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 $\Sigma_c\bar{ D}^{ *}$ bound states, we demonstrate how one can determine their spins by measuring the $\Sigma_c^+\bar{ D}^{ (*)0}$ correlation functions. We show that one can use the $\Sigma_c^+\bar{ D}^0$ correlation function to fix the size of the Gaussian source and then determine the strength of the $\Sigma_c^+\bar{ D}^{ *0}$ 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.
Categories: hep-ph hep-ex