Study on the $φ$-meson photoproduction off the proton target with the pentaquark-like $K^*Σ$ bound state $P_s$

Abstract: We utilize the effective Lagrangian method within the tree-level Born approximation to explore $\phi$-meson photoproduction, i.e., $\gamma p \to \phi p$. Our analysis encompasses contributions from various sources, including the Pomeron, $f_1$-Regge, pseudoscalar particles ($\pi$, $\eta$), scalar particles ($a_0$, $f_0$), protons, and three-nucleon resonance states. In addition, we consider a possible pentaquark-like $K^* \Sigma$-bound state $P_s$. The findings indicate that, apart from the region near the threshold, contributions other than the Pomeron generally have a limited impact on the total cross section. However, at specific angles, alternative contributions become crucial, particularly at smaller values of ${\rm cos}\,\theta$. The incorporation of $P_s$ and other nucleon resonances proves essential to elucidate the bump observed near $W \sim 2.15$ GeV at very forward angles and behaviors within the range of $W=(2.0-2.3)$ GeV. Furthermore, in the region with $W\ge 2.5$ GeV, where nucleon resonances become negligible, contributions from the t-channel mesons become pivotal. Our calculations for spin density matrix components, examined in various frames, exhibit improvement when considering all contributions. This comprehensive approach successfully reproduces the observed bump by including $P_s$. We also briefly estimate the $P_s$ production via $\phi$-meson photoproduction in the future Electron-Ion Collider (EIC), resulting in the luminosity of 10 fb$^{-1}$ per month.