Loop-induced form factors in light-meson physics

Abstract

The hadronic sector is a part of the Standard Model (SM) of particle physics that is not yet fully understood. Specifically, the energy dependence of the coupling of hadrons to photons, described by form factors, is an active field of research. We investigate two processes where form factors play a crucial role. In the first project, we calculate decay widths and branching ratios of rare semileptonic decays of the <em>η</em> and <em>η</em>' mesons into <em>π</em>⁰/<em>η</em> and two leptons. These decays proceed via a two-photon intermediate state, which couples to the hadrons via transition form factors (TFFs). Different parameterisations of these TFFs are implemented and their effect on the results is discussed. Thus, we obtain a prediction for the SM contribution with some control over these systematic effects, which can be tested against future experimental results in order to investigate the possibility of beyond-the-SM (BSM) effects. In the second project, we construct a framework to dynamically generate doubly-virtual TFFs of the <em>a</em>₁ and <em>a</em>₂ mesons, for which not much experimental data exists, from a <em>&rho;π</em> intermediate state. For this, we describe the <em>&rho;π</em> → <em>γ</em>^*<em>γ</em>^* system in a gauge-invariant way and, making use of unitarity, reconstruct it from left-hand cuts, taking care to remove kinematic singularities. We connect this system to the TFFs via the imaginary part of a loop diagram, reconstructing the real part dispersively; the convergence of said loop diagram limits our framework. These TFFs are relevant for a precise determination of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.