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 $\mathrm{ NNLL}^\prime$ ($\mathrm{ NNLL}^\prime_{ \text{ a}}$). 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 $\mathrm{ NNLL}^\prime_{ \text{ a}}+\mathrm{ NLO}$ accuracy.
Categories: hep-ph hep-ex