Hadronic vacuum polarization using gradient flow

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 α 3 s .

The effective electroweak Hamiltonian in the gradient-flow formalism

“…3 Again, analytical results are provided in the ancillary file. 4 We note in passing that the matching matrix also determines the small-t behavior of the flowed operators through the equation [9]…”

“…[5][6][7]. More recently, the matching matrix has also been calculated for the quark dipole operators at nextto-leading order (NLO) QCD [8], and for the hadronic vacuum polarization through NNLO QCD [9].…”

The gradient flow at higher orders in perturbation theory

“…The spectrum of possible applications is enormous (see Refs. [29][30][31][32][33][34][35][36], for example). The idea is to define flowed operators Õ𝑛 (𝑡) by replacing the regular by flowed fields in Eq.…”

A novel nonperturbative renormalization scheme for local operators

“…We anticipate that our renormalization scheme can be implemented for a wide range of local operators in lattice QCD, from flavor-changing weak currents and four-quark operators, to twist-2 operators relevant to hadron structure calculations. Calculations for further quantities are discussed in [9][10][11][12][13]. Future work will be required to identify the region of applicability, quantify the associated systematic uncertainties, and assess the viability of our scheme for different local operators.…”