase space. We find that the resummation effects on the differential distributions are significant, bringing theoretical predictions into better agreement with experimental data compared to fixed-order calculations. Moreover, such effects are not well described by the next-to-next-to-leading-order approximation of the resummation formula, especially in the high-energy tails of the distributions, highlighting the importance of all-orders resummation in dedicated studies of boosted top production.

Figure 1

Resummed prediction (blue band) for the normalized $p_T$ distribution at the 8 TeV LHC compared with CMS data (red crosses) [3] and the NNLO result (green band) [1]. The lower panel shows results normalized to the default $\mathrm{NLO}+{\mathrm{NNLL}}^{\prime }$ prediction.

Figure 2

Resummed prediction (blue band) for the absolute $p_T$ distribution at the 8 TeV LHC in the boosted region compared with the ATLAS data (red crosses) [4] and the NLO result (green band).

Figure 3

Resummed prediction (blue band) for the absolute $M_{t\overline{t}}$ distribution at the 8 TeV LHC compared with ATLAS data (red crosses) [16] and the NLO result (green band).

Figure 4

Resummed predictions (blue bands) for the $p_T$ and $M_{t\overline{t}}$ distributions at the 13 TeV LHC compared with the NLO results (green bands).

Figure 5

Relative sizes of the corrections at approximate NNLO (blue) and beyond (black), with respect to NLO. See Eq. (3) and the explanations there for precise definitions.