Meson Bootstraps for Unnatural-Parity States

Abstract

In this paper we study the possibility of bootstrapping the unnatural-parity meson states, using finite-energy sum rules. Previous work on this bootstrap scheme was confined to natural-parity states. We find a large number of sum rules involving particles which are not firmly established, with results that are in good agreement with experiment (10%). The equations, though not mathematically consistent, are such that the two sides (Regge and resonances) are equal when $t$ is varied over a large region, and we find several mass formulas, including ${{m}_{H}}^{2}=2{{m}_{\ensuremath{\rho}}}^{2}\ensuremath{-}\frac{3}{2}{{m}_{\ensuremath{\pi}}}^{2}$, ${m}_{B}={m}_{{A}_{2}}\ensuremath{-}{m}_{\ensuremath{\pi}}$, $2{{m}_{B}}^{2}=0.5 \mathrm{Be}{\mathrm{V}}^{2}+2{{m}_{\ensuremath{\delta}}}^{2}+{{m}_{\ensuremath{\omega}}}^{2}+{{m}_{\ensuremath{\pi}}}^{2}$, and relations between coupling constants.