A novel nonperturbative renormalization scheme for local operators

Lattice quantum chromodynamics (QCD) provides the only systematic nonperturbative approach to calculating the properties of the strong nuclear force at low energies. Lattice calculations discretize spacetime on a Euclidean lattice and sample the path integral stochastically to obtain Monte Carlo estimates of QCD correlation functions. One common challenge for lattice calculations is constructing nonperturbative renormalization schemes and relating those schemes to the standard MS-bar scheme typically used in perturbative calculations. The gradient flow, which exponentially suppresses ultraviolet field fluctuations and removes ultraviolet divergences (up to a multiplicative fermionic wavefunction renormalization), can be used to describe real-space Wilsonian renormalization group transformations and determine the corresponding beta function. We propose a new nonperturbative renormalization scheme for local operators that uses the gradient flow and is amenable to lattice QCD calculations, and present some preliminary results for quark bilinear operators.