Determination of the $W$-boson mass at hadron colliders

We introduce an observable relevant for the determination of the $W$-boson mass $m_W$ at hadron colliders. This observable is defined as an asymmetry around the jacobian peak of the charged-lepton transverse-momentum distribution in the charged-current Drell-Yan process. We discuss the observable's theoretical prediction, presenting results at different orders in QCD, and showing its perturbative stability. Its definition as a single scalar number and its linear sensitivity to $m_W$ allow a clean extraction of the latter and a straightforward discussion of the associated theoretical systematics: a determination of $m_W$ with a perturbative QCD uncertainty at the $\pm 5$ MeV level is viable, with the advantage of solely relying on charged-current Drell-Yan information. The observable displays desirable properties also from the experimental viewpoint, especially for the unfolding of detector effects. We show that, with a conservative estimate of systematic errors, it can lead to an experimental determination of $m_W$ at the level of $\pm 15$ MeV at the LHC.