Zero-jettiness resummation for top-quark pair production at the LHC

We study the resummation of the 0-jettiness resolution variable T${}_0$ for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the T${}_0$→0 limit. We then calculate the O(α${}_s$) corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL′, NNLL and approximate NNLL′ (NNLL${}_a^{\prime }$). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the $t\overline{t}$+jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at NNLL${}_a^{\prime }$+NLO accuracy.