Dynamical generation of the gauged SU(2) linear sigma model

TL;DR

This paper derives a dynamical SU(2) linear sigma model from a meson-quark Lagrangian, predicting meson and quark masses, couplings, and generating vector meson interactions while preserving current conservation.

Contribution

It introduces a dynamical generation approach for the gauged SU(2) linear sigma model from a meson-quark framework, including vector meson couplings and mass predictions.

Findings

Predicted quark mass $m_q = f_ g$ in the chiral limit.

Calculated vector meson masses $M_ ho \u223c 700$ MeV, $m_{A_1} \u223c \u221a3 M_ ho$.

Determined coupling constants $g = 2\u221arac{\u221a3 ewline}{N_c}$, $g' = 2gm_q$, and $_  90$ MeV.

Abstract

The fermion and meson sectors of the quark-level SU(2) linear sigma model are dynamically generated from a meson-quark Lagrangian, with the quark (q) and meson ($\sigma,\pi$) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be $m_q = f_\pi g, m_\pi = 0, m_\sigma = 2m_q$, and we also find that the quark-meson coupling $g = 2\pi/sqrt{N_c}$, the three-meson coupling is $g' = m_\sigma^2/2f_\pi = 2gm_q$ and the four-meson coupling is $\lambda = 2g^2 = g'/f_\pi$, where $f_\pi \simeq 90$ MeV is the pion decay constant and $N_c = 3$ is the color number. By gauging this model one can generate the couplings to the vector mesons $\rho$ and $A_1$, including the quark-vector coupling constant $g_\rho = 2\pi, g_{\rho\pi\pi}, g_{A_1\rho\pi}$ and the masses $M_\rho\sim 700$ MeV, $m_{A_1}\simeq \sqrt{3}m_\rho$; of course the vector and axial vector currents remain conserved throughout.