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 ($σ,π$) fields all treated as elementary, having neither bare masses nor expectation values. In the chiral limit, the masses are predicted to be $m_q = f_πg, m_π= 0, m_σ= 2m_q$, and we also find that the quark-meson coupling $g = 2π/sqrt{N_c}$, the three-meson coupling is $g' = m_σ^2/2f_π= 2gm_q$ and the four-meson coupling is $λ= 2g^2 = g'/f_π$, where $f_π\simeq 90$ 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 $ρ$ and $A_1$, including the quark-vector coupling constant $g_ρ= 2π, g_{ρππ}, g_{A_1ρπ}$ and the masses $M_ρ\sim 700$ MeV, $m_{A_1}\simeq \sqrt{3}m_ρ$; of course the vector and axial vector currents remain conserved throughout.