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

TL;DR

This paper develops a theoretical framework for resumming the 0-jettiness variable in top-quark pair production at the LHC, achieving high logarithmic accuracy and matching with fixed-order calculations for precise predictions.

Contribution

It derives a factorisation formula for 0-jettiness in top-quark pair production and computes corrections up to NNLL accuracy, improving the precision of theoretical predictions.

Findings

Resummation formula derived for 0-jettiness at any logarithmic order.

NNLL corrections calculated and incorporated into predictions.

Matched resummed results with fixed-order calculations for enhanced accuracy.

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 $\mathrm{NNLL}^\prime$ ($\mathrm{NNLL}^\prime_{\text{a}}$). 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.