Nonperturbative quark dynamics in a baryon

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