N${}^3$LL resummation of one-jettiness for $Z$-boson plus jet production at hadron colliders

We present the resummation of one-jettiness for the colour-singlet plus jet production process $pp\to ({\gamma }^{\ast }\mathrm{/}Z\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-})+\text{jet}$ at hadron colliders up to the fourth logarithmic order (N${}^3$LL). This is the first resummation at this order for processes involving three coloured partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for colour-singlet plus jet production matched to parton showers in the GENEVA framework.