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Systematic study of the strong decays of the $P_c$ states and their possible isospin cousins via the QCD sum rules

Xiu-Wu Wang, Xin Li, Zhi-Gang Wang

TL;DR

This paper investigates the strong decays of the exotic $P_c$ states under a meson–baryon molecular interpretation. It deploys QCD sum rules with twelve three-point correlators linking $P_c$ states to $η_c$ or $J/ψ$ with $N$ or $Δ$, using a double Borel transformation and quark–hadron duality to extract hadronic couplings. The results reproduce the widths of $P_c(4380)$, $P_c(4440)$, and $P_c(4457)$ and predict decay patterns for isospin partners $P_c(4410)$, $P_c(4470)$, and $P_c(4620)$, providing testable channels for future experiments. Overall, the work supports the $P_c$ meson–baryon molecular picture and offers concrete signatures to distinguish from alternative interpretations.

Abstract

In the present work, the strong decays of the discovered $P_c(4380)$, $P_c(4440)$, $P_c(4457)$ and their possible isospin cousins are systematically studied via the assignment that they are the meson-baryon molecular states. In detail, the strong decay constants, partial decay widths of their decay channels are calculated under the framework of QCD sum rules. The decay withes of the discovered $P_c(4380)$, $P_c(4440)$ and $P_c(4457)$ are in good agreement with the experiments. The predictions of the decays of these three related possible isospin cousins are presented which would shed light for their findings in experiment, in return, this may testify the assignments of the discovered $P_c$ states.

Systematic study of the strong decays of the $P_c$ states and their possible isospin cousins via the QCD sum rules

TL;DR

This paper investigates the strong decays of the exotic states under a meson–baryon molecular interpretation. It deploys QCD sum rules with twelve three-point correlators linking states to or with or , using a double Borel transformation and quark–hadron duality to extract hadronic couplings. The results reproduce the widths of , , and and predict decay patterns for isospin partners , , and , providing testable channels for future experiments. Overall, the work supports the meson–baryon molecular picture and offers concrete signatures to distinguish from alternative interpretations.

Abstract

In the present work, the strong decays of the discovered , , and their possible isospin cousins are systematically studied via the assignment that they are the meson-baryon molecular states. In detail, the strong decay constants, partial decay widths of their decay channels are calculated under the framework of QCD sum rules. The decay withes of the discovered , and are in good agreement with the experiments. The predictions of the decays of these three related possible isospin cousins are presented which would shed light for their findings in experiment, in return, this may testify the assignments of the discovered states.
Paper Structure (4 sections, 77 equations, 6 figures, 1 table)

This paper contains 4 sections, 77 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. QCD sum rules for strong decays of the pentaquark molecular states
  3. Numerical results and discussions
  4. Conclusions

Figures (6)

  • Figure 1: The hadronic coupling constants for $P_c(4380)\rightarrow \eta_cN$ (Left) and $P_c(4380)\rightarrow J/\psi N$ (Right) among the Borel windows.
  • Figure 2: The hadronic coupling constants for $P_c(4410)\rightarrow \eta_c\Delta$ (Left) and $P_c(4410)\rightarrow J/\psi\Delta$ (Right) among the Borel windows.
  • Figure 3: The hadronic coupling constants for $P_c(4440)\rightarrow \eta_cN$ (Left) and $P_c(4440)\rightarrow J/\psi N$ (Right) among the Borel windows.
  • Figure 4: The hadronic coupling constants for $P_c(4470)\rightarrow \eta_c\Delta$ (Left) and $P_c(4470)\rightarrow J/\psi\Delta$ (Right) among the Borel windows.
  • Figure 5: The hadronic coupling constants for $P_c(4457)\rightarrow \eta_cN$ (Left) and $P_c(4457)\rightarrow J/\psi N$ (Right) among the Borel windows.
  • ...and 1 more figures