Local and renormalizable framework for the gauge-invariant operator A(min)(2) in Euclidean Yang-Mills theories in linear covariant gauges

摘要

We address the issue of the renormalizability of the gauge-invariant nonlocal dimension-two operator A(min)(2), whoseminimization is defined along the gauge orbit. Despite its nonlocal character, we show that the operator A(min)(2) can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action that turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operatorA(min)(2) turnsout to be independent fromthe gauge parametera enteringthegauge-fixing condition, thus being given by the anomalous dimension of the operator A(2) in the Landau gauge.