Measurement of the Higgs boson mass in the $H \rightarrow ZZ^* \rightarrow 4\ell$ decay channel using 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV $pp$ collisions recorded by the ATLAS detector at the LHC

The mass of the Higgs boson is measured in the $H \rightarrow ZZ^* \rightarrow 4\ell$ decay channel. The analysis uses proton-proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector between 2015 and 2018, corresponding to an integrated luminosity of 139 fb$^{-1}$. The measured value of the Higgs boson mass is $124.99\pm0.18\text{(stat.)}\pm0.04\text{(syst.)}$ GeV and is based on improved momentum-scale calibration for muons relative to previous publications. The measurement also employs an analytic model that takes into account the invariant-mass resolution of the four-lepton system on a per-event basis and the output of a deep neural network discriminating signal from background events. This measurement is combined with the corresponding measurement using 7 and 8 TeV $pp$ collision data, resulting in a Higgs boson mass measurement of $124.94\pm0.17\text{(stat.)}\pm0.03\text{(syst.)}$ GeV.