Renormalisation of the tensor current in lattice QCD and the $J/\psi$ tensor decay constant

TL;DR

This paper improves the renormalisation of tensor currents in lattice QCD by using nonperturbative schemes and calculating the $J/$ tensor decay constant, reducing systematic uncertainties in form factor calculations.

Contribution

It introduces a nonperturbative momentum-subtraction scheme for tensor current renormalisation and computes the $J/$ tensor decay constant to correct for condensate effects.

Findings

Calculated $f_{J/}^T$ at 2 GeV as 0.3927(27) GeV.

Determined $Z_T$ factors with condensate contamination correction.

Found condensate effects reach 1.5% at 2 GeV, impacting renormalisation accuracy.

Abstract

Lattice QCD calculations of form factors for rare Standard Model processes such as $B \to K \ell^+ \ell^-$ use tensor currents that require renormalisation. These renormalisation factors, $Z_T$, have typically been calculated within perturbation theory and the estimated uncertainties from missing higher order terms are significant. Here we study tensor current renormalisation using lattice implementations of momentum-subtraction schemes. Such schemes are potentially more accurate but have systematic errors from nonperturbative artefacts. To determine and remove these condensate contributions we calculate the ground-state charmonium tensor decay constant, $f_{J/\psi}^T$, which is also of interest in beyond the Standard Model studies. We obtain $f_{J/\psi}^T(\bar{\text{MS}}, 2\ \mathrm{GeV})=0.3927(27)$ GeV, with ratio to the vector decay constant of 0.9569(52), significantly below 1. We also give $Z_T$ factors, converted to the $\bar{\mathrm{MS}}$ scheme, corrected for condensate contamination. This contamination reaches 1.5\% at a renormalisation scale of 2 GeV (in the preferred RI-SMOM scheme) and so must be removed for accurate results.