Constituent quarks, chiral symmetry, and chiral point of the constituent quark model

Abstract

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 $O(M_{\pi }^2)$, where $M_{\pi }$ is the mass of the lowest pseudoscalar $\bar{Q}Q$ bound state, we derive important constraints on (i) the axial coupling $g_A$ of the constituent quark and (ii) the $\bar{Q}Q$ 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 the constituent quarks and the couplings in the $\bar{Q}Q$ potential, for which $M_{\pi }$ 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.

arXiv comment10 pages, typo in eq. (46) of the published version is corrected

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• More Lepton Flavor Violating Observables for LHCb's Run 2
• Heavy-to-light form factors: sum rules on the light cone and beyond
• Strong three-meson couplings of $J/\psi$ and ${\eta }_c$
• Strong Couplings of Three Mesons with Charm(ing) Involvement