Thesis defense of Cornelius Grunwald

In this thesis, methods for Bayesian data analysis are employed in the search for physics beyond the Standard Model (BSM). A new implementation of the Bayesian Analysis Toolkit in Julia (BAT.jl) is introduced as a modern data analysis framework providing algorithms for Bayesian inference. The EFTfitter.jl package for interpreting measurements in the context of effective field theories (EFTs) is presented. It facilitates combining measurements and estimating underlying parameters with Bayesian inference. Both tools are employed for indirect BSM searches using EFTs. Wilson coefficients of dimension-six operators from the top-quark sector of the Standard Model effective field theory (SMEFT) are constrained, and approaches for enhancing fits of SMEFT coefficients are investigated. Studies on the effects of correlations between the uncertainties of measurements on the results of SMEFT fits are conducted. It is demonstrated that the correlations can significantly impact the resulting constraints and can be the crucial components deciding whether deviations from the Standard Model of particle physics are observed or not, in particular when assuming future measurements with reduced
uncertainties. Moreover, studies on combining measurements of top-quark and flavor physics observables for SMEFT interpretations are performed, and the steps necessary for a combined fit are discussed. Powerful synergies between top-quark processes and b --> s transitions are observed when constraining SMEFT Wilson coefficients of the top-quark sector. It is demonstrated that due to complementary sensitivities, combining observables from different energy scales can tighten the constraints significantly. Future scenarios assuming measurements from HL-LHC, Belle II, and CLIC are investigated, and their potential for improving constraints on up to eleven SMEFT Wilson coefficients is pointed out. The benefits of orthogonal constraints in multidimensional phase spaces for resolving ambiguous solutions are highlighted. The SMEFT studies presented in this thesis demonstrate the capabilities of the new BAT.jl and EFTfitter.jl packages for BSM analyses.