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Lattice QCD calculations of form factors for rare Standard Model processessuch as $B \to K \ell^+ \ell^-$ use tensor currents that requirerenormalisation. These renormalisation factors, $Z_T$, have typically beencalculated within perturbation theory and the estimated uncertainties frommissing higher order terms are significant. Here we study tensor currentrenormalisation using lattice implementations of momentum-subtraction schemes.Such schemes are potentially more accurate but have systematic errors fromnonperturbative artefacts. To determine and remove these condensatecontributions 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, withratio to the vector decay constant of 0.9569(52), significantly below 1. Wealso give $Z_T$ factors, converted to the $\bar{\mathrm{MS}}$ scheme, correctedfor condensate contamination. This contamination reaches 1.5\% at arenormalisation scale of 2 GeV (in the preferred RI-SMOM scheme) and so must beremoved for accurate results.

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