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

Abstract

We study the resummation of the $0$-jettiness resolution variable ${\mathcal{T}}_0$ 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 ${\mathcal{T}}_0\to 0$ limit. We then calculate the $\mathcal{O}({\alpha }_s)$ 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 ($\mathrm{NNLL}$) accuracy. We study the impact of these corrections to the $0$-jettiness distribution by comparing predictions at different accuracy orders: $\mathrm{NLL}$, ${\mathrm{NLL}}^{\prime }$, $\mathrm{NNLL}$ and approximate ${\mathrm{NNLL}}^{\prime }$ (${\mathrm{NNLL}}_{\text{a}}^{\prime }$). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the $t\bar{t}+$jet production process, obtaining the most accurate prediction of the $0$-jettiness distribution for the top-quark pair production process at ${\mathrm{NNLL}}_{\text{a}}^{\prime }+\mathrm{NLO}$ accuracy.

Comments: 42 pages, 5 figures