Dispersive analysis of charmed meson decays

Abstract

The Standard Model comprises most of today's knowledge of particle physics and is overall well tested and understood. However the dynamics of strong interactions, given by Quantum Chromodynamics (QCD), are still a challenge at low energies. The running coupling constant prevents a direct perturbative calculation of QCD at the hadronic scale and therefore other methods have to be employed.<br /> In this thesis we apply dispersion theory to study strong final-state interactions in three-particle decays and investigate the J/ψ → π⁰ γ^* transition form factor.<br /> In the first part of this thesis we introduce a dispersive framework for three-body decays, based on Khuri—Treiman equations, that satisfies analyticity, unitarity, and crossing symmetry by construction and includes crossed-channel rescattering effects.<br /> We explicitly display the derivation of the Khuri—Treiman equations on general vector-meson decays into three pions V → 3π with V∈{ω, Φ, J/ψ}. These decays provide an ideal test case as the equations are of simple form. In this context we study the general dependence of the resulting amplitude on the vector-meson mass and investigate the employed iterative solution strategy and its convergence. <br /> Building on the obtained J/ψ → 3π amplitude we study the J/ψ transition form factor. The transition form factors of light vector mesons have been of great interest over the last years because of their importance in the theoretical determination of the anomalous magnetic moment of the muon. However the available experimental data is difficult to understand theoretically. With the larger phase space available, the J/ψ → π⁰ γ^* transition may shed light onto the lighter vector-meson transition form factors.<br /> In the second part we resume our study of three-particle decays on the Cabibbo-favored D⁺ → K π π⁺ decays. Heavy-flavor three-body decays into light mesons provide a valuable source for Standard Model tests and beyond. They play an important role due to their richer kinematic structure compared to two-body decays which can be exploited e.g. in CP-violation studies. So far the Khuri—Treiman-type equations have been applied successfully to light meson decays but not to heavy-flavor decays. Thus the Cabibbo favored D⁺ → K π π⁺ decays provide an ideal test to establish the framework in the open-charm sector. We introduce a new numerical method to solve the Khuri—Treiman-type equations, compare the obtained decay amplitudes to the data from the CLEO, FOCUS, and BES III collaboration as well as previous theoretical studies and discuss the impact of crossed-channel rescattering effects in these decays.