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The Nambu - Jona-Lasinio model in its SU(2) and SU(
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The present review gives a survey of recent developments and applications of the Nambu--Jona-Lasinio model with $N_f=2$ and $N_f=3$ quark flavors for the structure of baryons. The model is an effective chiral quark theory which incorporates the SU(N$_f$)$_Lotimes$SU(N$_f$)$_Rotimes$U(1)$_V$ approximate symmetry of Quantum chromodynamics. The approach describes the spontaneous chiral symmetry breaking and dynamical quark mass generation. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. For the evaluation of the baryon properties the present review concentrates on the non-linear Nambu--Jona-Lasinio model with quark and Goldstone degrees of freedom which is identical to the Chiral quark soliton model obtained from the instanton liquid model of the QCD vacuum. In this non-linear model, a wide variety of observables of baryons of the octet and decuplet is considered. These include, in particular, electromagnetic, axial, pseudoscalar and pion nucleon form factors and the related static properties like magnetic moments, radii and coupling constants of the nucleon as well as the mass splittings and electromagnetic form factors of hyperons. Predictions are given for the strange form factors, the scalar form factor and the tensor charge of the nucleon.
We report results from a study of heavy-baryon spectroscopy within a relativistic constituent- quark model, whose hyperfine interaction is based on Goldstone-boson-exchange dynamics. While for light-flavor constituent quarks it is now commonly accepted that the effective quark-quark interaction is (predominantly) furnished by Goldstone-boson exchange - due to spontaneous chiral-symmetry breaking of quantum chromodynamics at low energies - there is currently still much speculation about the light-heavy and heavy-heavy quark-quark interactions. With the increasing amount of experimental data on heavy-baryon spectroscopy these issues might soon be settled. Here, we show, how the relativistic constituent-quark model with Goldstone-boson-exchange hyperfine interactions can be extended to charm and bottom baryons. It is found that the same model that has previously been successful in reproducing the light and strange baryon spectra is also in line with the existing phenomenological data on heavy-baryon spectroscopy. An analogous model with one-gluon-exchange hyperfine interactions for light-heavy flavors does not achieve a similarly good performance.
Transverse densities describe the distribution of charge and current at fixed light-front time and provide a frame-independent spatial representation of hadrons as relativistic systems. We calculate the transverse densities of the octet baryons at peripheral distances b = O(M_pi^{-1}) in an approach combining chiral effective field theory (ChEFT) and dispersion analysis. The densities are represented as dispersive integrals of the imaginary parts of the baryon electromagnetic form factors in the timelike region (spectral functions). The spectral functions on the two-pion cut at t > 4 M_pi^2 are computed using relativistic ChEFT with octet and decuplet baryons in the EOMS renormalization scheme. The calculations are extended into the rho-meson mass region, using a dispersive method that incorporates the timelike pion form-factor data. The approach allows us to construct densities at distances b > 1 fm with controlled uncertainties. Our results provide insight into the peripheral structure of nucleons and hyperons and can be compared with empirical densities and lattice-QCD calculations.
We compute the helicity-dependent strange quark distribution in the proton in the framework of chiral effective theory. Starting from the most general chiral SU(3) Lagrangian that respects Lorentz and gauge invariance, we derive the complete set of hadronic splitting functions at the one meson loop level, including the octet and decuplet rainbow, tadpole, Kroll-Ruderman and octet-decuplet transition configurations. By matching hadronic and quark level operators, we obtain generalized convolution formulas for the quark distributions in the proton in terms of hadronic splitting functions and quark distributions in the hadronic configurations, and from these derive model-independent relations for the leading nonanalytic behavior of their moments. Within the limits of parameters of the Pauli-Villars regulators derived from inclusive hyperon production, we find that the polarized strange quark distribution is rather small and mostly negative.
The mass spectra of singly charmed and bottom baryons, $Lambda_{c/b}(1/2^pm,3/2^-)$ and $Xi_{c/b}(1/2^pm,3/2^-)$, are investigated using a nonrelativistic potential model with a heavy quark and a light diquark. The masses of the scalar and pseudoscalar diquarks are taken from a chiral effective theory. The effect of $U_A(1)$ anomaly induces an inverse hierarchy between the masses of strange and non-strange pseudoscalar diquarks, which leads to a similar inverse mass ordering in $rho$-mode excitations of singly heavy baryons.
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