High-energy $η^{(\prime)}π$ photoproduction and the nature of exotic waves

TL;DR

This work models high-energy $η^{(\prime)}π$ photoproduction in the double-Regge regime using a parameter-free, fixed-spin double-vector exchange with Reggeized $ρ$ and $ω$ trajectories, calibrated from independent data. The Reggeization enforces correct analyticity and unitarity, yielding realistic $s$ and $t$ dependences and forward/backward angular peaks, and reproducing CLAS data at $E_γ=5$ GeV while predicting a larger forward-backward asymmetry for $η'π$ than for $ηπ$. The results imply that sizeable exotic $1^{-+}$-wave production in the $η'π$ channel can arise without a gluon-rich Pomeron exchange, aligning with COMPASS observations and Regge theory expectations. The framework lays groundwork for finite-energy sum rules to connect high-energy Regge behavior to low-energy resonances, guiding upcoming GlueX analyses and partial-wave extractions.

Abstract

The observation of hybrid mesons in photoproduction experiments can provide essential insight into the inner workings of quantum chromodynamics in the strong coupling regime. In particular, the study of final $η^{(\prime)}π$ states is of great interest due to the presence of the lowest lying hybrid candidate with manifestly exotic quantum numbers, the $π_1(1600)$. In this work, a double-vector exchange model with Reggeized $ρ$ and $ω$ trajectories is developed to describe the photoproduction of $η^{(\prime)}π$ in the high-mass region. Results are presented for the differential cross sections and forward-backward asymmetries in the energy region of interest to the GlueX experiment. The model contains no free parameters, and reproduces the magnitude and $t$-dependence of existing CLAS data at $E_γ=5$\gev. The model predicts a stronger asymmetry in the $η^\prime π$ channel than in the $ηπ$ channel, consistent with what has previously been observed in pion beam experiments. This suggests that the sizeable production of exotic odd waves in $η'π$ is not necessarily related to the presence of gluon-rich environments. Confirmation of these predicted asymmetries from forthcoming GlueX data would enable further predictions of the low-energy spectrum.

Figures (7)

• Figure 1: Generic diagram for the photoproduction of two pseudoscalars $P_1$ and $P_2$ off a proton via the exchange of two vectors $V_1$ and $V_2$; $s$, $s_1$, $s_2$ denote squared center-of-mass energies of the subsystems, and $t_1$, $t_2$ the squared momentum transfers.
• Figure 2: Differential cross section as a function of the $m_{\eta\pi} = \sqrt{s_{\eta\pi}}$ invariant mass for $E_\gamma=5{\mathrm{\,Ge V}}\xspace$, in slices of $t_{pp}$. Experimental data are from CLAS:2020rdz.
• Figure 3: Differential cross section for the photoproduction of $\eta\pi$ and $\eta'\pi$ as a function of $-t_{pp}$ for values of the beam energy corresponding to the CLAS and GlueX experiments.
• Figure 4: Angular distribution of the differential cross section as a function of the $\eta\pi$ (left) and $\eta'\pi$ (right) invariant mass squared. Top: two-dimensional distribution; bottom: corresponding slices at fixed $s_{\eta^{(\prime)}\pi}$.
• Figure 5: Forward-backward asymmetry as a function of $\eta^{(\prime)}\pi$ invariant mass.