Effects of strange molecular partners of $P_c$ states in $γp \to K Σ$ reactions

Abstract: Our previous studies revealed evidence of the strange molecular partners of $P_c$ states, $N(2080)3/2^-$ and $N(2270)3/2^-$, in the $\gamma p \to K^{*+} \Sigma^0 / K^{*0} \Sigma^+$ and $\gamma p \to \phi p$ reactions. Motivated by the differential cross-section data for $\gamma p \to K^+ \Sigma^0$ from CLAS 2010, which exhibits some bump structures at $W \approx$ 1875, 2080 and 2270 MeV, we extend our previous analysis by investigating the effects of $N(1535)1/2^-$, $N(1875)3/2^-$, $N(2080)1/2^- &\ 3/2^-$ and $N(2270)1/2^- , 3/2^- &\ 5/2^-$, as strange partners of $P_c$ molecular states, in the reactions $\gamma p \to K^+ \Sigma^0$ and $\gamma p \to K^0 \Sigma^+$. The theoretical model employed in this study utilizes an effective Lagrangian approach in the tree-level Born approximation. It contains the contributions from $s$-channel with exchanges of $N$, $\Delta$, $N^*$ (including the hadronic molecules with hidden strangeness), and $\Delta^*$; $t$-channel; $u$-channel; and the generalized contact term. The results corresponding to the final fitted parameters are in good agreement with all available experimental data of both cross-sections and polarization observables for $\gamma p \to K^+ \Sigma^0$ and $\gamma p \to K^0 \Sigma^+$. Notably, the $s$-channel exchanges of molecules significantly contribute to the bump structures in cross-sections for $\gamma p \to K \Sigma$ at $W \approx$ 1900, 2080 and 2270 MeV, and show considerable coherence with contributions from $s$-channel exchanges of general resonances to construct the overall structures of cross-sections. More abundant experiments, particularly for the reaction $\gamma p \to K^0 \Sigma^+$, are necessary to further strengthen the constraints on the theoretical models.