Boosted and semi-boosted all-hadronic $t\bar{t}$ reconstruction performance on kinematic variables for selected BSM models using a 2D extesion of the BumpHunter algorithm

We explore the usage of boosted as well as semi-boosted topologies in all-hadronic $t\bar{t}$ final states in simulated $pp$ collisions at $\sqrt{s} = 14\,$TeV, with top quarks decaying into a boosted hadronic top-jet or a $W$-jet and an isolated $b$-jet. Correlations between selected kinematic variables and their shapes are studied for scalar and vector resonances decaying to a pair of top quarks, and also for a models of $t\bar{t}$-associated production with an invisible dark matter particle pair. Stacked signal$+$background samples have been investigated in terms of the ability to resolve an excess of events over the Standard Model background in terms of the $t\bar{t}$ invariant mass, top quark transverse momentum and other 1D and 2D spectra using a parameterized detector simulation. A 2D extension of the BumpHunter algorithm is proposed, resulting in an improved signal sensitivity in specific 2D areas. We identify the most promising variables with the largest signal significance and smaller sensitivity to experimental uncertainties realated to the jet energy calibration. We compare to statistical tests computing the background-only hypothesis compatibility and a likelihood fit of the signal strength.