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Strong decays of the hidden-charm molecular pentaquarks

Jin-Cheng Deng, Yong Ru, Xin-Yue Wan, Tai-Fu Feng, Bo Wang

Abstract

We investigate the strong decays of the recently observed hidden-charm pentaquarks \(P_ψ^N(4312)\), \(P_ψ^N(4440)\), and \(P_ψ^N(4457)\), as well as \(P_{ψs}^Λ(4338)\) and \(P_{ψs}^Λ(4459)\), within the molecular framework using the effective Lagrangian approach. We construct the effective Lagrangians describing the S-wave couplings between these pentaquarks and their constituent hadrons, namely \(Σ_c\bar{D}^{(*)}\) and \(Ξ_c\bar{D}^{(*)}\), and determine the coupling constants via the residues of the scattering \(T\)-matrix at the bound-state poles. Our results show that the decay widths are sensitive to the cutoff parameters in the form factors, whereas the branching fractions exhibit only weak dependence. Using \(P_ψ^N(4312)\) to calibrate the cutoff range, we further explore the spin assignments of \(P_ψ^N(4440)\) and \(P_ψ^N(4457)\). Our calculations favor the assignment where the lower-mass state \(P_ψ^N(4440)\) carries higher spin \(J = 3/2\) and the higher-mass state \(P_ψ^N(4457)\) carries lower spin \(J = 1/2\). In addition, the experimental widths of \(P_{ψs}^Λ(4338)\) and \(P_{ψs}^Λ(4459)\) can both be well reproduced under the molecular interpretation. We look forward to future experimental analyses with more accumulated data to clarify whether the lineshape of \(P_{ψs}^Λ(4459)\) contains contributions from both spin-\(1/2\) and spin-\(3/2\) states.

Strong decays of the hidden-charm molecular pentaquarks

Abstract

We investigate the strong decays of the recently observed hidden-charm pentaquarks \(P_ψ^N(4312)\), \(P_ψ^N(4440)\), and \(P_ψ^N(4457)\), as well as \(P_{ψs}^Λ(4338)\) and \(P_{ψs}^Λ(4459)\), within the molecular framework using the effective Lagrangian approach. We construct the effective Lagrangians describing the S-wave couplings between these pentaquarks and their constituent hadrons, namely \(Σ_c\bar{D}^{(*)}\) and \(Ξ_c\bar{D}^{(*)}\), and determine the coupling constants via the residues of the scattering -matrix at the bound-state poles. Our results show that the decay widths are sensitive to the cutoff parameters in the form factors, whereas the branching fractions exhibit only weak dependence. Using \(P_ψ^N(4312)\) to calibrate the cutoff range, we further explore the spin assignments of \(P_ψ^N(4440)\) and \(P_ψ^N(4457)\). Our calculations favor the assignment where the lower-mass state \(P_ψ^N(4440)\) carries higher spin and the higher-mass state \(P_ψ^N(4457)\) carries lower spin . In addition, the experimental widths of \(P_{ψs}^Λ(4338)\) and \(P_{ψs}^Λ(4459)\) can both be well reproduced under the molecular interpretation. We look forward to future experimental analyses with more accumulated data to clarify whether the lineshape of \(P_{ψs}^Λ(4459)\) contains contributions from both spin- and spin- states.
Paper Structure (12 sections, 48 equations, 7 figures, 9 tables)

This paper contains 12 sections, 48 equations, 7 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Effective Lagrangians, coupling constants, and decay amplitudes
  3. Effective Lagrangians
  4. Determination of the coupling constants in Eqs. \ref{['eq:5']}-\ref{['eq:8']}
  5. Decay amplitudes and form factors
  6. Numerical results and discussions
  7. $\Sigma_c\bar{D}$ system: $P_\psi^N(4312)$
  8. $\Sigma_c\bar{D}^\ast$ system: $P_\psi^N(4440)$ and $P_\psi^N(4457)$
  9. $\Xi_c\bar{D}$ system: $P_{\psi s}^\Lambda(4338)$
  10. $\Xi_c\bar{D}^\ast$ system: $P_{\psi s}^\Lambda(4459)$
  11. Summary
  12. decay amplitudes

Figures (7)

  • Figure 1: Triangle loop diagrams for the strong decays of the $P_{\psi}^N$ and $P_{\psi s}^\Lambda$ states. The double lines denote the corresponding pentaquarks.
  • Figure 2: The elastic scattering process of particles $A$ and $B$, where $\mathbb{P}$ represents the bound state of $A$ and $B$.
  • Figure 3: An illustration of the Eqs. \ref{['eq:iso12']} and \ref{['eq:iso0']} in calculating the decay amplitudes, respectively.
  • Figure 4: The dependence of the total decay width of $P_\psi^N(4312)$ on the cutoff parameters, where the horizontal shaded band represents the width measured by the LHCb Collaboration LHCb:2019kea, and the band corresponding to our results originates from the range of coupling constants given in Table \ref{['tab:gvalues']}.
  • Figure 5: The dependence of the total decay widths of $P_\psi^N(4440)$ and $P_\psi^N(4457)$ on the cutoff parameters, where the first two rows correspond to the results for Case 1, and the latter two rows correspond to those for Case 2. The vertical yellow band indicates the constrained range of the corresponding cutoff parameters, with values $\Lambda_1 \in [0.28, 0.38]$ GeV, $\Lambda_2 \in [0.29, 0.41]$ GeV, and $\alpha_\Lambda \in [0.32, 0.48]$. The other notations used in the figure are the same as those in Fig. \ref{['fig:tot_Pc4312']}.
  • ...and 2 more figures