Quark model of light mesons with dynamically broken chiral symmetry

We study the meson spectrum in a model with a confining Lorentz-vector—and hence chiral-invariant—interaction between massless quark fields. As shown in a previous work, chiral invariance is spontaneously broken. In the case of the harmonic oscillator, as the Fourier transform of the potential is the Laplacian of a δ function, the Bethe-Salpeter (BS) equation—a system of linear integral equations in general—splits into a system of differential equations that we solve in the broken vacuum. Without appealing to any spin-spin interaction, we find, besides the massless pseudoscalar, a vector meson at the right scale and an excited pion and two vectors in the 1–2-GeV region. Moreover, we find a large L-S splitting with the expected ordering for a vector interaction. We study in detail the BS wave function for the pion in motion, necessary to compute axial-vector-current matrix elements, and recover well known relations of current algebra. We compute $f_{\pi }$ and find on general grounds that $f_{\pi \mathcal{’}}$=0 in the chiral limit, where π’ is any radially excited pion. The pion satisfies the expected dispersion law for a Goldstone boson, ω(p)→cp (p→0). .AE