A renormalization group invariant scalar glueball operator in the (Refined) Gribov-Zwanziger framework

Abstract

This paper presents a complete algebraic analysis of the renormalizability of the $d=4$ operator $F_{\mu \nu }^2$ in the Gribov-Zwanziger (GZ) formalism as well as in the Refined Gribov-Zwanziger (RGZ) version. The GZ formalism offers a way to deal with gauge copies in the Landau gauge. We explicitly show that $F_{\mu \nu }^2$ mixes with other $d=4$ gauge variant operators, and we determine the mixing matrix $Z$ to all orders, thereby only using algebraic arguments. The mixing matrix allows us to uncover a renormalization group invariant including the operator $F_{\mu \nu }^2$. With this renormalization group invariant, we have paved the way for the study of the lightest scalar glueball in the GZ formalism. We discuss how the soft breaking of the BRST symmetry of the GZ action can influence the glueball correlation function. We expect non-trivial mass scales, inherent to the GZ approach, to enter the pole structure of this correlation function.

27 pages

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Cited by in corpus (15)

• Gauge bosons at zero and finite temperature
• Gribov horizon and i-particles: about a toy model and the construction of physical operators
• Glueball scattering cross section in lattice SU(2) Yang-Mills theory
• On the analytic structure of scalar glueball operators at Born level
• Gluon confinement, i-particles and BRST soft breaking
• Renormalizability of a quark-gluon model with soft BRST breaking in the infrared region
• More on the renormalization of the horizon function of the Gribov-Zwanziger action and the Kugo-Ojima Green function(s)
• Renormalizability of the linearly broken formulation of the BRST symmetry in presence of the Gribov horizon in Landau gauge Euclidean Yang-Mills theories
• Goldstone bosons and fermions in QCD
• On the reanimation of a local BRST invariance in the (Refined) Gribov-Zwanziger formalism
• On bounds and boundary conditions in the continuum Landau gauge
• On Gauge Independence for Gauge Models with Soft Breaking of BRST Symmetry
• Refined Gribov-Zwanziger theory coupled to scalar fields in the Landau gauge
• Gribov as a Phase Transition
• Exploring new horizons of the Gribov problem in Yang-Mills theories