NPR step-scaling across the charm threshold

TL;DR

This paper develops a strategy within the Rome-Southampton framework to increase the matching scale for non-perturbative renormalisation across the charm threshold, enabling more precise calculations of observables like BK.

Contribution

It introduces a method to push the renormalisation scale higher across the charm threshold and applies it to study BK running from 3 GeV to 9 GeV on specific lattice ensembles.

Findings

Successful implementation of higher scale matching across the charm threshold.

Quantitative analysis of discretisation effects on BK running.

Enhanced precision in lattice renormalisation procedures.

Abstract

Matching Non-Perturbative Renormalisation on the lattice and perturbative renormalisation would benefit from higher matching scales, which are needed for observables entering their permile era such as BK. In this work we lay down a strategy, within the Rome-Southampton framework, to push this scale higher across the charm threshold, and apply it to an exploration of the BK running from 3 GeV to 9 GeV. This is done on Nf = 2+1+1 ensembles generated by the RBC-UKQCD collaboration, and features a close study of the discretisation effects.