Quark mean-field theory and consistency with nuclear matter

Jishnu Dey, Lauro Tomio, Mira Dey, T. Frederico
1991 Physical Review C  
1/N, expansion in QCD (with N, the number of colors) suggests using a potential from meson sector (e.g., Richardson) for baryons. For light quarks a 0. field has to be introduced to ensure chiral symmetry breaking (ySB). It is found that nuclear matter properties can be used to pin down the ySB modeling. All masses, M&, m, m", are found to scale with density. The equations are solved self-consistently. Low-energy physics is essentially controlled by the Goldstone particle, i.e. , the pion. The
more » ... elevant parameter is the pion decay constant, f . This is related to the quark condensate (qq ) through the Weinberg sum rule. In the QCD sum-rule approach also, the nucleon mass is determined predominantly by the odd-dimensional operator (qq ) (Ioffe [1], Reinders, Rubinstein, and Yazaki [2]). At higher density the condensate decreases in magnitude (Bailin, Cleymans, and Scadron [3], Dey, Dey, and Ghose [4]) and f also decreases correspondingly (Dey and Dey [5]). 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. 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]). Can one show the compatibility of this model with the meanfield quark model'7 In a crude way this was done by Guichon [14] and Frederico et al. [15] where they assumed that there is a scalar o. and a vector cu field coupled to the quark. As clearly stated by Guichon, this is a very strong assumption since neither the o. nor the co are fundamental at the quark level. One can think of the running quark mass m(x) as being due to a o field. There are two problems in doing this. First one has to take care of the Goldstone pion since one is breaking chiral symmetry. This is hard to do since the pion-quark coupling is a highly nonlinear one and only in the Zahed model [16] in lower dimension can one treat this exactly. But we need not worry about this here since we can introduce the well-established one-pion-exchange potential (OPEP) at the QHD level in nuclear matter and thus correct for the deficiency of the quark model. In some models, pions may indeed couple to the quarks themselves, but we do not consider such models. The problem is that the pions have a dual character, being Goldstone particles as well as quark-antiquark composites; their role in QCD-inspired models is still ambiguous. For the present we prefer to ignore the pion-quark interaction and replace this by the nucleon-pion interaction, which does not introduce any additional parameters in the theory. The energy due to the OPEP in nuclear matter has been estimated in second-order perturbation theory by Cenni, Conte, and Dillon [17] using wave functions in nuclear matter derived from the Reid soft-core potential [18] . This is almost model independent since the OPEP tail is the same in all modern nucleon-nucleon interactions. And the second-order OPEP contribution is insensitive to the finer details of the nuclear matter wave functionit only depends on the wound in the wave function in a crude sort of way. One can see that the error due to this cannot be very large even if pions couple to the quarks themselves as Goldstones, since the coupling must be cut off for a radius of around 0.35 fm or so. This is because from deep-inelastic scattering we know that at short distances the quarks are free and massless. In fact, in models like the o.-m soliton bag this restoration of chiral symmetry at short distance is hard to achieve. In some sense the Reid soft-core wound cuts off the pion from the nucleon, and therefore also from the quarks at about this distance, since in the nuclear-matter wave function, the nucleon is taken to be pointlike, apart from this wave-function effect. At the present moment, exact treatment of the nucleon-nucleon interaction with pions in the quark picture, is an insoluble problem. The o. fits in nicely with the running quark mass, but again there is problem with the vector mesons. In the Walecka model 2181
doi:10.1103/physrevc.44.2181 pmid:9967638 fatcat:okrdvyi2hjc3fjm6cle2lj2m2q