Improvement on the $H\rightarrow\gamma\gamma$ mass measurement by constraining the photon energy scale uncertainty and search for Higgs boson pair production in the $b\bar{b}\gamma\gamma$ final state with the ATLAS experiment using the full Run 2 at $\sqrt{s}=13$TeV $pp$ collision of LHC

After the Higgs discovery in 2012 by ATLAS and CMS at LHC, precision measurements and Higgs couplings are important for validation of the Standard model (SM), but also for search of new physics Beyond the Standard Model (BSM), as any deviation from the SM prediction can indicate the presence of new physics. This thesis presents a work on the calibration of the ATLAS electromagnetic calorimeter. Using the known lineshape of the Z boson peaked around 91 GeV with a precision of $2\times10^{-5}$, the energy response of the calorimeter is calibrated with a energy scale factor and resolution constant term. This work contributes to final calibration recommendation of ATLAS Run 2, which is important for the Higgs mass measurement with $H\rightarrow\gamma\gamma$ decay mode. The linearity of the calorimeter is measured, as energy-dependent scale factor, which is afterwards used to constrain the energy scale systematics. The performance of such constraint is tested on the $H\rightarrow\gamma\gamma$ mass analysis. The 139 fb$^{-1}$ Run 2 data is expected to measure the Higgs boson mass with a statistical uncertainty around 125 MeV and a experimental systematic uncertainty around 260 MeV. Benefiting from the constraint with linearity, the experimental systematic uncertainty is reduced by around 1.5. The search for the di-Higgs production probes the Higgs potential and the Higgs self-coupling. This thesis exploits the di-Higgs production via the $HH\rightarrow b\bar{b}\gamma\gamma$ decay with the ATLAS Run~2 data. The observed (expected) limit of the di-Higgs production cross section is set to 4.2 (5.7) times the SM prediction at 95% confidence level. The Higgs self-coupling modifier $\kappa_\lambda$ is constrained to be between -1.5 and 6.7, while the expected constraint is $-2.4<\kappa_\lambda<7.7$.