Perturbative static four-quark potentials

Abstract

A first attempt to understand hadron dynamics at low energies in terms of the fundamental quark and gluon degrees of freedom incorporates the effects of the gluonic field into a potential depending only on the spatial positions of the quarks, which are considered in the infinite mass limit. A suitable framework for calculating such potentials between static quarks, i.e. a generalization of the Wilson loop will be discussed.Making a connection with recent Monte Carlo lattice simulations for the lowest two energies of a system of two quarks and two antiquarks, the static qqqq-potential will be calculated in perturbation theory to fourth order. The result will be shown to be exactly equal to the prediction of a straightforward two-body approach, which in Monte Carlo lattice simulations has been found to be a reasonable approximation for very small interquark distances. *

Four-quark flux distribution and binding in lattice SU(2)

“…Perturbation theory to O(α 2 ) also produces the two-state model of Eqs. 18-20 with f = 1 [17]. A working parameterization for f is…”

Study of degenerate four-quark states with SU(2) lattice Monte Carlo techniques

“…These are also discussed qualitatively in Ref. [17] and contribute at O(a3) to two-, three-, and fourquark potentials.…”

“…04 I* F;, once the separable form or the more symmetrical one in Eqs. (13) or (17) have been chosen, the only decision to be made is the value of kM; the number of terms (Vi) to be determined. This is varied between 1 and 3.…”

“…In Ref. [17] it was shown that the two-state model of Eqs. (19) with the overlap factor j = 1 agreed with perturbation theory up to fourth order in the quark-gluon coupling [i.e., to O(a')] and gives El,z=O for tetrahedra.…”

“…Some perturbative possibilities are discussed in Ref. [17]. There it is shown that all three-quark terms arising from three gluon vertices always vanish, but that the four gluon vertex can contribute to two-, three-, and four-quark terms at O(a3).…”