Applications of Non-Perturbative Methods for Heavy Quark Physics

The Standard Model of Particle Physics (SM) is one of the most successful theories, describing the interactions of the fundamental building blocks of nature. However, a number of questions remain unanswered and require the exploration of physics beyond the SM. Aside from some fundamental problems like dark matter and dark energy, there are also small tensions in the data on flavour physics processes, indicating that physics beyond the SM must exist. Flavour physics, and in particular heavy quark physics, involve a broad range of theoretical methods, including tools to estimate or even compute non-perturbative quantities. The focus of this thesis lies on the application of non-perturbative methods for heavy quark systems.
This will be exemplified by describing three projects. First, we discuss the treatment of quark masses within the heavy quark expansion and effective field theory. This framework provides powerful predictions for inclusive heavy hadron decays where the treatment of the quark mass plays a crucial role. Since the quark mass itself is not a physical observable, several short-distance mass schemes have been developed to minimize uncertainties induced by the quark mass. We suggest replacing the quark mass directly with an observable.
Then we switch to another method by studying the exclusive decay process B → pΨ, observed as a proton and missing energy in the final state indicating the presence of a dark antibaryon Ψ. We determine the decay width using the QCD light-cone sum rule framework. In order to parameterize the non-perturbative effects in the operator product expansion, we systematically include all contributions up to twist six in the nucleon distribution amplitudes.
Finally, we apply lattice QCD to a non-perturbative study of the exclusive Bs → Ds* ℓ νℓ decay parameterized by four form factors. Such b → c quark decays are of great phenomenological interest because they allow extraction of the CKM matrix element |Vcb| or testing of lepton flavour universality. We use ratios of two-point over three-point correlation functions evaluated on RBC/UKQCD’s set of 2+1 flavour gauge field ensembles. Following renormalization and extrapolation to the physical charm mass, we present a preliminary chiral-continuum fit in the simulated q² region.