Effects of hadronic molecule $N(2080)3/2^-$ on $K^{*+}Λ$ photoproduction

TL;DR

This study tests the hadronic-molecular interpretation of the $N(2080)3/2^-$ state by incorporating it as a $K^*\Sigma$ molecule into an effective Lagrangian model for $\gamma p \to K^{*+} \Lambda$. The authors calculate full triangle-loop couplings of $N(2080)3/2^-$ to $K^{*}\Lambda$ and $\gamma N$, fix the molecular coupling via Weinberg's compositeness criterion, and fit to existing differential cross-section and spin-density-matrix data. The inclusion of $N(2080)3/2^-$ markedly improves the description of the near-threshold $\rho_{00}$ data, with substantial interference effects among $K$, $N(2000)5/2^+$, $N(2060)5/2^-$, and $N(2080)3/2^-$ in the low-energy region, while maintaining good overall cross-section agreement. The results support the hadronic-molecular picture for $N(2080)3/2^-$ and suggest future work on unitarization and exploration of additional molecular states as more data become available.

Abstract

In our previous work [Phys. Rev. C {\bf 101}, 014003 (2020)], we have analyzed all available data on differential cross sections and spin density matrix elements for the $γp \to K^{\ast +} Λ$ reaction using an effective Lagrangian approach. There, the $t$-channel $K$, $K^*$, and $κ$ exchanges, the $u$-channel $Λ$, $Σ$, and $Σ^*$ exchanges, the $s$-channel $N$, $N(2060)5/2^-$, and $N(2000)5/2^+$ exchanges, and the interaction current were taken into account in constructing the reaction amplitudes. It was found that, overall, the agreement of the theoretical results with the corresponding data is fairly good. However, noticeable discrepancies between the model results and the data on spin density matrix elements $ρ_{00}$ are still observed in the center-of-mass energy region around $W \approx 2.08$ GeV, indicating the need for additional reaction mechanisms. On the other hand, the hidden-strange pentaquark-like state $N(2080)3/2^-$, which is proposed to be a $K^*Σ$ molecular state as the strange partner of $P_c(4457)$ hadronic molecule, has been found to play quite active roles in reproducing the data for $K^{*+}Σ^0$, $K^{*0}Σ^+$, and $φp$ photoproduction reactions. Based on these observations, in the present work, we reanalyze the data for the $γp \to K^{\ast +} Λ$ reaction by incorporating the pentaquark-like state $N(2080)3/2^-$ in our previously proposed model. The results show that with the inclusion of the contributions of $N(2080)3/2^-$, the quality of the theoretical description of the $γp \to K^{*+}Λ$ data can be considerably improved.

Figures (8)

• Figure 1: The model results for the spin density matrix elements $\rho_{00}$ for $\gamma p\rightarrow K^{*+}\Lambda$ as a function of $\cos \theta$ in the center-of-mass frame at $W = 2041$ MeV and $2086$ MeV from Ref. Wei:2020fmh compared with the corresponding experimental data CLAS:2017sgi. The numbers in parentheses on the left denote the photon laboratory incident energies, in MeV.
• Figure 2: Generic structure of the photoproduction amplitude for $\gamma N\to K^{*}\Lambda$. Time proceeds from left to right. (a) $s$ channel, (b) $u$ channel, (c) $t$ channel, and (d) Interaction current.
• Figure 3: Couplings of $N(2080)3/2^-$ as $K^*\Sigma$ molecule to $K^{*}\Lambda$ and $\gamma N$.
• Figure 4: Differential cross sections for $\gamma p\rightarrow K^{*+}\Lambda$ as a function of $\cos \theta$ in the center-of-mass frame (black solid line). The red dotted, blue dashed, green dash-dotted, and orange double-dot-dashed lines represent the individual contributions from the $K$, $N(2000)5/2^+$, $N(2060)5/2^-$, and $N(2080)3/2^-$ exchanges, respectively. Data are taken from the CLAS Collaboration CLAS:2013qgi. The numbers in parentheses denote the photon laboratory incident energy (left number) and the total center-of-mass energy of the system (right number), both in MeV.
• Figure 5: Spin density matrix elements $\rho_{00}$ for $\gamma p\rightarrow K^{*+}\Lambda$ as a function of $\cos \theta$ in the center-of-mass frame (black solid line). The red dotted, blue dashed, green dash-dotted, and orange double-dot-dashed lines denote effects of the individual contributions from the $K$, $N(2000)5/2^+$, $N(2060)5/2^-$, and $N(2080)3/2^-$ exchanges, respectively, obtained by switching off the corresponding amplitude in the full reaction amplitude. Data are taken from the CLAS Collaboration CLAS:2017sgi. The numbers in parentheses denote the photon laboratory incident energy (left number) and the total center-of-mass energy of the system (right number), both in MeV.