Effects of strange molecular partners of $P_c$ states in $\gamma p\to K\Sigma$ 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 $\gamma p\to K^{\ast +}{\Sigma }^0/K^{\ast 0}{\Sigma }^{+}$ and $\gamma p\to \varphi p$ 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 $N$, $\Delta$, $N^{\ast }$ (including the hadronic molecules with hidden strangeness), and ${\Delta }^{\ast }$; $t$-channel; $u$-channel; and the generalized contact term. The results based on 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.

Comments: 28 pages, 15 figures, 5 tables