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.
Highlights
Rare Standard Model processes, for example those that first appear at one-loop order through so-called “penguin” diagrams, are of great interest in searches for new physics
In the discussion of the tensor current presented there, uncertainties associated with missing terms in the matching to the MS scheme were added to the renormalization factors
We have shown here that it is possible to renormalize lattice tensor currents to give accurate results for continuum matrix elements in the MS scheme using nonperturbative determination of intermediate renormalization factors in momentum-subtraction schemes
Summary
Rare Standard Model processes, for example those that first appear at one-loop order through so-called “penguin” diagrams, are of great interest in searches for new physics. The HPQCD Collaboration has recently performed a series of b physics calculations using the HISQ formalism for all quarks, working upwards in mass from that of the c quark and mapping out the dependence on the heavy-quark mass [5,6,7,8] The success of this methodology indicates the possibility of improvement on previous B → K calculations for which it would be important to reduce the uncertainty arising from the tensor current renormalization. We show here how to remove such systematic effects in the tensor renormalization factor by calculating a simple matrix element of the tensor operator that we can determine accurately in the continuum limit. For this purpose we use the J=ψ tensor decay constant fTJ=ψ.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
