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

International Symposium on Lattice Field Theory (LATTICE), pp. 263

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 short flow time expansion.

Authors 5

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

   Karlsruhe Institute of Technology · University of Southern Denmark · University of Zurich · University of Siegen · Paul Scherrer Institute · RWTH Aachen University

   Affiliation as printed

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

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

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

   𝑐 Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

   𝑑 Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

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

   𝑔 IMADA and Quantum Theory Center, University of Southern Denmark, Odense, Denmark

2. Fabian Lange Aachen 𝑏 Institute for Theoretical Particle Physics and Cosmology

   Karlsruhe Institute of Technology · University of Southern Denmark · University of Zurich · University of Siegen · Paul Scherrer Institute · RWTH Aachen University

   Affiliation as printed

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

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

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

   𝑐 Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

   𝑑 Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

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

   𝑓 Institut für Astroteilchenphysik, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

   𝑔 IMADA and Quantum Theory Center, University of Southern Denmark, Odense, Denmark

3. Antonio Rago Aachen 𝑏 Institute for Theoretical Particle Physics and Cosmology

   Karlsruhe Institute of Technology · University of Southern Denmark · University of Zurich · University of Siegen · Paul Scherrer Institute · RWTH Aachen University

   Affiliation as printed

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

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

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

   𝑐 Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

   𝑑 Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

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

   𝑓 Institut für Astroteilchenphysik, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

   𝑔 IMADA and Quantum Theory Center, University of Southern Denmark, Odense, Denmark

4. Andrea Shindler Aachen 𝑏 Institute for Theoretical Particle Physics and Cosmology

   Karlsruhe Institute of Technology · University of Southern Denmark · University of Zurich · University of Siegen · Paul Scherrer Institute · RWTH Aachen University

   Affiliation as printed

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

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

   𝑐 Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

   𝑑 Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

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

   𝑓 Institut für Astroteilchenphysik, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

   𝑔 IMADA and Quantum Theory Center, University of Southern Denmark, Odense, Denmark

5. Oliver Witzel Aachen 𝑏 Institute for Theoretical Particle Physics and Cosmology

   Karlsruhe Institute of Technology · University of Southern Denmark · University of Zurich · University of Siegen · Paul Scherrer Institute · RWTH Aachen University

   Affiliation as printed

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

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

   𝑐 Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

   𝑑 Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

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

   𝑓 Institut für Astroteilchenphysik, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

   𝑔 IMADA and Quantum Theory Center, University of Southern Denmark, Odense, Denmark