[Paper Review] Model comparison of Delta and Omega masses in a covariant Faddeev approach

Hèlios Sanchis-Alepuz, Reinhard Alkofer+2 more|arXiv (Cornell University)|Dec 14, 2011

Quantum Chromodynamics and Particle Interactions9 references4 citations

TL;DR

This study computes the masses of vector mesons, nucleons, and Δ/Ω baryons using a covariant Faddeev approach within the rainbow-ladder truncation of Dyson-Schwinger equations. It compares two effective quark-gluon interactions—Maris-Tandy and AFW—and finds that both yield consistent results within ∼10% of experimental and lattice data across light to bottom quark masses, indicating robust model-independent features in the mid-momentum regime relevant for dynamical chiral symmetry breaking.

ABSTRACT

We compute the vector-meson, nucleon and delta/omega-baryon masses and their evolution with the current-quark mass using a covariant generalized Bethe-Salpeter equation approach. The interaction kernel is truncated to a dressed gluon exchange. We study the model dependence of our results with the quark-gluon dressing to assess the validity of the truncation.

Motivation & Objective

• To investigate the quark-mass dependence of baryon and meson masses in a covariant three-body framework.
• To assess model dependence within the rainbow-ladder truncation by comparing two distinct effective quark-gluon interactions.
• To identify model-independent features in hadron masses by studying their evolution with current-quark mass.
• To evaluate the role of the quark-dressing functions and interaction kernels in determining hadron properties, particularly in the heavy-quark domain.
• To lay the groundwork for future studies on beyond-Rainbow-Ladder corrections in electromagnetic form factors.

Proposed method

• Uses a covariant Faddeev approach to solve three-quark bound states in the context of Dyson-Schwinger equations.
• Employs the rainbow-ladder (RL) truncation for the quark-gluon vertex and interaction kernel, with the kernel derived from dressed gluon exchange.
• Solves the quark Dyson-Schwinger equation to obtain the dressed quark propagator, using two different effective interactions: Maris-Tandy and AFW.
• Computes hadron masses (vector mesons, nucleons, Δ/Ω baryons) by solving the Bethe-Salpeter equation with the truncated kernel.
• Traces the evolution of hadron masses with current-quark mass, using the pseudoscalar meson mass as a proxy.
• Compares results from the two effective interactions to quantify model dependence and identify robust features.

Experimental results

Research questions

• RQ1 How do different effective quark-gluon interactions affect the computed masses of Δ and Ω baryons in the covariant Faddeev approach?
• RQ2 What is the degree of model dependence in hadron masses when using the rainbow-ladder truncation across the quark mass range from u/d to b quarks?
• RQ3 To what extent do the results remain consistent with experimental and lattice QCD data across different current-quark masses?
• RQ4 How do the quark mass function and dressing functions influence the hadron mass spectrum, particularly in the heavy-quark domain?
• RQ5 What insights can be drawn about the relevance of dynamical chiral symmetry breaking in the mid-momentum region from the comparison of two distinct interactions?

Key findings

• Both the Maris-Tandy and AFW effective interactions yield hadron masses that agree with experimental and lattice data within ∼10% across the entire current-quark mass range.
• The model dependence is small in the light-quark region, with the Maris-Tandy model slightly underestimating AFW results for heavier quark masses.
• The spread in hadron masses between the two models closely follows the spread in the quark mass function $ M(p^2=0) $, indicating that hadron properties are dominated by the quark DSE solution rather than the specific form of the interaction kernel.
• The mid-momentum region ($|q| \sim 0.5\dots1$ GeV) is crucial for dynamical chiral symmetry breaking and governs the overall strength of ground-state hadron properties.
• In the heavy-quark domain, the sensitivity to the interaction kernel diminishes, and hadron masses become increasingly dominated by the current-quark mass and the quark mass function.
• The results suggest that beyond-Rainbow-Ladder corrections—such as vertex corrections and non-vector interactions—may be more relevant in the chiral and low-momentum regime, but are less critical for heavy-quark hadron masses.