Production of high-spin $ω_J/ρ_J$ ($J=3,4,5$) mesons in $π^{-}p$ reactions

TL;DR

This work develops an effective Lagrangian framework with Reggeized $t$-channel exchanges to study the production of high-spin $\omega_J$ and $\rho_J$ mesons in $\pi^- p$ scattering. By fitting a single universal cutoff $\Lambda_t$ to the $J=3$ data for $\omega_3(1670)$ and $\rho_3(1690)$ ("$\Lambda_t = 3.5 \pm 0.5$ GeV"), the authors achieve a nearly parameter-free description that is then extrapolated to the higher-spin partners $J=4,5$. They predict cross sections and forward-peaked differential distributions for $\omega_4(2250)$, $\rho_4(2230)$, $\omega_5(2250)$, and $\rho_5(2350)$, with typical $J=4$ results around $0.1$–$0.3$ $\mu$b and $J=5$ showing more varied isospin patterns (e.g., $\omega_5(2250)$ up to $\sim0.68$ $\mu$b, $\rho_5(2350)$ suppressed). The framework connects decay-channel expectations from the QPC model to production dynamics, providing concrete, testable predictions for upcoming experiments at facilities such as J-PARC and COMPASS, and offering guidance for completing the light-hadron spectroscopy via meson-beam probes.

Abstract

In this work, we perform a comprehensive investigation of the production of high-spin $ω_J$ and $ρ_J$ mesons ($J=3,4,5$) in $π^{-}p$ 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 $ω_3(1670)$ and $ρ_3(1690)$. Within the same framework, we predict the production cross sections for the higher-spin partners $ω_4(2250)$, $ρ_4(2230)$, $ω_5(2250)$, and $ρ_5(2350)$. Our results show that these states exhibit measurable cross sections with characteristically forward-peaked angular distributions, underscoring their strong potential for observation in future $πp$ meson-beam experiments.

Figures (9)

• Figure 1: A concise summary of light mesons.
• Figure 2: Feynman diagrams for the $\pi^{-} p\to \omega_3(1670) n$ (a) and $\pi^{-} p\to \rho_3(1690) n$ (b) reactions.
• Figure 3: The total cross section for the reaction $\pi^{-}p\to\omega_{3}(1670)n$. The black points with error bars correspond to the experimental data from Refs. Corden:1977xuDiaz:1974bqMatthews:1971brKenyon:1969abArmenise:1968hhd.
• Figure 4: The differential cross section $d\sigma/d\cos\theta$ of the $\omega_3(1670)$ production at different c.m. energy $E_{cm}$. The black points with error bars correspond to the experimental data from Ref. Corden:1977xu.
• Figure 5: The total cross section for the reaction $\pi^- p \to \rho_3(1690)n$. The black points with error bars correspond to the experimental data from Refs. Engler:1974pdBARI-BONN-CERN-GLASGOW-LIVERPOOL-MILAN-VIENNA:1980wqxCERN-MUNICH:1975yngGAMS:1994jop.