Abstract
Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form.
Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schrödinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm cT derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions.
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Acknowledgments
J.H. wishes to thank the Yukawa Institute for Theoretical Physics, Kyoto University, for its hospitality. This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through the Research Training Group “GRK 2149: Strong and Weak Interactions — from Hadrons to Dark Matter” (J.H. and F.J.). We acknowledge the computer resources provided by the WWU-IT of the University of Münster (PALMA II) and thank its staff for support. F.J. is supported by UKRI Future Leader Fellowship MR/T019956/1. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 813942 (L.C.). The work of C.P. and D.P. has been supported by the Spanish Research Agency (Agencia Estatal de Investigación) through the grants IFT Centro de Excelencia Severo Ochoa SEV-2016-0597 and CEX2020-001007-S and, grants FPA2015-68541-P, PGC2018-094857-B-I00 and PID2021-127526NB-I00, all of which are funded by MCIN/AEI/10.13039/501100011033. C.P. and D.P. also acknowledge support from the project H2020-MSCAITN-2018-813942 (EuroPLEx) and the EU Horizon 2020 research and innovation programme, STRONG-2020 project, under grant agreement No 824093. The work of M.P. has been partially supported by the Italian PRIN “Progetti di Ricerca di Rilevante Interesse Nazionale — Bando 2022”, prot. 2022TJFCYB and by the Spoke 1 “FutureHPC & BigData” of the Italian Research Centre in High-Performance Computing, Big Data and Quantum Computing (ICSC), funded by the European Union — NextGenerationEU.
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Chimirri, L., Fritzsch, P., Heitger, J. et al. Non-perturbative renormalisation and improvement of non-singlet tensor currents in Nf = 3 QCD. J. High Energ. Phys. 2024, 89 (2024). https://doi.org/10.1007/JHEP07(2024)089
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DOI: https://doi.org/10.1007/JHEP07(2024)089