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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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Within the ACCMM model the average kinetic energy of heavy quark in a heavy-light meson is calculated as hp, solely from the fact that the Gaussian momentum probability distribution has been taken in the ACCMM model. Therefore, the Fermi momentum parameter p F of the ACCMM model is not a truly free parameter, but is closely related to the average kinetic energy of heavy quark, which is theoretically calculable in principle. In this context, we determine p F by comparing the theoretical prediction of the ACCMM model with the model independent lepton energy spectrum of B ! eX from the recent CLEO analysis, and nd that p F = 0 : 51 0:08 0:07 GeV. We also calculate p F in the relativistic quark model by applying the quantum mechanical variational method, and obtained p F = 0 : 5 0 : 6 GeV. We show the correspondences between the relativistic quark model and the heavy quark eective theory. W e then clarify the importance of the value of p F in the determination of jV ub =V cb j.

We investigate the B and D mesons in the relativistic quark model by applying the variational method with the Gaussian wave function. We calculate the Fermi momentum parameter p F , and obtain p F ϭ0.50Ϫ0.54 GeV, which is almost independent of the input parameters ␣ s , m b , m c , and m sp . We then calculate the ratio f B /f D , and obtain a result which is larger, by a factor of about 1.3, than ͱM D /M B given by the naive nonrelativistic analogy. This result is in a good agreement with the recent lattice calculations. We also calculate the ratio (M B* ϪM B )/(M D* ϪM D ). In these calculations the wave function at the origin (0) is essential. We also determine p F by comparing the theoretical prediction of the ACCMM model with the lepton energy spectrum of B→eX from the recent ARGUS analysis, and find that p F ϭ0.27Ϯ 0.27 0.22 GeV, when we use m c ϭ1.5 GeV. However, this experimentally determined value of p F is strongly dependent on the value of the input parameter m c .

Vacuum polarization and spontaneous symmetry breaking in a two-dimensional massless fermion field theory with quartic interactions (the Gross-Neveu model) are studied in a cylindrical ( R ' x S ' ) space-time topology. In the case of untwisted fermion fields the symmetry-breaking behavior is similar to the model in Minkowski space-time except that the location of the effective potential minima depends upon the size of the space. In the case of a twisted fermion field there exists a critical size of the space such that the symmetry breaking occurs only for space larger than the critical one.

The Gaussian width of Fermi momentum, p F , is the most important parameter of the ACCMM model, and its value is essential in the determination of |V ub /V cb | because the experimental analysis is allowed only at the end-point region of inclusive semileptonic B-decay spectrum. We extract the value of |V ub /V cb | as a function of p F . We also calculate the parameter p F in the relativistic quark model using the variational method, and obtain p F = 0.54 GeV which is much larger than the commonly used value, ∼ 0.3 GeV, in experimental analyses. When we use p F = 0.

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