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

TL;DR

This work investigates whether strange-mad molecular partners of hidden-charm $P_c$ states influence $γp o KΣ$ photoproduction. Using a gauge-invariant, tree-level effective-Lagrangian framework that includes $s$-channel exchanges of seven hidden-strangeness molecules and several general resonances, along with $t$- and $u$-channel backgrounds and a generalized interaction current, the authors fit 77 parameters to extensive cross-section and polarization data. The results indicate that $s$-channel molecular exchanges produce significant, coherent structures at $W≈1900$, $2080$, and $2270$ MeV and interfere notably with conventional resonances, shaping both differential and total cross sections. The analysis highlights the importance of high-precision data, particularly for $γp o K^0Σ^+$, to better constrain the models and disentangle molecular contributions from standard resonances. All mathematical expressions are presented with explicit $-$delimited notation to ensure precise replication and interpretation of the model.

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 $γp \to K^{*+} Σ^0 / K^{*0} Σ^+$ and $γp \to φp$ reactions. Motivated by the differential cross-section data for $γp \to K^+ Σ^0$ 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 $γp \to K^+ Σ^0$ and $γp \to K^0 Σ^+$. 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 $N$, $Δ$, $N^*$ (including the hadronic molecules with hidden strangeness), and $Δ^*$; $t$-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 $γp \to K^+ Σ^0$ and $γp \to K^0 Σ^+$. Notably, the $s$-channel exchanges of molecules significantly contribute to the bump structures in cross-sections for $γp \to K Σ$ 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 $γp \to K^0 Σ^+$, are necessary to further strengthen the constraints on the theoretical models.

Figures (15)

• Figure 1: Generic structure of the amplitude for $\gamma N \to K \Sigma$. Time proceeds from left to right.
• Figure 2: Electromagnetic and hadronic couplings of $N(2080)3/2^-$ as $K^* \Sigma$ molecule.
• Figure 3: Differential cross-sections for $\gamma p \to K^+ \Sigma^0$ as a function of the total center-of-mass energy $W$. The collaborations for the experimental data are listed in the legend, with detailed information provided in Tab. \ref{['Table1']}. The red solid line denotes our theoretical result based on the parameters in Tabs. \ref{['Table3']} and \ref{['Table4']}, while the other three dashed lines represent contributions from $s$-channel molecule exchanges, $s$-channel general resonance exchanges, and the background (all other terms).
• Figure 4: Differential cross-sections for $\gamma p \to K^0 \Sigma^+$ as a function of the total center-of-mass energy $W$. Except for A2 2019 A2:2018doh, which was excluded from the fitting database due to inconsistencies, all other experimental data are available in Tab. \ref{['Table1']}. The notation for theoretical results follows that in Fig. \ref{['dsigmap']}.
• Figure 5: The total cross-section for $\gamma p \to K^+ \Sigma^0$, along with the individual contributions from single particle exchanges labeled on the right.