Isospin eigenstates of the color singlet-singlet type pentaquark states

TL;DR

This paper constructs specific color singlet-singlet five-quark currents to explore and support the interpretation of certain pentaquark states observed experimentally as molecular-like states using QCD sum rules.

Contribution

It unambiguously constructs isospin-specific five-quark currents and applies QCD sum rules to analyze the nature of observed pentaquark states, providing new insights into their structure.

Findings

Supports assigning observed P_c states as specific molecular pentaquark states.

Predicts slightly larger masses for isospin 3/2 pentaquark states.

Highlights the importance of higher pentaquark candidates in understanding their nature.

Abstract

In this article, we construct the color singlet-singlet type five-quark currents with the isospins $(I,I_3)=(\frac{1}{2},\frac{1}{2})$ and $(\frac{3}{2},\frac{1}{2})$ unambiguously to explore the $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$ and $\bar{D}^*\Sigma_c^*$ pentaquark states via the QCD sum rules for the first time, where the $\bar{D}$, $\Sigma_c$, $\cdots$ represent the color-singlet clusters having the same quantum numbers as the corresponding physical mesons or baryons. The numerical results support assigning the $P_c(4312)$, $P_c(4380)$, $P_c(4440)$ and $P_c(4457)$ as the $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$ and $\bar{D}^*\Sigma_c^*$ pentaquark states with the isospin $I=\frac{1}{2}$, respectively. The corresponding $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^*\Sigma_c$ and $\bar{D}^*\Sigma_c^*$ pentaquark states with the isospin $I=\frac{3}{2}$ have slightly larger masses, the observations of the higher pentaquark candidates in the $J/\psi \Delta$ invariant mass spectrum would shed light on the nature of the $P_c$ states, and make contributions in distinguishing the scenarios of color antitriplet-antitriplet-antitriplet type and color singlet-singlet type pentaquark states.