Gradient Flow Renormalisation for Meson Mixing and Lifetimes

TL;DR

This paper introduces a gradient flow renormalisation method that simplifies lattice calculations of hadronic matrix elements, demonstrated on meson mixing and lifetimes, including preliminary results for charm-strange mesons.

Contribution

The paper presents a novel gradient flow renormalisation technique that addresses operator mixing issues in lattice QCD calculations of meson properties.

Findings

Validated the method with meson mixing matrix elements

Provided preliminary results for charm-strange meson lifetimes

Simplified renormalisation process for operators with different mass dimensions

Abstract

Fermionic gradient flow in combination with the short-flow-time expansion provides a computational method where the renormalisation of hadronic matrix elements on the lattice can be simplified to address e.g. the issue that operators with different mass dimension can mix. We demonstrate our gradient flow renormalisation procedure by determining matrix elements of four-quark operators describing neutral meson mixing or meson lifetimes. While meson mixing calculations are well-established on the lattice and serve to validate our procedure, a lattice calculation of matrix elements for heavy meson lifetimes is still outstanding. Preliminary results for mesons formed of a charm and strange quark are presented.