a Numerical Study of Quark Confinement in Low - Abelian Gauge Models

The strong force between quarks and gluons has the peculiar property of preventing them from being isolated, as they always seem to be confined inside hadrons. Quantum Chromodynamics, or QCD, is the leading candidate as a theory of this strong interaction; however, its quark confinement properties are very difficult to study theoretically. Hoping to gain some useful and general insight on the physics of QCD, we have studied two models which are qualitatively similar to, and much simpler than Quantum Chromodynamics. Using numerical lattice gauge theory techniques, we have inves- tigated the potential V(L) between two heavy quarks. As suggested by charmonium phenomenology, V(L) has the form: V(,(L)) = -A/L + T L; L < L(,o), V(,(L)) (TURN) c = constant; L >> L(,o). First, we have computed the string tension "T" in compact Quan- tum Electrodynamics in three dimensions, without light fermions (quarks). As a function of the coupling "g", our data shows T to be constrained between the two envelopes g('2)/2 and (4SQRT.(8) g('-2)) exp ( -4.4g('-2)) , in similarity with QCD. Moreover, we have found the lines of force of this model to behave like a string for g (LESSTHEQ) 1.16, i.e., to have an energy density proportional to (1/1nL). In the second part of this work, we consider Quantum Electro- dynamics in two dimensions, this time including the light fermions; the latter are responsible for the screening of the (color) electric field between the heavy quarks, leading to the cut-off "c" and the screening length "L(,o)" above. We have found L(,o) to depend on the light quark mass "m/e" in the following way: for the case of only one dynamical flavor present, eL(,o)('(1)) (TURN) 3SQRT.((pi)/16 + (m/e)('2)) m/e < 1, while, in the case of two flavors of about the same mass, eL(,o)('(1)) (LESSTHEQ) 2eL(,o)('(2)) (LESSTHEQ) (eL(,o)('(1)))('2) (eL(,o)('(1)) -1))('-1). The last result shows the presence of a flavor -flavor interaction through mutual screening, in addition to the usual independent screening of the heavy quark by each flavor.