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Register a new userBaryons as non-topological chiral solitons
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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.
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The Nambu - Jona-Lasinio model in its SU(2) and SU(
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $pi N sigma$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy. These objects are, therefore, interpreted as totally incompressible solitons. As a first, particular example we consider (1+1) dimensional kinks in theories with a nonstandard kinetic term or, equivalently, in models with the so-called runaway (or vacummless) potentials. But incompressible solitons exist also in higher dimensions. As specific examples in (3+1) dimensions we study Skyrmions in the dielectric extensions both of the minimal and the BPS Skyrme models. In the the latter case, the skyrmionic matter describes a completely incompressible topological perfect fluid.
We construct an effective hadronic model including single heavy baryons (SHBs) belonging to the $(mathbf{3},mathbf{3})$ representation under $mbox{SU}(3)_L times mbox{SU}(3)_R$ symmetry, respecting the chiral symmetry and heavy-qaurk spin-flavor symmetry. When the chiral symmetry is spontaneously broken, the SHBs are divided into the baryons with negative parity of $bar{mathbf 3}$ representation under $mbox{SU}(3)$ flavor symmetry which is the chiral partners to the ones with positive parity of ${mathbf 6}$ representation. We determine the model parameters from the available experimental data for the masses and strong decay widths of $Sigma_c^{(ast)}$, $Lambda_c (2595)$, $Xi_c (2790)$, and $Xi_c (2815)$. Then, we predict the masses and strong decay widths of other baryons including $Xi_b$ with negative parity. We also study radiative decays of SHBs including $Omega_c^ast$ and $Omega_b^ast$ with positive parity.
It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral restoration for these states. We argue how the idea of chiral symmetry restoration high in the spectrum is consistent with the concept of quark-hadron duality. If chiral symmetry is effectively restored for highly-lying states, then the baryons should fall into representations of $SU(2)_Ltimes SU(2)_R$ that are compatible with the given parity of the states - the parity-chiral multiplets. We classify all possible parity-chiral multiplets: (i) $(1/2,0)oplus(0, 1/2)$ that contain parity doublet for nucleon spectrum;(ii) $(3/2,0) oplus (0, 3/2)$ consists of the parity doublet for delta spectrum; (iii) $(1/2,1) oplus (1, 1/2)$ contains one parity doublet in the nucleon spectrum and one parity doublet in the delta spectrum of the same spin that are degenerate in mass. Here we show that the available spectroscopic data for nonstrange baryons in the $sim$ 2 GeV range is consistent with all possibilities, but the approximate degeneracy of parity doublets in nucleon and delta spectra support the latter possibility with excited baryons approximately falling into $(1/2,1) oplus (1, 1/2)$ representation of $SU(2)_LtimesSU(2)_R$ with approximate degeneracy between positive and negative parity $N$ and $Delta$ resonances of the same spin.
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