Using Gradient Flow to Renormalise Matrix Elements for Meson Mixing and Lifetimes

arXiv (Cornell University)

Abstract

Neutral meson mixing and meson lifetimes are theory-side parametrised in terms four-quark operators which can be determined by calculating weak decay matrix elements using lattice Quantum Chromodynamics. While calculations of meson mixing matrix elements are standard, determinations of lifetimes typically suffer from complications in renormalisation procedures because dimension-6 four-quark operators can mix with operators of lower mass dimension and, moreover, quark-line disconnected diagrams contribute. We present work detailing the idea to use fermionic gradient flow to non-perturbatively renormalise matrix elements describing meson mixing or lifetimes, and combining it with a perturbative calculation to match to the $\overline{\rm MS}$ scheme using the shoft-flow-time expansion.

Authors 5

1. Robert V. Harlander Aachen Institute for Theoretical Particle Physics and Cosmology

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Particle Physics and Cosmology , RWTH Aachen University , 52056 Aachen , Germany

2. Fabian Lange

   Karlsruhe Institute of Technology

   Affiliation as printed

   Institut für Theoretische Teilchenphysik , Karlsruhe Institute of Technology , Wolfgang-Gaede-Straße 1 , 76128 Karlsruhe , Germany

3. Antonio Rago

   University of Siegen

   Affiliation as printed

   𝑎 Center for Particle Physics Siegen , Theoretische Physik 1 , Naturwissenschaftlich-Technische Fakultät , Universität Siegen , 57068 Siegen , Germany

4. Andrea Shindler
5. Oliver Witzel