[Paper Review] Masses and Magnetic Moments of Charmed Baryons Using Hyper Central Model

Bhavin Patel, Ajay Kumar+1 more|ArXiv.org|Mar 3, 2008

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This study computes the masses and magnetic moments of charmed baryons (with one or two charm quarks) using a hypercentral quark model with a Coulomb-plus-power potential. It finds that results stabilize for potential index ν > 1.0, with predictions in good agreement with lattice QCD and experimental data, particularly for spin splittings and magnetic moments without free parameters.

ABSTRACT

Heavy flavour baryons containing one or two charm quarks with light flavour combinations are studied using the hyper central description of the three-body system. The confinement potential is assumed as hyper central coulomb plus power potential with power index $ν$. The ground state masses and the magnetic moments of charmed, $J^P={1/2}^+$ and ${3/2}^+$ baryons are computed for different power index, $ ν$ starting from 0.5 to 2.0.

Motivation & Objective

• To compute the ground state masses and magnetic moments of charmed baryons with one or two charm quarks using a hypercentral quark model.
• To investigate the dependence of baryon properties on the power index ν of the hypercentral potential.
• To test the model's predictive power for doubly charmed baryons, where experimental data are limited.
• To compare results with lattice QCD and nonrelativistic quark model predictions to validate the model's consistency.
• To assess the role of three-body interactions in determining hadronic properties in heavy baryons.

Proposed method

• Employing the hypercentral approximation to map the three-quark baryon system into a two-body problem using Jacobi coordinates.
• Defining the hypercentral potential as a combination of hyper-Coulomb and power-law terms: V(x) = -τ/x + βx^ν + κ + A e^(-αx) Σ σ_i·σ_j.
• Using a hyper-Coulomb radial trial wave function to solve the Schrödinger equation in hyperspherical coordinates.
• Fixing model parameters using the experimental spin-average mass and hyperfine splitting of the Σ_c*(2518)–Σ_c(2454) system.
• Calculating magnetic moments within the nonrelativistic quark model framework using the same wave functions.
• Varying the potential index ν from 0.5 to 2.0 to study convergence and saturation of results.

Experimental results

Research questions

• RQ1 How do the masses and magnetic moments of charmed baryons depend on the power index ν of the hypercentral potential?
• RQ2 To what extent do the model predictions for charmed baryon masses and magnetic moments agree with lattice QCD and experimental data?
• RQ3 What is the role of three-body interactions in the hypercentral potential in determining baryonic properties?
• RQ4 How stable are the predictions for doubly charmed baryons across different values of ν, and how do they compare to other theoretical models?
• RQ5 Can the model predict magnetic moments without free parameters, and how do they compare to relativistic and nonrelativistic quark model results?

Key findings

• Baryon masses show minimal variation (within ~100 MeV) for potential index ν > 1.0, indicating saturation of the quark-quark interaction at higher ν.
• The model predicts a hyperfine splitting of 73 MeV for the Ξ_cc*–Ξ_cc doublet, close to the lattice QCD result of 76.6 MeV.
• Magnetic moments of single-charm baryons (e.g., Σ_c^++ with J^P=1/2+) are predicted as 1.9692 μ_N for ν=2.0, in good agreement with NRQM (1.86) and RQM (1.76) results.
• For doubly charmed baryons, the magnetic moment of Ξ_cc^++ is predicted as -0.0156 μ_N at ν=2.0, consistent with AL1 model (-0.208) and NRQM (-0.01).
• The magnetic moment of Ξ_cc^*++ is predicted as 2.2649 μ_N at ν=2.0, matching the AL1 prediction of 2.670 μ_N within acceptable range.
• The model achieves good agreement with experimental and lattice data across all studied baryons without adjusting free parameters, confirming the robustness of the hypercentral potential approach.