Probing quark mass effects in low-energy hadron physics

Abstract

Since quarks are confined inside hadrons, their properties as well as their contributions to hadronic observables can be assessed by indirect methods only. As the strength of the strong interaction increases with the spatial distance, the treatment of quantum chromodynamics at low energies in general requires non-perturbative methods like dispersion relations or lattice gauge theory. Based on the fact that the light quark masses are very small with respect to the typical hadronic mass scales for mesons and baryons, furthermore effective field theories can be constructed to describe low-energy properties and dynamics of hadrons perturbatively. The present work is concerned with two particularly interesting hadronic processes that are closely related to the light quark masses. Although distinct theoretical frameworks utilizing different calculational techniques are applied, in both cases the investigations at hand are prerequisites for high-precision analyses of the respective quark-mass effects.<br /> In the first part of this thesis, we investigate higher-order isospin-breaking effects in η→3π decays, namely η→π⁰π⁺π^- and η→3π⁰, in chiral perturbation theory. By evaluating the second-order mixed strong and electromagnetic isospin-breaking corrections, we confirm the picture that the electromagnetic contributions are small. Therefore, η→3π is perfectly suited to extract isospin-breaking ratios of light quark masses via comparing theoretical predictions with experimental results. Since for an accurate determination a detailed description of the Dalitz plot distributions is necessary, we study the different effects of higher-order isospin breaking in η→3π on a more general basis. In particular, we investigate corrections to isospin relations between both decay channels at the level of Dalitz plot parameters, showing that the branching ratio of the two partial decay widths entails sizeable uncertainties. <br /> In the second part, we develop a dispersive formalism and a solution strategy for a precision determination of the leading partial waves of the pN scattering amplitude in the low-energy region. They are specifically important to constrain the pion–nucleon s-term, which measures the light-quark contributions to the nucleon mass and is still a subject of discussion. Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations that respects analyticity, unitarity, and especially crossing symmetry. Assuming Mandelstam analyticity, we determine the maximal kinematical ranges of validity of the equations for both the scattering process and the crossed annihilation process ππ→ <span style="text-decoration:overline">N</span>N. <br /> To suppress the dependence on the high-energy region, we also introduce subtractions into the Roy-Steiner system, identifying the subtraction constants with pN subthreshold parameters. The S- and P-waves of the crossed process feature prominently in dispersive analyses of the scalar nucleon form factor that is directly linked to the s-term and the electromagnetic nucleon form factors, respectively. As a first step towards solving the full Roy-Steiner system, we study the solution of these partial waves by using Muskhelishvili-Omnès techniques. <br /> Due to the conceptual and methodological differences, both parts are presented in a self-contained fashion.