Towards a precise top quark mass measurement: Improved in-situ jet response measurements and interpretation of the Monte Carlo top quark mass parameter

The advancements in collider technologies, particularly with facilities like the Large Hadron Collider reaching extremely high energy levels, have significantly enhanced the accuracy of measurements for quark masses, notably for the heaviest quark, the top quark. This leap in experimental accuracy, presents a unique set of challenges in interpreting the mass of the top quark. These challenges introduce uncertainties which can constrain the precision of these measurements. Indirect measurements are used to verify or question interpretations of renormalised top quark masses, such as the pole mass, yet the current uncertainties around the order of 1 GeV limit their effectiveness. To tackle these issues, this thesis presents two critical advancements. Firstly, it provides an interpretation of the top quark mass, establishing a precise and reliable relation between Monte Carlo top quark mass parameters and a suitable mass scheme, specifically the MSR mass scheme. Secondly, the first in-situ calibration of the b-Jet Energy Scale in photon+jet events with the ATLAS experiment has been conducted, in which this calibration is crucial for improving the accuracy of measurements related to couplings and decay processes involving b-quarks.