Distinguishing the spins of $P_c(4440)$ and $P_c(4457)$ with femtoscopic correlation functions

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 ${\mathrm{\Sigma }}_c{\bar{D}}^{\ast }$ bound states, we demonstrate how one can determine their spins by measuring the ${\mathrm{\Sigma }}_c^{+}{\bar{D}}^{(\ast )0}$ correlation functions. We show that one can use the ${\mathrm{\Sigma }}_c^{+}{\bar{D}}^0$ correlation function to fix the size of the Gaussian source and then determine the strength of the ${\mathrm{\Sigma }}_c^{+}{\bar{D}}^{\ast 0}$ interaction of spin $1\mathrm{/}2$ and $3\mathrm{/}2$ 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.