Phenomenological Six-Pion Amplitude

To test the multiparticle, zero-width bootstrap, we have constructed a six-pion amplitude by modifying the general chiral pion amplitudes of Neveu, Schwarz, and Thorn. We show that imposing the chiral constraints to the six-pion dual amplitude does not fix the mass of the $\omega$. The masses and widths of the low-mass resonances (e.g., $\rho$, $\omega$, $f$, $A_2$, $g$, $A_1$, $H$, $\sigma$, and ${\pi }^{\prime }$) are given in terms of two masses ($m_{\pi }$ and $m_{\omega }$), one coupling ($g^2\sim {\Gamma }_{\rho }$), and a universal trajectory slope (${\alpha }^{\prime }$). We estimate $\Gamma (\omega \to 3\pi )=6\mathrm{}$ MeV, $\Gamma (A_1\to \rho \pi )=154\mathrm{}$ MeV, and $\Gamma (A_2\to \rho \pi )=7.5\mathrm{}$ MeV. Further phenomenological investigations are recommended.