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

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.