Parity and signature determination by theV1V2decay mode

The $\phi \phi$ parity test is generalized to any specific $X\to V_1{V}_2$ decay mode where the vector mesons $V_1$ and $V_2$ each either decays into two spin-zero bosons, or is $\omega$. From a $V_1{V}_2$ mode with a $V_1\leftrightarrow V_2$ exchange property, the parity $\eta$ of $X$ can always be determined as can ${\mathrm{}(-)\mathrm{}}^J$ of $X$ except in certain circumstances. For modes without such an exchange property, $\eta {\mathrm{}(-)\mathrm{}}^J$ can be determined provided certain amplitudes do not accidentally vanish. Empirical tests for unexpected violations of $V_1\leftrightarrow V_2$ exchange properties are enumerated.