Dispersively improved vector-meson-dominance approaches to precision observables
Creators: name: Zanke, Marvin
Publisher: name: Universitäts- und Landesbibliothek Bonn
Year: 2024
Subjects: subject: anomalous magnetic moment
subject: hadronic light-by-light scattering
subject: axial-vector mesons
subject: semileptonic decays
subject: rare decays
subject: B-meson decays
subject: transition form factors
subject: Bardeen–Tung–Tarrach procedure
subject: vector-meson dominance
subject: dispersion relations
subject: z expansion
subject: ddc:530

description: To this day, describing the interaction of hadrons poses a challenge. Although quantum chromodynamics is well established by now, its non-perturbative nature at low energies renders it impossible to perform perturbative calculations in this energy regime, as, <em>e.g.</em>, feasible in the realm of quantum electrodynamics. Conjectured to be related to this behavior is the observation of confinement, stating that quarks and gluons cannot exist as free particles under ordinary conditions but invariably form hadronic bound states, which thus represent the pertinent degrees of freedom at low and intermediate energies.<br> Together with the weak force, quantum chromo- and electrodynamics provide the framework that describes the non-gravitational interactions of the fundamental building blocks of nature we know of today, as compiled in the standard model of particle physics. Crucially, the standard model is known to be incomplete, reasons for this being, <em>e.g.</em>, its incompatibility with gravity, dark matter, and the apparent matter–antimatter asymmetry in the universe. However, the proper extension of the standard model remains to be identified, and to this end, it is necessary to scrutinize this model with the utmost diligence.<br> In this thesis, we discuss various probes of the standard model at the precision frontier. One such test is the anomalous magnetic moment of the muon, (<em>g</em> − 2)<sub><em>μ</em></sub>, which is the subject of discussion in Part I and its Addendum. Therein, we analyze the transition form factors of axial-vector mesons, which are essential input quantities for an improved evaluation of the axial-vector contributions to hadronic light-by-light scattering. For our analysis, we use the framework of vector-meson dominance, include short-distance constraints from the light-cone expansion, and constrain the free parameters from experiment. Our final result consists of novel parameterizations for the transition form factors of the <em>f</em><sub>1</sub>, <em>f</em><sub>1</sub><sup>′</sup>, and <em>a</em><sub>1</sub>, which are eligible for a revised estimate of the axial-vector contributions to (<em>g</em> − 2)<sub><em>μ</em></sub>.<br> Another test of the standard model at the precision frontier is provided by rare semileptonic <em>η</em><sup>(′)</sup> decays, which are investigated in Part II. Due to the strong suppression of these decays within the standard model, they are excellent candidates for searches for physics beyond this theory. For the analysis of the semileptonic <em>η</em><sup>(′)</sup> decays, we consider vector-meson-dominance parameterizations and determine the free parameters from phenomenological input. Using the constructed framework, we calculate branching ratios and differential distributions, which can be confronted with experimental measurements.<br> In Part III, we study <em>B</em> → <em>γ</em><sup>*</sup> form factors, which entail valuable information on the leading-twist <em>B</em>-meson light-cone distribution amplitude. Our study is based on a set of dispersion relations that link these form factors to their <em>B</em> → <em>V</em> analogs. This is accompanied by a parameterization that employs a series expansion in a conformal variable and a vector-meson-dominance ansatz, with the free parameters fixed from input on <em>B</em> → <em>V</em>. The phenomenological analysis is performed in terms of integrated as well as differential branching ratios and forward–backward asymmetries for the four-lepton decay, which can probe our understanding of the standard model when compared with experiment.