Nonperturbative study of hadronization with heavy sources: The screening length as a function of the quark mass in the Schwinger model.

Abstract

We discuss the dynamical quark-mass dependence of the screening length (${L}_{0}$), the distance at which the interaction between two (heavy) quarks begins to be screened as a result of pair production. We compute ${L}_{0}$ in the one-flavored massive Schwinger model in the continuum limit of its lattice formulation. The results of our numerical simulation (ensemble projector Monte Carlo) are shown to follow closely the lower bound ${\mathrm{eL}}_{0}$\ensuremath{\ge}[\ensuremath{\pi}/16+(m/e${)}^{2}$${]}^{1/2}$ /(string tension), in which most of the quark-mass dependence is contained in the hadronic mass of the numerator. The vacuum expectation values of the electric field and the fermion occupation number have also been computed, showing directly the hadronization process. Finally, we apply those ideas in estimating the screening length in charmonium and \ensuremath{\Upsilon} systems.