Production of high-spin ${\omega }_J\mathrm{/}{\rho }_J$ ($J=2,3,4,5$) mesons in ${\pi }^{-}p$ reactions

In this work, we perform a comprehensive investigation of the production of high-spin ${\omega }_J$ and ${\rho }_J$ mesons ($J=2,3,4,5$) in ${\pi }^{-}p$ reactions using an effective Lagrangian approach. By constructing the relevant $t$-channel processes and calibrating the model with a single adjustable parameter fitted to existing data, we successfully reproduce the measured total and differential cross sections for the $J=3$ states ${\omega }_3(1670)$ and ${\rho }_3(1690)$. Within the same framework, we predict the production cross sections for their lower- and higher-spin partners: ${\omega }_2(1975)$, ${\rho }_2(1940)$, ${\omega }_4(2250)$, ${\rho }_4(2230)$, ${\omega }_5(2350)$, and ${\rho }_5(2350)$. Our results show that these states exhibit measurable cross sections with characteristically forward-peaked angular distributions, underscoring their strong potential for observation in future $\pi p$ meson-beam experiments.