Factorisation: Applications in collider and flavour physics

In many applications of particle physics, we encounter a variety of different energy scales, which tend to be widely separated in many cases. The concept of factorisation exploits this scale separation in order to simplify the intricate physics of scattering processes by disentangling the short-distance and long-distance effects. The theoretical description of these processes is usually provided by effective field theories (EFTs), which naturally implement factorisation for both collider and flavour physics applications. Asymptotic freedom allows to use techniques from perturbation theory to describe short-distance effects in typical problems of flavour physics, while additional methods like QCD sum rules or light-cone sum rules are necessary to parameterise long-distance effects. However, the physical situation is more complicated in the case of collider physics, since we additionally encounter a soft scale Λsoft, which is still perturbatively treatable in the regime Λsoft >> ΛQCD. In the first project, we focus on Soft-Collinear Effective Theory (SCET). In this approach, a large hierachy of scales arises since the QCD radiation is restricted to the soft and collinear phase-space regions. While soft modes are characterised by small energies, collinear modes contain small virtualities with respect to the typical hard scales of the process. This defines a small power-counting parameter λ such that cross sections factorise in terms of hard, soft and collinear functions at every order in the power expansion. As long as the underlying scales are perturbative, these functions can be computed order-by-order for each observable. In order to streamline the calculation of the functions that arise at leading order in the power expansion, the computation of soft and final-state collinear (jet) functions has been automated in recent years for a general class of observables. The goal of this project consists in developing a similar automated setup for the computation of initial-state collinear (beam) functions to next-to-next-to-leading order (NNLO) in perturbation theory. In particular, our calculation provides the last missing ingredient to fully automate resummations at a modified next-to-next-to-leading logarithmic (NNLL′) accuracy using SCET. In comparison to that, the second and third project deal with applications of factorisation in flavour physics. Specifically, we apply QCD sum rules in the second project and light-cone sum rules in the third project to parameterise non-perturbative effects. The second project aims to determine important parameters in the description of the B meson in the framework of Heavy-Quark Effective Theory (HQET), which are called λ²E,H. Contrary to previous works, we make use of a diagonal correlation function containing two three-particle currents to resolve the discrepancies between two prior determinations. In our analysis, we include all contributions to leading order in the strong coupling constant αS and all contributions up to vacuum condensates of mass dimension seven. The third project ventures into the domain of new physics effects and investigates the two-particle decay B → pΨ in the B-Mesogenesis model, where p denotes a proton, while Ψ corresponds to a new fermionic dark matter antibaryon, which interacts with the Standard Model via a colour-charged mediator boson Y. Light-cone sum rules are the appropriate framework to determine the relevant form factors up to twist six such that we can obtain an estimate for the branching fraction of this decay. Experimental facilities like Belle-II have recently started to look into decays of this particular model and our calculation is therefore particularly relevant for these studies.