Quark model

J. I. Friedman and H. W. Kendall (Massachusetts Institute of Technology) and R. E. Taylor (Stanford) pioneering investigations concerning deep elastic scattering of electrons on protons and bound neutrons, of essential importance for the development of the quark model in particle physics. 

Quark model of hadrons (Gell-Mann, Zweig). 

In order to test this experimental finding we are comparing with the eigenvalues of a Hamiltonian for a realistic quark model, namely the Goldstone-boson-exchange (GBE) constituent quark model (Glozman et al, 1998). It includes the kinetic energy in relativistic form... 

Aguirre, R. M., De Paoli, A. L. (2002). Neutron star structure in a quark model with excluded volume correction. Phys.Rev.C68 055804. 

Recently, the possible formation of diquark condensates in QCD at finite density has been re-investigated in a series of papers following Refs. [1, 2], It has been shown that in chiral quark models with nonperturbatrive 4-point interaction motivated from instantons [3] or nonperturbative gluon propagators [4, 5], the anomalous quark pair amplitudes can be very large - of the order of 100 MeV. The diquark pairs that are formed as a result of the attractive inter-... 

As a first step in this direction we will discuss here the two flavor color superconducting (2SC) quark matter phase which occurs at lower baryon densities than the color-flavor-locking (CFL) one, see [18, 32], Studies of three-flavor quark models have revealed a very rich phase structure (see [32] and references therein). However, for applications to compact stars the omission of the strange quark flavor within the class of nonlocal chiral quark models considered here may be justified by the fact that central chemical potentials in stable star configurations do barely reach the threshold value at which the mass gap for strange quarks breaks down and they appear in the system [20], Therefore we will not discuss here first applications to calculate compact star configurations with color superconducting quark matter phases that have employed non-dynamical quark models... 

We consider a nonlocal chiral quark model described by the effective action which generahzes the approach of Ref. [23] by including the scalar diquark pairing interaction channel with a coupling strength G 2. 

We will employ parametrisations of the nonlocal quark model which reproduce pion properties mass mn = 140 MeV, decay constant fn = 93 MeV and which have the same quark mass gap (7 = 0, /z = 0) = 330 MeV in the vacuum. The results for the Darameterization are taken from [23],... 

We have investigated the influence of diquark condensation on the thermodynamics of quark matter under the conditions of /5-equilibrium and charge neutrality relevant for the discussion of compact stars. The EoS has been derived for a nonlocal chiral quark model in the mean field approximation, and the influence of different form-factors of the nonlocal, separable interaction (Gaussian, Lorentzian, NJL) has been studied. The model parameters are chosen such that the same set of hadronic vacuum observable is described. We have shown that the critical temperatures and chemical potentials for the onset of the chiral and the superconducting phase transition are the lower the smoother the momentum dependence of the interaction form-factor is. 

The resulting grand canonical thermodynamic potential for 2SC quark matter within the instantaneous nonlocal chiral quark model (INCQM) [27, 28] in the mean field approximation is given by... 

Since the discovery of the parton substructure of nucleons and its interpretation within the constituent quark model, much effort has been spent to explain the properties of these particles and the structure of high density phases of matter is under current experimental investigation in heavy-ion collisions [17]. While the diagnostics of a phase transition in experiments with heavy-ion beams faces the problems of strong non-equilibrium and finite size, the dense matter in a compact star forms a macroscopic system in thermal and chemical equilibrium for which effects signalling a phase transition shall be most pronounced [8],... 

Barbour, I.M., Davies, A. T. (Eds.) Fundamentals of Quark Models, Proceedings of 17. Scottish Universities Summer School in Physics 1976. Edinburgh Physics Department (May field Road) 1977... 

Before discovery of the hadron particle (designated psi or J), and after much experimental and theoretical effort, physicists had about concluded that three massive, fractionally charged entities (quarks) were the primary building blocks of the universe. However, discovery of the psi particles in 1974 indicated a fourth quark was required. Previously, in the thrcc-quark model, all mesons were made up of one quark and one aiitiquark baryons, of three quarks and all anti-baryons, of three antiquarks. Prior to 1974, all of the known hadrons could be accommodated within this basic scheme Three of the possible meson combinations of quark-antiquark could have the same quantum numbers as the photon, and hence could be produced abundantly in e+e annihilation. These three predicted states had all been found. 

A brief review of the complexities to which the quark theory is addressed is in order. Particles which can interact via the strong nuclear force arc called hadrons. Hadrons can be divided into two main classes—the mesous (with baryon number zero) and the baryons (with nonzero baryon number). Within each of the classes there are small subclasses. The subclass of baryons which has been known ihe longest consists of those particles with spin j and even parity. The members of this class are the proton, the neutron, the A0 hyperon, the three hyperons and the two 3 hyperons. There are no baryons with spin 4 and even parity (or, to the usual notation, Jp = i+). The next family of baryons has ten members, each with Jp = l+. The mesons can be grouped into similar families. One of the first successes of the quark model was to explain just why there should be eight baryons with Jp = 1, ten with 1, etc., and why the various members of these families have the particular quantum numbers observed. 

The initial quark model was formulated to explain the diversity of the hadrons and not to explicitly describe the internal structure of any particle. It was inevitable, however, that with further research there w as a tendency to identify new findings with the hypothetical quarks. A number ofproperties of the partons, such as their intrinsic spin angular momentum, have been measured and have proved to be consistent with the predictions of the quark model. 

The use of quarks in atomic shell theory provides an alternative basis to the traditional one. The transformations between these bases can be complicated, but there are many special cases where our quarks can account for unusual selection rules and proportionalities between sets of matrix elements that, when calculated by traditional methods, go beyond what would be predicted from the Wigner-Eckart theorem [4,5], This is particularly true of the atomic f shell. An additional advantage is that fewer phase choices have to be made if the quarks are coupled by the standard methods of angular-momentum theory, for which the phase convention is well established. This is a strong point in favor of quark models when icosahedral systems are considered. A number of different sets of icosahedral Clebsch-Gordan (CG) coefficients have been introduced [6,7], and the implications of the different phases have to be assessed when the CG coefficients are put to use. 

P need confirmation. Quantum numbers shown are quark-model predictions. 

Quantum numbers shown are quark model predictions. Mass m = 6.286 0.005 GeV Mean life t = (0.46j Q jg) x 10- s B modes are charge conjugates of the modes below. 

See also the table of suggested qq quark-model assignments in the Quark Model section. 

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