Renormalizing a Becchi-Rouet-Stora-Tyutin-invariant composite operator of mass dimension 2 in Yang-Mills theory

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Abstract
We discuss the renormalization of a Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariant composite operator of mass dimension 2 in Yang-Mills theory with general BRST and anti-BRST invariant gauge-fixing terms of Lorentz type. The interest of this study stems from a recent claim that the nonvanishing vacuum condensate of the composite operator in question can be an origin of mass gap and quark confinement in any manifestly covariant gauge, as proposed by one of the authors. First, we obtain the renormalization group flow of the Yang-Mills theory. Next, we show the multiplicative renormalizability of the composite operator and that the BRST and anti-BRST invariance of the bare composite operator is preserved under the renormalization. Third, we perform the operator product expansion of the gluon and ghost propagators and obtain the Wilson coefficient corresponding to the vacuum condensate of mass dimension 2. Finally, we discuss the connection of this work with previous works and argue the physical implications of the obtained results.

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