Baryon Masses in a Relativistic Quark-Diquark Model

Abstract

Masses of ground-state spin-| baryons are calculated in a relativistic quark-diquark model with a potential motivated by QCD. The parameters of the model are determined by fitting vector-meson masses, and so the calculation for baryons contains no free parameters. Results are in rather good agreement with experiment. Moreover, starting from dynamical quark masses close to the so-called current masses, effective quark masses are obtained in the right range to be identified with constituent masses. PACS numbers: 12.70.+q, 12.35.Ht, In his original paper on the quark model, Gell-Mann 1 raised the possibility of the existence of free diquarks. Later, diquarks were considered as bound constituents of baryons, 2 * 3 exotic mesons, 3 " 7 or other hadronic matter. 6 " 9 During recent years arguments have been given 6 " 14 for the existence of diquark substructure in baryons. Despite this fact, except for a nonrelativistic calculation of P-and Z/-state baryons, 15 little has been done in the way of actual quantitative calculations of baryon masses in a dynamical quark-diquark model. This is surprising, since the use of diquarks considerably reduces the mathematical difficulties by converting a threebody problem into a two-body one.Here we consider a baryon to be composed of a quark and a diquark and calculate baryon masses by solving a relativistic wave equation for the motion of the quark and diquark in a phenomenological potential which depends only on their separation. The form and color dependence of the potential are motivated by considerations from quantum chromodynamics (QCD). The parameters of the potential and the input quark current masses are first determined from the meson sector. With no free parameters left, we calculate the properties of diquark states, and then, using the diquark masses found in the preceding step, we find the spectrum of quarkdiquark (baryon) states. In this way a relativistic three-body problem is reduced to solving a twobody problem twice. In this introductory note we restrict ourselves to spin-independent interactions and illustrate the method by calculating the masses of the ground-state spin--| baryons. We plan to include spin effects and calculate the masses of other baryons in a more complete investigation in the future.Our results can be summarized as follows: (i) Using a potential containing two adjustable parameters, we obtain a good spectrum of vec-tor mesons (including mesons containing only light quarks), (ii) Starting from current quark masses, we calculate effective quark masses which turn out to be quite close to the usual constituent masses, (iii) Without any adjustable parameters we calculate the absolute spectrum of the ground-state spin-- § baryons with surprising success.First of all we discuss the framework in which these results are obtained. Although a nonrelativistic Schrodinger equation is adequate to treat mesons of the J/ip and T families, which contain only the heavy c and b quarks, this equation, with a potential motivated by QCD, fails to give even an approx...

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