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Title: Chiral properties of the constituent quark model

Abstract

We show that, in a model based exclusively on constituent-quark degrees of freedom interacting via a potential, the full axial current is conserved if the spectrum of Q-barQ states contains a massless pseudoscalar. The current conservation emerges nonperturbatively if the model satisfies certain constraints on (i) the axial coupling gA of the constituent quark and (ii) the Q-barQ potential at large distances. We define the chiral point of the constituent quark model as that set of values of the parameters (such as the masses of the constituent quarks and the couplings in the Q-barQ potential) for which the mass of the lowest pseudoscalar Q-barQ bound state vanishes. At the chiral point the main signatures of the spontaneously broken chiral symmetry are shown to be present, namely: the axial current is conserved, the decay constants of the excited pseudoscalar bound states vanish, and the pion decay constant has a nonzero value.

Authors:
 [1];  [1];  [2];  [3]
  1. HEPHY, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria)
  2. (Russian Federation)
  3. INFN, Sezione di Roma 3, Via della Vasca Navale 84, I-00146, Roma (Italy)
Publication Date:
OSTI Identifier:
21056832
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 892; Journal Issue: 1; Conference: QCHS7: 7. conference on quark confinement and the hadron spectrum, Ponta Delgada, Acores (Portugal), 2-7 Sep 2006; Other Information: DOI: 10.1063/1.2714395; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUND STATE; CHIRAL SYMMETRY; CHIRALITY; COUPLING; DEGREES OF FREEDOM; DISTANCE; PARTICLE DECAY; PIONS; POTENTIALS; QUANTUM CHROMODYNAMICS; QUARK MODEL; QUARK-ANTIQUARK INTERACTIONS; QUARKS; SYMMETRY BREAKING

Citation Formats

Lucha, Wolfgang, Melikhov, Dmitri, Institute of Nuclear Physics, Moscow State University, 119992, Moscow, and Simula, Silvano. Chiral properties of the constituent quark model. United States: N. p., 2007. Web. doi:10.1063/1.2714395.
Lucha, Wolfgang, Melikhov, Dmitri, Institute of Nuclear Physics, Moscow State University, 119992, Moscow, & Simula, Silvano. Chiral properties of the constituent quark model. United States. doi:10.1063/1.2714395.
Lucha, Wolfgang, Melikhov, Dmitri, Institute of Nuclear Physics, Moscow State University, 119992, Moscow, and Simula, Silvano. Tue . "Chiral properties of the constituent quark model". United States. doi:10.1063/1.2714395.
@article{osti_21056832,
title = {Chiral properties of the constituent quark model},
author = {Lucha, Wolfgang and Melikhov, Dmitri and Institute of Nuclear Physics, Moscow State University, 119992, Moscow and Simula, Silvano},
abstractNote = {We show that, in a model based exclusively on constituent-quark degrees of freedom interacting via a potential, the full axial current is conserved if the spectrum of Q-barQ states contains a massless pseudoscalar. The current conservation emerges nonperturbatively if the model satisfies certain constraints on (i) the axial coupling gA of the constituent quark and (ii) the Q-barQ potential at large distances. We define the chiral point of the constituent quark model as that set of values of the parameters (such as the masses of the constituent quarks and the couplings in the Q-barQ potential) for which the mass of the lowest pseudoscalar Q-barQ bound state vanishes. At the chiral point the main signatures of the spontaneously broken chiral symmetry are shown to be present, namely: the axial current is conserved, the decay constants of the excited pseudoscalar bound states vanish, and the pion decay constant has a nonzero value.},
doi = {10.1063/1.2714395},
journal = {AIP Conference Proceedings},
number = 1,
volume = 892,
place = {United States},
year = {Tue Feb 27 00:00:00 EST 2007},
month = {Tue Feb 27 00:00:00 EST 2007}
}
  • We construct the full axial current of the constituent quarks by a summation of the infinite number of diagrams describing constituent quark soft interactions. By requiring that the conservation of this current is violated only by terms of order O(M{sub {pi}}{sup 2}), where M{sub {pi}} is the mass of the lowest pseudoscalar QQ bound state, we derive important constraints on (i) the axial coupling g{sub A} of the constituent quark and (ii) the QQ potential at large distances. We define the chiral point of the constituent quark model as those values of the parameters, such as the masses of themore » constituent quarks and the couplings in the QQ potential, for which M{sub {pi}} vanishes. At the chiral point the main signatures of the spontaneously broken chiral symmetry are shown to be present, namely: the axial current of the constituent quarks is conserved, the leptonic decay constants of the excited pseudoscalar bound states vanish, and the pion decay constant has a nonzero value.« less
  • The chiral constituent quark model is applied to predict the magnetic M1 and electric E2 amplitudes of the {Delta}{leftrightarrow}{gamma}N transition. It is found that the one-meson-exchange quark-quark potential due to the chiral fields enhances the E2/M1 ratio by a factor of about 2. The predicted M{sub 1{sup +}} amplitude and the E2/M1 ratio {approx_equal}{minus}1.0{percent} are within the range determined from a recent analysis of the data of pion photoproduction. {copyright} {ital 1997} {ital The American Physical Society}
  • We study the short-range nucleon-nucleon interaction in a chiral constituent quark model by diagonalizing a Hamiltonian comprising a linear confinement and a Goldstone boson exchange interaction between quarks. The six-quark harmonic oscillator basis contains up to two excitation quanta. We show that the highly dominant configuration is {vert_bar}s{sup 4}p{sup 2}[42]{sub O}[51]{sub FS}{r_angle} due to its specific flavor-spin symmetry. Using the Born-Oppenheimer approximation we find a strong effective repulsion at zero separation between nucleons in both {sup 3}S{sub 1} and {sup 1}S{sub 0} channels. The symmetry structure of the highly dominant configuration implies the existence of a node in the S-wavemore » relative motion wave function at short distances. The amplitude of the oscillation of the wave function at short range will be, however, strongly suppressed. We discuss the mechanism leading to the effective short-range repulsion within the chiral constituent quark model as compared to that related with the one-gluon exchange interaction. {copyright} {ital 1997} {ital The American Physical Society}« less
  • The form factor g{sub {rho}{pi}}{sup (S)}(Q{sup 2}) of the strange vector current transition matrix element {l_angle}{rho}{vert_bar}{bar s}{gamma}{sub {mu}}s{vert_bar}{pi}{r_angle} is calculated within the chiral quark model. A strange vector current of the constituent {ital U} and {ital D} quarks is induced by kaon radiative corrections and this mechanism yields the nonvanishing values of g{sub {rho}{pi}}{sup (S)}(0). The numerical result at the photon point is consistent with the one given by the {phi}-meson dominance model, but the falloff in the Q{sup 2} dependence is faster than the monopole form factor. Mesonic radiative corrections are also examined for the electromagnetic {rho}-to-{pi} and K{supmore » {asterisk}}-to-K transition amplitudes. {copyright} {ital 1998} {ital The American Physical Society}« less
  • The charge radii and magnetic moments of all the light and strange baryons are investigated within the framework of a constituent-quark model based on Goldstone-boson-exchange dynamics. Following the pointform approach to relativistic quantum mechanics, the calculations are performed in a manifestly covariant manner. Relativistic (boost) effects have a sizeable influence on the results. The direct predictions of the constituent-quark model are found to fall remarkably close to the available experimental data.