From Current to Constituent Quarks: a Renormalization Group Improved Hamiltonian-based Description of Hadrons

A model which combines the perturbative behavior of QCD with low energy phenomenology in a uni ed framework is developed. This is achieved by applying a similarity transformation to the QCD Hamiltonian which removes interactions between the ultraviolet cuto and an arbitrary lower scale. Iteration then yields a renormalization group improved e ective Hamiltonian at the hadronic energy scale. The procedure preserves the standard ultraviolet behavior of QCD. Furthermore, the Hamiltonian evolves smoothly to a phenomenological low energy behavior below the hadronic scale. This method has the bene t of allowing radiative corrections to be directly incorporated into nonperturbative many-body techniques. It is applied to Coulomb gauge QCD supplemented with a low energy linear con nement interaction. A nontrivial vacuum is included in the analysis via a Bogoliubov-Valatin transformation. Finally, the formalism is applied to the vacuum gap equation, the quark condensate, and the dynamical quark mass. Typeset using REVTEX 1