# Model independent determination of the spins of the $P_{c}$(4440) and $P_{c}$(4457) from the spectroscopy of the triply charmed dibaryons

## TL;DR

This paper proposes a model-independent method to determine the spins of the $P_c(4440)$ and $P_c(4457)$ pentaquarks using heavy-quark symmetry relations with triply charmed dibaryons, linking experimental data to fundamental QCD predictions.

## Contribution

It introduces a novel, model-independent relation between pentaquark spin splittings and triply charmed dibaryon mass differences based on heavy antiquark-diquark symmetry.

## Key findings

- Relates pentaquark spin splittings to dibaryon mass differences.
- Suggests lattice QCD can test the pentaquark spin assignments.
- Predicts existence of ten triply charmed dibaryons as molecular states.

## Abstract

The LHCb collaboration has recently observed three narrow pentaquark states --- the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ ---that are located close to the $\bar{D} \Sigma_c$ and $\bar{D}^* \Sigma_c$ thresholds. Among the so-far proposed theoretical interpretations for these pentaquarks, the molecular hypothesis seems to be the preferred one. Nevertheless, in the molecular picture the spins of the $P_c(4440)$ and $P_c(4457)$ have not been unambiguously determined yet. In this letter we point out that heavy antiquark-diquark symmetry induces a model-independent relation between the spin-splitting in the masses of the $P_c(4440)$ and $P_c(4457)$ $\bar{D}^* \Sigma_c$ pentaquarks and the corresponding splitting for the $0^+$ and $1^+$ $\Xi_{cc} \Sigma_c$ triply charmed dibaryons. This is particularly relevant owing to a recent lattice QCD prediction of the $1^+$ triply charmed dibaryon, which suggests that a calculation of the mass of its $0^+$ partner might be within reach. This in turn would reveal the spins of the $P_c(4440)$ and $P_c(4457)$ pentaquarks, providing a highly nontrivial test of heavy-quark symmetry and the molecular nature of the pentaquarks. Furthermore, the molecular interpretation of the hidden-charm pentaquarks implies the existence of a total of ten triply charmed dibaryons as $\Xi_{cc}^{(*)} \Sigma_c^{(*)}$ molecules, which, if confirmed in the lattice, will largely expand our understanding of the non-perturbative strong interaction in the heavy-quark sector.