In the standard model of particle physics, the masses of the W and Z bosons, the carriers
of the weak interaction, are uniquely related. A precise determination of their masses is
important because quantum loops of heavy, undiscovered particles could modify this
relationship. Although the Z mass is known to the remarkable precision of 22 parts per
million (2.0 MeV), the W mass is known much less precisely. A global fit to measured
electroweak observables predicts the W mass with 6 MeV uncertainty1–3. Reaching
a comparable experimental precision would be a sensitive and fundamental test of
the standard model, made even more urgent by a recent challenge to the global fit
prediction by a measurement from the CDF Collaboration at the Fermilab Tevatron
collider4. Here we report the measurement of the W mass by the CMS Collaboration at
the CERN Large Hadron Collider, based on a large data sample of W → μν events collected
in 2016 at the proton–proton collision energy of 13 TeV. The measurement exploits
a high-granularity maximum likelihood fit to the kinematic properties of muons
produced in W decays. By combining an accurate determination of experimental effects
with marked in situ constraints of theoretical inputs, we reach a precise measurement of
the W mass, of 80,360.2 ± 9.9 MeV, in agreement with the standard model prediction.
