Universality of Effective Potentials in Models of Mesons

Abstract

Many simple pictures of hadrons have been inspired by QCD. They are formulated in the instant-form (IF) of dynamics as well as in the front-form (FF). One can observe that nearly all considerations in the IF lead to the conclusion that the potential between quarks and antiquarks should be linear at large distances. In contrast, the FF formulation favors a quadratic potential. We discuss examples and show that the linear IF confinement potential corresponds to the quadratic FF potential. An important tool in our discussion is the WKB method which allows one to relate the maximum distances of separation between quarks within mesons in different models.