PROBING THE HIGGS BOSON WITH THE ATLAS DETECTOR: PRECISION MEASUREMENTS OF THE MASS AND SEARCH FOR RARE DECAYS TO A LOW-MASS DILEPTON SYSTEM AND A PHOTON IN PROTON-PROTON COLLISIONS AT THE LHC

This thesis presents three analyses based on proton--proton collision data recorded by the ATLAS detector at the Large Hadron Collider, using the full Run~2 dataset collected between 2015 and 2018 at a centre-of-mass energy of $\sqrt{s} = 13$~TeV, corresponding to an integrated luminosity of 140~fb$^{-1}$, and data recorded during the first part of Run~3 between 2022 and 2024 at $\sqrt{s} = 13.6$~TeV, corresponding to 165~fb$^{-1}$. The analyses focus on a detailed investigation of the Higgs boson within the Standard Model (SM), through the precision measurement of one of its fundamental parameters, the Higgs boson mass $m_H$, and the search for a rare SM decay mode not yet observed, namely the decay into a low-mass dilepton system and a photon. \noindent The first analysis presents a precision measurement of the Higgs boson mass in the diphoton decay channel, $H \rightarrow \gamma\gamma$, using the full Run~2 dataset. The Higgs boson mass is measured to be $m_H = 125.17 \pm 0.11\,(\mathrm{stat.}) \pm 0.09\,(\mathrm{syst.})~\mathrm{GeV} = 125.17 \pm 0.14~\mathrm{GeV}$. The improved precision with respect to previous measurements is driven by the larger dataset and by significant advances in the calibration of the photon energy response, resulting in a measurement that is now statistically limited. A combination with the corresponding Run~1 measurement yields $m_H = 125.22 \pm 0.14~\mathrm{GeV}$. \noindent The second analysis furthermore combines the Higgs boson mass measurements obtained in the $H \rightarrow \gamma\gamma$ and $H \rightarrow ZZ^* \rightarrow 4\ell$ decay channels using ATLAS Run~1 and Run~2 data. The combined result, $m_H = 125.11 \pm 0.09\,(\mathrm{stat.}) \pm 0.06\,(\mathrm{syst.})~\mathrm{GeV} = 125.11 \pm 0.11~\mathrm{GeV}$, achieves a relative precision of 0.9 per mille and represents the most precise determination of the Higgs boson mass to date. All mass measurements are found to be consistent with each other and with previous ATLAS and CMS results. \noindent The third analysis presents a search for the rare Higgs boson decay into a low-mass dilepton system with a photon, $H \rightarrow \ell\ell\gamma$ ($\ell = e, \mu$), using partial Run~3 data. The search targets the low dilepton mass region $m_{\ell\ell} < 30$~GeV, where the decay proceeds predominantly via an off-shell photon. The analysis is currently under ATLAS internal review, and preliminary expected results based on statistical uncertainties only are reported. The expected 95\% confidence level upper limit on the production cross section times branching ratio is 1.65 (0.70) times the SM prediction under the signal-plus-background (background-only) hypothesis, and an expected significance of $Z = 2.53\,\sigma$ is obtained for a SM signal. \noindent In addition, studies of the ATLAS detector performance relevant for these analyses are presented, including the optimisation of the multivariate Monte Carlo--based energy calibration for electrons and photons in Run~2 and Run~3, and dedicated studies of merged-electron identification, which are essential for the rare-decay $H \rightarrow \ell\ell\gamma$ search.