[Paper Review] Universal Constituent-Quark Model for Baryons

Joseph P. Day, W. Plessas+1 more|arXiv (Cornell University)|May 31, 2012

Scientific Research and Discoveries1 references3 citations

TL;DR

This paper presents a relativistic constituent-quark model (RCQM) that unifies the description of all known baryons—from nucleons to bottom baryons like Ω_bbb—using a Poincaré-invariant invariant mass operator with linear confinement and a flavor-dependent hyperfine interaction based on Goldstone-boson exchange (GBE). The model successfully reproduces light, strange, charm, and bottom baryon spectra with high accuracy, predicting missing states in the heavy-flavor sectors.

ABSTRACT

We present a relativistic constituent-quark model that covers all known baryons from the nucleon up to $Ω_{bbb}$. The corresponding invariant mass operator includes a linear confinement and a hyperfine interaction based on effective degrees of freedom. The model provides for a unified description of practically all baryon spectra in good agreement with present phenomenology and it can tentatively be employed for the relativistic treatment of all kinds of baryon reactions. Predictions of states still missing in the phenomenological data base, especially in the lesser explored heavy-flavor sectors of charm and bottom baryons, should be important especially for future experiments in these areas.

Motivation & Objective

• To develop a single, relativistic constituent-quark model capable of describing all known baryons across light, strange, charm, and bottom flavors.
• To incorporate both linear confinement and a flavor-dependent hyperfine interaction based on chiral dynamics to reproduce observed baryon spectra.
• To provide a unified framework for predicting missing baryon states, especially in the underexplored heavy-flavor sectors.
• To ensure compatibility with both phenomenological data and lattice QCD results for heavy baryons.
• To enable future relativistic treatments of baryon reactions, including resonance excitations and decays.

Proposed method

• Formulates a Poincaré-invariant invariant mass operator M̂ = M̂_free + M̂_int, where M̂_free describes the relativistic kinetic energy of three quarks and M̂_int includes quark-quark interactions.
• Uses a linear confinement potential V_conf_ij = V₀ + C·r_ij with C = 2.33 fm⁻² (string tension) and V₀ = -402 MeV to set the proton mass.
• Implements a hyperfine interaction V_hf_ij based on Goldstone-boson exchange (GBE) with pseudoscalar coupling to account for flavor dependence and chiral symmetry breaking.
• Solves the eigenvalue problem of the mass operator in the baryon's rest frame to obtain relativistically invariant mass spectra and baryon eigenstates.
• Employs a relativistic framework that preserves the full Poincaré algebra, ensuring Lorentz invariance and consistency with relativistic quantum mechanics.
• Validates the model against PDG data and lattice QCD results, particularly for charm and bottom baryons.

Experimental results

Research questions

• RQ1 Can a single relativistic constituent-quark model consistently describe baryons across all flavors (u, d, s, c, b) with a unified dynamical framework?
• RQ2 How well can a Goldstone-boson exchange-based hyperfine interaction reproduce the level ordering and spacings in nucleon, delta, and lambda spectra?
• RQ3 To what extent do hyperfine interactions involving charm and bottom quarks influence baryon mass splittings compared to light-quark interactions?
• RQ4 Can the model predict previously unobserved excited states in charm and bottom baryons that are missing in the phenomenological data base?
• RQ5 How does the model’s prediction compare with existing lattice QCD results for heavy baryons, especially in the charm sector?

Key findings

• The model reproduces the nucleon and delta excitation spectra (N and Δ) with accuracy comparable to or better than previous GBE-based RCQMs, correctly capturing level orderings.
• The strange baryon spectra (Λ, Σ, Ξ) are also well described, including the correct level ordering in the SU(3)_F multiplets, consistent with phenomenological data.
• For charm baryons (Λ_c, Σ_c), the model reproduces all known states with three- or four-star PDG status, and predicts additional excited states not yet observed.
• For bottom baryons (Λ_b, Σ_b), the model accurately reproduces the known spectra and predicts missing excited states, particularly in the Σ_b and Ξ_b sectors.
• The hyperfine interaction remains significant for heavy-flavor baryons, with contributions to level splittings comparable in magnitude to those in light-quark systems.
• Theoretical spectra from the model show good agreement with recent lattice QCD results for charm baryons, validating its predictive power in the heavy-flavor regime.