Interactions of Pions with the QCD String and Light Quark Mass Dependencies

Abstract

This thesis is centered around computing interactions between string excitations (quarkonium) and pion states, with the aim of understanding how observables are influenced by the light quark masses. The pion mass serves as a parameter to express this dependence on the quark mass. By incorporating the pion mass into the analysis, we investigate how the light quark masses affect the long-distance behavior of the quarkonium hyperfine potential. To achieve this, we employ Chiral Theory and Effective String Theory methodologies, deriving mathematical functions for some observables that depend on the length of the string, the pion mass, and the momentum of the external pions involved. This analysis provides insights into the corrections to the static potential due to the presence of the pion mass and the interplay between potential and pion mass (light quark mass). We find a dependence of the light quark masses on the string tension and successfully compute the elastic collision between a pion and the string ground state. Additionally, we calculate transition amplitudes from string excited states to the string ground state by the emission of two pions, covering a range from N = 1 up to one state of N = 3. These results are particularly relevant for studying transitions with pion emission between states of large principal quantum number in quarkonium and between hybrids and quarkonium states.