Nonperturbative quark dynamics in a baryon

Abstract

Field-correlator method is used to calculate nonperturbative dynamics of quarks in a baryon. General expression for the 3q Green's function is obtained using Fock-Feynman-Schwinger (world-line) path integral formalism, where all dynamics is contained in the 3q Wilson loop with spin-field insertions. Using lowest cumulant contribution for Wilson loop one obtains an Y-shaped string with a deep hole at the string junction position. Using einbein formalism for the quark kinetic terms one automatically obtains constituent quark masses, calculable through the string tension. Resulting effective action for 3q plus Y-shaped strings is quantized in the path-integral formalism to produce two versions of Hamiltonian,one -in the c.m. and another in the light-cone system. Hyperspherical formalism is used to calculate masses and wave functions. Simple estimates in lowest approximation yield baryon masses in good agreement with experiment without fitting parameters.