QCD-based relativistic Hartree-Fock calculations for identical quarks

Abstract

As was first pointed out by Witten, a large number of colors ( N c ) leads to a simplification in the theory of baryon masses in that the quarks may be assumed to move in a mean field which can be found self-consistently. The interquark potential in such a description can be borrowed from the meson-sector phenomenology in the absence of an accurate evaluation of it from large-Nc quantum chromodynamics (QCD). We have camed out this program with such a potential due to Richardson, used often by workers in the meson sector. This potential has the advantage of incorporating the two main features of QCD: namely, confinement and asymptotic freedom. In view of the small number of parameters involved, the results agree surprisingly well with experiment for the case of three identical quarks.

Quark mean-field theory and consistency with nuclear matter

“…This results in changes in the nucleon property, for example, in the increase in the radius expected from the European Muon Collaboration experimental data through rescaling (Close, Roberts, and Ross [6]). In the formalism of relativistic Hartree-Fock theory (Dey, Dey, and Le Tourneux [7]),justified by the large N, theory of t'Hooft [8) and Witten [9], one gets a weakening of the confinement (Dey et al [10]) at higher density. If one uses the potential due to Richardson [11], this means a decrease in A, the only parameter present in the interaction.…”

“…If one uses the potential due to Richardson [11], this means a decrease in A, the only parameter present in the interaction. We wish to recall that for light quarks one has to use a running quark mass m(r) to get correct nucleon radius and other properties [7]. Relativistic description of nuclear structure and reactions within quantum hadrodynamics (QHD) has been greatly developed during the last several years (Serot and Walecka [12], Celenza, Rozenthal, and Shakin [13] There are two problems in doing this.…”

“…(u, d ) quarks one has to split the potential into a vector and a scalar part arbitrarily to take care of the chiral symmetry breaking [7]. An alternative has been tried recently by Dey et al [20], where forms are m, """(x ) = -4~'x'(4%'), (10) where (%%)=( -2S5 MeV) and the Eq.…”

“…(17) we calculate the nucleon mass from the relativistic Hartree-Fock equation self-consistently [7]. The center-of-mass correction is also done as in Ref.…”

“…The center-of-mass correction is also done as in Ref. [7] [11][see Eqs. (1) and (2)] for diff'erent values of the parameter A, for the corresponding nuclear densities.…”