Hadronic origin of the pion mass

Abstract

We construct generalized gauge models of hadrons (and leptons) including π, ϱ, A 1, π′, ϱ, A 1, π′, ϱ′ A 1′, … In these models, the pion may be taken a psuedo-Goldstone boson. In a lone loop approximation to the simplest of these models, we obtain a strikingly accurate pion mass, as a function of hadronic (large) parameters. In a supporting current algebra derivation, we see that the essential ingredients for the smallness are (a) asymptotic chiral symmetry and (b) a low energy cut-off imposed by Weinberg's second spectral function sum rule. The model also agrees with ϱ′ data, and predicts an A 1′ around 3 (GeV) 2. In addition, the pion form factor is essentially monopole, while the baryon form factors are dipole.