Improving Precision for Hadronic Observables in the Standard Model and Beyond

Searching for new physics not described by the Standard Model (SM) is of great importance to enhance our understanding the universe. One possibility to discover new physics is to perform precision tests of the SM by comparing experimental measurements with theoretical predictions. Taking advantage of the vast set of experimental results, we first perform global fits to test and constrain a class of extensions to the SM referred to as Two-Higgs-Doublet models (2HDMs). In addition, we discuss a motivation for collider searches for the rare process Bs → e+e− which can be greatly enhanced in a 2HDM without conflicting with other data. Large uncertainties from non-perturbative hadronic observables limit the ability to constrain the parameter space of 2HDMs or other new physics scenarios.
Next we focus at improving predictions for hadronic observables by non-perturbatively calculating matrix elements of four-quark operators for neutral meson mixing and heavy meson lifetimes using lattice quantum chromodynamics (QCD). In particular, we perform a pilot study establishing a non-perturbative renormalisation procedure via the gradient flow and its short-flow-time expansion allowing us to quote final results in the MS scheme. Considering for simplicity a neutral charm-strange (Ds) meson on the lattice, we determine the O1 operator for neutral meson mixing as well as the O1 and T1 operators describing heavy meson lifetimes. Our short-distance contribution to mixing for a neutral Ds meson is BMS s (3 GeV) = 0.787(5) where the quoted error accounts for statistical and perturbative truncation uncertainties only. This value is in good agreement with literature results for short-distance D0 mixing where only the spectator quark differs. In addition we pioneer the calculation of the four-quark operators O1 and T1 for heavy meson lifetimes in lattice QCD. Essential for this determination is that our gradient flow procedure suppresses the mixing with operators of lower mass dimension on the lattice. Although our lattice calculation does not include all diagrams and also the perturbative matching to the MS scheme is still incomplete, we observe that our values BMS 1 = 1.110(2) and ϵMS 1 = 0.119(1) have the same order of magnitude as corresponding determinations based on HQET sum rules.