Distinguishing the spins of <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>4440</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <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> with femtoscopic correlation functions
Zhi-Wei Liu, Jun-Xu Lu, Ming-Zhu Liu, Li‐Sheng Geng
Abstract
The spins of the pentaquark states ${P}_{c}(4440)$ and ${P}_{c}(4457)$ play a decisive role in unraveling their nature, but remain undetermined experimentally. Assuming that they are ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ bound states, we demonstrate how one can determine their spins by measuring the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{+}{\overline{D}}^{(*)0}$ correlation functions. We show that one can use the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{+}{\overline{D}}^{0}$ correlation function to fix the size of the Gaussian source and then determine the strength of the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{+}{\overline{D}}^{*0}$ interaction of spin $1/2$ and $3/2$ and therefore the spins of the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ states. The method proposed can be applied to decipher the nature of other hadronic molecules and thus deepen our understanding of the nonperturbative strong interaction.