Dynamical Calculation of theA1

Abstract

A relativistic three-body theory previously used to generate the $\omega$ has been applied to the $1^{+}$ state of three pions. An $A_1$ resonance pole is produced with $M_{A_1}=1160\mathrm{}$ MeV, $\frac{\Gamma }{2}=90\mathrm{}$ MeV, but there is no associated phase variation of the amplitude.