Determination of the Muonic Branching Ratio of the W Boson and its Total Width via Cross-Section Measurements at the Tevatron and LHC

The total $W$-boson decay width $\Gamma_W$ is an important observable which allows testing of the standard model. The current world average value is based on direct measurements of final state kinematic properties of $W$-boson decays, and has a relative uncertainty of 2\%. The indirect determination of $\Gamma_W$ via the cross-section measurements of vector-boson production can lead to a similar accuracy. The same methodology leads also to a determination of the leptonic branching ratio. This approach has been successfully pursued by the CDF and D0 experiments at the Tevatron collider, as well as by the CMS collaboration at the LHC. In this paper we present for the first time a combination of the available measurements at hadron colliders, accounting for the correlations of the associated systematic uncertainties. Our combination leads to values of $\textrm{BR}(W\rightarrow\mu\nu)=(10.72 \pm 0.16)\%$ and $\Gamma_W = 2113 \pm 31$ MeV, respectively, both compatible with the current world averages.