Data-driven searches for physics beyond the Standard Model in high energy collision data using the eμ-symmetry method

In pursuit of New Physics (NP) to extend the Standard Model (SM), no effort is spared, as evidenced by the LHC and its experiments at CERN, the world's largest scientific enterprise. But with no conclusive evidence of deviations from SM predictions, novel and complementary approaches for discovery should be considered. The amount of LHC data recorded is the greatest ever accumulated and is largely unexplored. Hence the proposed data-directed paradigm (DDP); letting the data itself guide us towards its regions of interest, significantly enhancing our discovery potential. Symmetries of the SM can be utilized for this endeavor, as they provide two exclusive datasets that can be compared without requiring simulation. Focusing on the data, selections which exhibit significant asymmetry can be identified efficiently and marked for further study. An example is the approximate symmetry between electrons and muons in SM processes. This property can be exploited to probe the data for deviations from SM features such as Lepton Universality (LU) or Lepton Flavor Conservation (LFC). To this end, the $e/\mu$-symmetry method is developed. This analysis method provides a data-driven approach to estimate SM background contributions. It involves, in particular, a technique to account for detection effects that invalidate the expected SM symmetry and a statistical analysis procedure. A direct search for the LFV decays of the Higgs boson $H \rightarrow e\tau$ and $H \rightarrow \mu\tau$ using the $e/\mu$-symmetry method is presented, which uses the Run-2 dataset of $pp$ collisions delivered by the LHC at $\sqrt{s} = 13$ TeV and recorded by the ATLAS detector, corresponding to an integrated luminosity of 138.42 fb$^{-1}$. The final results are combined results of this analysis with two other MC-based searches for the same signals. Some tension from SM predictions is observed at the level of $2.5\sigma$ in the search for $H \rightarrow \mu\tau$, while no evidence of the $H \rightarrow e\tau$ decay is found. Upper limits on the branching ratios (BR) are set at a 95\% confidence level (CL): $0.230\%~(0.192\%)$ for $H \rightarrow e\tau$ and $0.163\%~(0.182\%)$ for $H \rightarrow \mu\tau$ when the two searches are conducted independently (simultaneously). The successful completion of this analysis is an important endorsement of the $e/\mu$-symmetry method. However, only a specific signal is searched for in a small theoretically motivated data region. In terms of the DDP proposed, the broadest possible region is scanned for any deviation from SM predictions. Implementing such data-directed and generic searches based on symmetries of the SM is still at an initial stage. Towards laying the groundwork, a generic approach to identify asymmetries between two measurements is developed in a simplified framework. With little optimization, the sensitivity achieved is only slightly lower than that of optimal likelihood-based tests, which have full knowledge of the signal. This approach has the advantage of being extremely fast, enabling to efficiently scan large portions of the data for any hints of NP.