Abstract
The gradient-flow operator product expansion for QCD current correlators including operators up to mass dimension four is calculated through NNLO. This paves an alternative way for efficient lattice evaluations of hadronic vacuum polarization functions. In addition, flow-time evolution equations for flowed composite operators are derived. Their explicit form for the non-trivial dimension-four operators of QCD is given through order {alpha}_s^3.
Highlights
The underlying idea in this case is the smallflow-time expansion of composite operators [11], leading to the flowed Operator Product Expansion (OPE), where the regular operators are replaced by operators taken at finite flow time
We presented the flowed OPE for general current correlators and its matching to regular QCD through next-to-next-to-leading order (NNLO) in the strong coupling αs and through mass dimension four by using the small-flow-time expansion
Our calculation is based on the renormalization procedure for the regular QCD dimension-four operators worked out in refs. [27, 28], the mixing matrix between flowed and regular operators derived in ref. [21], the method of projectors [66], and the tools and results for perturbative calculations in the gradient-flow formalism (GFF) presented in ref. [65]
Summary
Our results are presented for a general non-Abelian gauge theory based on a simple compact. Lie group with nf quark fields ψ1, . Ψnf in the fundamental representation, of which the first nh are degenerate with mass m, while the remaining nl are massless. The generators T a of the fundamental representation are normalized as Tr(T aT b) = −TRδab, and the structure constants f abc are defined through the Lie algebra [T a, T b] = f abcT c. The dimensions of the fundamental and the adjoint representation are nc and nA, respectively, and their quadratic Casimir eigenvalues are denoted by CF and CA. We often use “QCD” to refer to the more general gauge theory in the following
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