Eur. Phys. J. C (2009) 64: 147-159
https://doi.org/10.1140/epjc/s10052-009-1139-3

Regular Article - Theoretical Physics

A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator

¹ Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA
² Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281-S9, 9000, Gent, Belgium
³ Departamento de Física Teórica, Instituto de Física, UERJ—Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, Maracanã, Brasil

^* e-mail: david.dudal@ugent.be

Received: 7 January 2009
Published online: 17 September 2009

Abstract

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant d=4 operator F _{μ ν} ² (x) to all orders of perturbation theory in pure Yang–Mills gauge theory, whereby working in the Landau gauge. This renormalization is far from being trivial as mixing occurs with other d=4 gauge variant operators, which we identify explicitly. We determine the mixing matrix Z to all orders in perturbation theory by using only algebraic arguments and consequently we can uncover a renormalization group invariant by using the anomalous dimension matrix Γ derived from Z. We also present a future plan for calculating the mass of the lightest scalar glueball with the help of the framework we have set up.