Understanding ${\eta }^{\prime }\to \eta \pi \pi$ and Allied Processes Despite Adler Zeros

With use of the (hitherto obscure) negative-parity meson matrix $N_{+}$ of partial symmetry, an ${\eta }^{\prime }\to \eta \pi \pi$ amplitude, explicitly satisfying the Adler conditions, has been constructed within the relativistic quark pair-creation model without any adjustable parameters. The model yields a total ${\eta }^{\prime }$ width of 388 keV and $\eta \pi \pi$, ${\rho }^0\gamma$, and $\gamma \gamma$ branching ratios of 68.0%, 29.9%, and 1.88%, all in excellent agreement with data. The same model gives the $\pi -\pi$ scattering lengths as $m_{\pi }{a}_0=0.19\mathrm{}$, $m_{\pi }{a}_2=0.08\mathrm{}$.