Peaks within peaks and the possible two-peak structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4457</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>: The effective field theory perspective
Fang‐Zheng Peng, Jun-Xu Lu, Mario Sánchez Sánchez, Mao-Jun Yan, Manuel Pavón Valderrama
Abstract
The LHCb pentaquarks---the ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$---have been theorized to be ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ S-wave molecules. Here, we explore the possibility that two of these pentaquarks---the ${P}_{c}(4440)$ and ${P}_{c}(4457)$---contain in addition a ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595)\overline{D}$ component in the P-wave. We will analyze the effects of this extra channel within two effective field theories: the first one will be a standard contact-range effective field theory, and the second one will include the nondiagonal pion dynamics connecting the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595)\overline{D}$ channels, which happens to be unusually long ranged. The impact of the coupled-channel dynamics between the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595)\overline{D}$ components is modest at best for the ${P}_{c}(4440)$ and ${P}_{c}(4457)$, which will remain predominantly ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ molecules. However, if the quantum numbers of the ${P}_{c}(4457)$ are ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$, the coupled-channel dynamics is likely to induce the binding of a $\mathrm{\ensuremath{\Lambda}}(2595)\overline{D}$ S-wave molecule (coupled to ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ in the P-wave) with ${J}^{P}={\frac{1}{2}}^{+}$ and a mass similar to the ${P}_{c}(4457)$. If this is the case, the ${P}_{c}(4457)$ could actually be a double peak containing two different pentaquark states.