Speaker
Description
Wilson et al. proposed in Phys. Rev. D 49, 6720, (1994) to deal with the QCD front form Hamiltonian divergences due to gluons with small hadron momentum fraction x, such as in the instantaneous gluon exchange between quarks, by introducing tree level counter terms. These small-x divergences and counter terms significantly complicate access to the logarithmically scale-dependent dynamics of hadronic constituents. An alternative approach will be discussed. The transverse gluons are given an arbitrarily small mass and a scalar octet field is introduced to stand for the longitudinal gluons. The scalar field couples to the quark and gluon color currents proportionally to the gluon mass so that the coupling vanishes in the limit of the mass going to zero. Ultraviolet and small-x divergences are treated in a common way using a correspondingly adjusted regularization and renormalization group procedure. There is no need for the tree-level counter terms proposed by Wilson et al. The Hamiltonian approach is thus simplified. The limit of the resulting renormalized, logarithmically scale-dependent theory when the gluon mass parameter is going to zero appears worth studying for application in phenomenology of hadrons made of quarks and gluons that are asymptotically free at short and confined at long distances.
