[Paper Review] Light and heavy baryon masses: the 1/N_c expansion and the quark model

Fabien Buisseret, Claude Semay+2 more|ArXiv.org|Oct 16, 2008

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper establishes a quantitative connection between the constituent quark model and the 1/N_c expansion for light and heavy baryons, showing that the band number classification in the 1/N_c framework arises naturally from quark model excitation patterns. It demonstrates strong agreement between the two approaches in predicting baryon masses, with quark model parameters reproducing 1/N_c expansion coefficients to within 5% for quark masses and ~10% for QCD scale parameters.

ABSTRACT

We establish a connection between the quark model and the 1/N_c expansion mass formulas used in the description of baryon resonances. We show that a remarkable compatibility exists between the two methods in the light and heavy baryon sectors. In particular, the band number used to classify baryons in the 1/N_c expansion is explained by the quark model and the mass formulas for both approaches are consistent.

Motivation & Objective

• To establish a quantitative link between the constituent quark model and the 1/N_c expansion in baryon spectroscopy.
• To explain the physical origin of the band number N in the 1/N_c expansion using quark model excitation patterns.
• To test the compatibility of mass formulas derived from both approaches in light and heavy baryon sectors.
• To assess whether quark model parameters can reproduce the coefficients in the 1/N_c mass operator, independent of fitted quark masses.
• To provide a parameter-free validation of the 1/N_c expansion coefficients using quark model dynamics.

Proposed method

• Derives analytic mass formulas from a relativistic quark model Hamiltonian including kinetic, confinement, and hyperfine interactions.
• Applies the 1/N_c expansion to baryons, using SU(4) × SO(3) tensor operators scaled by powers of 1/N_c to construct the mass operator.
• Compares the quark model mass formula with the 1/N_c mass formula up to order 1/N_c, identifying matching terms.
• Uses power counting rules to assign scaling factors 1/N_c^{n-1} to n-body operators, with n being the minimum number of gluon exchanges.
• Fits quark model parameters using light baryon masses and compares resulting coefficients with those extracted from 1/N_c fits.
• Evaluates the consistency of the QCD scale parameter Λ and SU(3) flavor-breaking terms between both frameworks.

Experimental results

Research questions

• RQ1 Can the band number N in the 1/N_c expansion be explained by the quark model's harmonic oscillator excitation scheme?
• RQ2 Do the mass formulas derived from the quark model and the 1/N_c expansion yield consistent predictions for light and heavy baryon masses?
• RQ3 Can the coefficients in the 1/N_c mass operator be quantitatively reproduced by the quark model without fitting quark masses?
• RQ4 What is the dynamical origin of the QCD scale parameter Λ in the 1/N_c expansion, and does it match the quark model estimate?
• RQ5 How well do the SU(3) flavor-breaking terms in the 1/N_c framework compare to those derived from the quark model?

Key findings

• The quark model reproduces the 1/N_c expansion coefficient c₀ = 0.324 GeV to within 3% (0.333 GeV), showing strong agreement for the QCD scale parameter.
• The 1/N_c coefficient c′₀ ≈ 0.096 GeV² is reproduced by the quark model at 0.091 GeV², indicating consistency at the dominant order.
• The SU(3) flavor-breaking term εΛχ is estimated at 0.206 GeV in 1/N_c and 0.170 GeV in the quark model, showing satisfactory quantitative agreement.
• The quark masses m_c and m_b derived from both models differ by less than 5%, confirming compatibility at the leading order.
• The dynamical origin of the band number N in the 1/N_c expansion is explained by the quark model as corresponding to the number of oscillator quanta.
• The ratio c′′₂/c₂ ≈ μ₁ ≈ 356 MeV is consistent with the 1/N_c prediction, suggesting compatibility even when spin-dependent terms are included.