Searching for strange hidden-charm pentaquark state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4459</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>p</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4459</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> reaction
Cai Cheng, F. Yang, Yin Huang
Abstract
We investigate the possibility of studying the strange hidden-charm pentaquark state ${P}_{cs}(4459)$ by photon-induced reactions on a proton target in an effective Lagrangian approach. The production process is described by the $t$-channel ${K}^{\ensuremath{-}}$ exchange, the $u$-channel $\mathrm{\ensuremath{\Lambda}}$ exchange, the contract term, and the $s$- channel nucleon pole. Our theoretical approach is based on the assumption that ${P}_{cs}(4459)$ with ${J}^{P}=1/{2}^{\ensuremath{-}}$ or ${J}^{P}=3/{2}^{\ensuremath{-}}$ can be interpreted as a molecule composed of ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}$. Using the coupling constants of the ${P}_{cs}^{{J}^{P}}$ to $\ensuremath{\gamma}\mathrm{\ensuremath{\Lambda}}$ and ${K}^{\ensuremath{-}}p$ channels obtained from molecule picture of the ${P}_{cs}^{{J}^{P}}(4459)$, the total cross-sections of the process $\ensuremath{\gamma}p\ensuremath{\rightarrow}{P}_{cs}^{{J}^{P}}{K}^{+}$ is evaluated. Our calculation indicates that the cross-section for $\ensuremath{\gamma}p\ensuremath{\rightarrow}{P}_{cs}^{1/{2}^{\ensuremath{-}}}{K}^{+}$ and $\ensuremath{\gamma}p\ensuremath{\rightarrow}{P}_{cs}^{3/{2}^{\ensuremath{-}}}{K}^{+}$ are of the order of 10.0 pb and 5.0 pb, respectively. In addition, we compute the cross section by assuming ${P}_{cs}(4459)$ as a compact pentaquark and find it is quite different from the results of ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}$ molecule. Those results can be measured in future experiments, such as the Electron-Ion Collider in China and the United States, and can be used to test the nature of the ${P}_{cs}$.