Exact formula of the spectrum of the pseudoscalar octet

Abstract

Non-perturbative proof is presented of a generalized version of Goldstone theorem, where the Lagrangian conserves an approximate SU(3) chiral symmetry, that both quark masses and electromagnetism make contributions to the masses of spinless particles of pseudoscalar octet. We show that apart from what comes in the form of some projections of a two-body Bethe–Salpeter amplitude for which the photon lines like the gluon ones are all internal in the case of neutral pseudo-Goldstone bosons, the charged pseudoscalar mesons receive additional contributions that may be expressed in terms of the axial–vectorial projection of a three-body Bethe–Salpeter amplitude with an extra external photon line. Keywords: Spontaneously broken approximate chiral symmetry, Pseudo-Goldstone bosons, Pseudoscalar meson masses, Electromagnetic corrections, Non-perturbative methods