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

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 $g^{\prime }=m_{\sigma }^2/2f_{\pi }=2g{m}_q$ and the four-meson coupling is $\lambda =2g^2=g^{\prime }/f_{\pi }$, 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.

18 pages, including 9 figures (eps files). Paper was originally published in 1995, but inadvertently not archived

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