Non-perturbative renormalization of tensor currents: strategy and results for $N_f=0$ and $N_f=2$ QCD

Abstract

Tensor currents are the only quark bilinear operators lacking a non-perturbative determination of their renormalisation group (RG) running between hadronic and electroweak scales. We develop the setup to carry out the computation in lattice QCD via standard recursive finite-size scaling techniques, and provide results for the RG running of tensor currents in $N_f=0$ and $N_f=2$ QCD in the continuum for various Schrödinger Functional schemes. The matching factors between bare and renormalisation group invariant currents are also determined for a range of values of the lattice spacing relevant for large-volume simulations, thus enabling a fully non-perturbative renormalization of physical amplitudes mediated by tensor currents.

50 pages, 14 Figures

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• Proton tensor charges from a Poincaré-covariant Faddeev equation
• Strong coupling from non-equilibrium Monte Carlo simulations
• Off-shell quark bilinear operator Green's functions at two loops