Is theε(700)Meson the Goldstone Boson of Broken Scale Invariance?

Abstract

We examine low-energy theorems of broken scale invariance, using for our tests phenomenological ($\pi \pi$) phase shifts and thus improving on the usual pole approximation for the $\epsilon \mathrm{}\left(700\right)\mathrm{}$ meson, commonly assumed to act as a Goldstone boson. Approximate consistency is found for a model based on broken S${\mathrm{U}}_3$ × S${\mathrm{U}}_3$ symmetry, provided that a certain subtraction constant, already present on the level of pole models, is used as a free parameter to be fitted by the data. Yet there are definite indications that contrary to the role of the pion in broken chiral symmetry, broken scale invariance cannot be understood in terms of the $\epsilon \mathrm{}\left(700\right)\mathrm{}$ meson alone and contributions from higher states are needed in an essential manner.