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.
Highlights
Hadronic matrix elements of tensor currents play an important rôle in several relevant problems in particle physics
We develop the setup to carry out the computation in lattice QCD via standard recursive finite-size scaling techniques, and provide results for the renormalisation group (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 determined for a range of values of the lattice spacing relevant for large-volume simulations, enabling a fully non-perturbative renormalization of physical amplitudes mediated by tensor currents
Summary
Hadronic matrix elements of tensor currents play an important rôle in several relevant problems in particle physics. Some prominent examples are rare heavy meson decays that allow to probe the consistency of the Standard Model (SM) flavour sector (see, e.g., [1,2,3] for an overview), or precision measurements of β-decay and limits on the neutron electric dipole moment (see, e.g., [4,5,6] for an up-to-date lattice-QCD perspective). One of the key ingredients in these computations is the renormalization of the current. Partial current conservation ensures that non-singlet vector and axial currents require at worst finite normalizations, and fixes the anomalous dimension of scalar and pseudoscalar densities to be
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