[Paper Review] Features of the Refined Gribov-Zwanziger theory: propagators, BRST soft symmetry breaking and glueball masses

S. P. Sorella, David Dudal+2 more|arXiv (Cornell University)|Feb 2, 2011

Quantum Chromodynamics and Particle Interactions9 references3 citations

TL;DR

This paper proposes a first-principles approach to estimating glueball masses in Yang-Mills theory using the Refined Gribov-Zwanziger (RGZ) framework, which incorporates the Gribov horizon and dimension-2 condensates. By matching the RGZ gluon propagator to recent lattice data, the study computes two-point correlation functions of gauge-invariant composite operators, yielding glueball masses in good agreement with lattice results for the $0^{++}$, $0^{-+}$, and $2^{++}$ states.

ABSTRACT

The present work discusses an approach to access the physical spectrum of the Yang-Mills theory quantized in the Landau gauge. By using recent lattice data on the gluon propagator, it is possible to study the two-point functions of gauge invariant composite operators, from which masses of glueballs can be extracted. It turns out that the momentum dependence of the gluon propagator is very well reproduced by the corresponding tree-level gluon propagator obtained from the Refined Gribov-Zwanziger theory, which takes into account the presence of the Gribov horizon as well as the effect of condensates of mass dimension two. The resulting glueball masses are in good agreement with the available lattice data

Motivation & Objective

• To develop a model-independent, analytic framework for estimating glueball masses in the non-perturbative regime of Yang-Mills theory.
• To test the consistency of the Refined Gribov-Zwanziger (RGZ) theory with recent lattice data on the gluon propagator.
• To compute correlation functions of gauge-invariant composite operators corresponding to glueball states using the RGZ framework.
• To extract physical glueball masses from the spectral representation of these correlation functions.
• To validate the RGZ approach as a viable tool for studying low-energy QCD spectrum beyond perturbation theory.

Proposed method

• The RGZ gluon propagator is used as an input, matching recent lattice data on the gluon two-point function in the Landau gauge.
• The theory incorporates the Gribov horizon via the Gribov parameter $\gamma$ and dimension-2 condensates $\langle \bar{\varphi}^{ac}_\mu \varphi^{ac}_\mu \rangle$.
• Two-point correlation functions are constructed for gauge-invariant composite operators with quantum numbers $J^{PC} = 0^{++}, 0^{-+}, 2^{++}$.
• The spectral function $\rho(t)$ is extracted from the correlation functions, with poles identifying glueball masses.
• A modified moment problem technique is applied to extract masses from the infrared-dominated spectral function.
• The $i$-particle representation is used to express the glueball operators in terms of auxiliary fields $\lambda^{a}_{\mu\nu}$ and $\eta^{a}_{\mu\nu}$.

Experimental results

Research questions

• RQ1 Can the Refined Gribov-Zwanziger theory provide a consistent and accurate description of the gluon propagator in the non-perturbative regime?
• RQ2 To what extent can the RGZ framework reproduce lattice data for the gluon and ghost propagators across dimensions?
• RQ3 Can the RGZ framework be used to estimate the masses of lightest glueball states without relying on phenomenological models?
• RQ4 How well do the glueball masses derived from RGZ correlation functions compare with available lattice results?
• RQ5 What is the role of dimension-2 condensates and the Gribov horizon in shaping the physical spectrum of Yang-Mills theory?

Key findings

• The RGZ gluon propagator provides an excellent fit to recent lattice data on the gluon two-point function in the non-perturbative regime.
• The estimated glueball masses are $m_{0^{++}} \approx 1.96\,\text{GeV}$, $m_{0^{-+}} \approx 2.19\,\text{GeV}$, and $m_{2^{++}} \approx 2.04\,\text{GeV}$.
• These values are within 20% of the corresponding lattice results: $m_{0^{++}}^{\text{lat}} \approx 1.73\,\text{GeV}$, $m_{0^{-+}}^{\text{lat}} \approx 2.59\,\text{GeV}$, $m_{2^{++}}^{\text{lat}} \approx 2.40\,\text{GeV}$.
• The predicted mass hierarchy $m_{0^{++}} < m_{2^{++}} < m_{0^{-+}}$ is correctly reproduced.
• The RGZ framework successfully accounts for non-perturbative features such as the Gribov horizon and dimension-2 condensates, which are essential for glueball physics.
• The method provides a first-principles, analytic estimate of glueball masses based on a consistent field-theoretic framework with strong lattice support.