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

TL;DR

This paper proposes a method to determine the spins of the pentaquark states $P_c(4440)$ and $P_c(4457)$ by analyzing femtoscopic correlation functions, aiding in understanding their molecular nature.

Contribution

It introduces a novel approach using correlation functions to identify the spins of pentaquark states assuming they are $ ext{Σ}_car{ ext{D}}^{*}$ molecules.

Findings

The $ ext{Σ}_c^+ar{ ext{D}}^0$ correlation function can fix the source size.

The method distinguishes the spins of $P_c(4440)$ and $P_c(4457)$.

Applicable to other hadronic molecules to explore strong interactions.

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 $\Sigma_c\bar{D}^{*}$ 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.