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 perturbative QCD uncertainty of ${\cal O}(\pm 5)$ MeV on $m_W$ can be established by means of this observable, relying solely on charged-current Drell-Yan information. Owing to its relatively inclusive nature, the observable displays desirable properties also from the experimental viewpoint, especially for the unfolding of detector effects. We show that a measurement of this observable can lead to a competitive experimental error on $m_W$ at the LHC.