  A search for the dimuon decay of the Standard Model (SM) Higgs boson is
performed using data corresponding to an integrated luminosity of 139 fb$^{-1}$
collected with the ATLAS detector in Run2 $pp$ collisions at $\sqrt{s}=13$ TeV
at the Large Hadron Collider. The observed (expected) significance over the
background-only hypothesis for a Higgs boson with a mass of 125.09 GeV is
$2.0\,\sigma$ ($1.7\,\sigma$). The observed upper limit on the cross section
times branching ratio for $pp \to H \to \mu\mu$ is 2.2 times the SM prediction
at 95% confidence level, while the expected limit on a $H \to \mu\mu$ signal
assuming the absence (presence) of a SM signal is $1.1$ ($2.0$). The best-fit
value of the signal strength parameter, defined as the ratio of the observed
signal yield to the one expected in the SM, is $\mu = 1.2 \pm 0.6$.
