  Since the discovery of the Higgs boson in 2012, detailed studies of its
properties have been ongoing. Besides its mass, its width - related to its
lifetime - is an important parameter. One way to determine this quantity is by
measuring its off-shell production, where the Higgs boson mass is far away from
its nominal value, and relating it to its on-shell production, where the mass
is close to the nominal value. Here, we report evidence for such off-shell
contributions to the production cross section of two Z bosons with data from
the CMS experiment at the CERN Large Hadron Collider. We constrain the total
rate of the off-shell Higgs boson contribution beyond the Z boson pair
production threshold, relative to its standard model expectation, to the
interval [0.0061, 2.0] at 95% confidence level. The scenario with no off-shell
contribution is excluded at a $p$-value of 0.0003 (3.6 standard deviations). We
measure the width of the Higgs boson as $\Gamma_{\mathrm{H}}$ = 3.2
$_{-1.7}^{+2.4}$ MeV, in agreement with the standard model expectation of 4.1
MeV. In addition, we set constraints on anomalous Higgs boson couplings to W
and Z boson pairs.
