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arXiv · 0812.2401

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

D. Dudal·S. P. Sorella·N. Vandersickel·H. Verschelde
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Abstract

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant $d=4$ operator $F_{μν}^2(x)$ 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.

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D. Dudal, S. P. Sorella, N. Vandersickel, H. Verschelde. 2008-12-12. A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator. https://doi.org/10.1140/epjc%2Fs10052-009-1139-3

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