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 ω. The masses and widths of the low-mass resonances (e.g., ρ, ω, f, A₂, g, A₁, H, σ, and π′) are given in terms of two masses ($m_{\pi }$ and $m_{\omega }$), one coupling ($g^2~{\Gamma }_{\rho }$), and a universal trajectory slope (α′). We estimate Γ(ω→3π)=6 MeV, Γ(A₁→ρπ)=154 MeV, and Γ(A₂→ρπ)=7.5 MeV. Further phenomenological investigations are recommended.