Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-12-12
Eur.Phys.J.C64:147-159,2009
Physics
High Energy Physics
High Energy Physics - Theory
17 pages
Scientific paper
10.1140/epjc/s10052-009-1139-3
This paper presents a complete algebraic proof of the renormalizability of the gauge invariant $d=4$ operator $F_{\mu\nu}^2(x)$ 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 $\Gamma$ 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.
Dudal David
Sorella Silvio Paolo
Vandersickel Nele
Verschelde Henri
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