Combined analysis of the data on cross sections and spin density matrix elements for $K^*\Sigma$ photoproduction reactions

In our earlier work [Phys. Rev. C \textbf{98}, 045209 (2018)], we analyzed the differential cross-section data from the CLAS Collaboration for the reactions $\gamma p \to K^{*+}\Sigma^0$ and $\gamma p \to K^{*0} \Sigma^+$ using an effective Lagrangian approach. We found that a satisfactory description of the data required the inclusion of the $s$-channel $\Delta(1905)5/2^+$ resonance, in addition to $t$-channel exchanges of $K$, $\kappa$, and $K^*$, $s$-channel contributions from nucleons ($N$) and $\Delta$, $u$-channel exchanges of $\Lambda$, $\Sigma$, and $\Sigma^*$, and a generalized contact term. In the present work, we extend our analysis to incorporate the data on spin density matrix elements from the LEPS Collaboration for the $\gamma p \to K^{*0}\Sigma^+$ reaction at photon energies $E_{\gamma} = 1.85$--$2.96$ GeV. Our goal is to impose more stringent constraints on the theoretical model and obtain a more reliable understanding of the reaction mechanisms. We obtain two fits that describe the experimental data equally well. In both fits, the $\Delta(1905)5/2^+$ resonance plays an important role. However, the contribution from $t$-channel $\kappa$ exchange is significant in one fit but negligible in the other. This finding contradicts earlier claims in the literature that the LEPS parity spin asymmetry $P_\sigma$ data support a dominant role of $\kappa$ exchange in $\gamma p \to K^{*0}\Sigma^+$. We also present predictions for $P_\sigma$ at $E_\gamma = 8.5$ GeV, which may help clarify whether $\kappa$ exchange is indeed dominant in this reaction.