QCD string in the baryon

Abstract

The QCD-motivated constituent string model is extended to consider the baryon. The system of three quarks propagating in the confining background field is studied in the Wilson loop approach, and the effective action is obtained. The resulting Lagrangian at large interquark distances corresponds to the Mercedes Benz string configuration. Assuming the quarks to be heavy enough to allow the adiabatic separation of quark and string junction motion and using the hyperspherical expansion for the quark subsystem we write out and solve the classical equation of motion for the junction. We quantize the motion of the junction and demonstrate that the account of these modes leads to the effective "swelling" of the baryon in comparison with the standard potential picture. We discuss the effects of the finite gluonic correlation length which do not affect the excited states but appear to be substantial for the baryonic ground state, reducing the "swelling" considerably and leaving room to the short range Coulomb force in the three quark system.