Neutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions part II: Non Perturbative Renormalisation of the $\Delta F=2$ four-quark operators

TL;DR

This paper calculates non-perturbative renormalisation factors for $ abla F=2$ four-quark operators in BSM kaon mixing using nf=2+1 domain-wall fermions, introducing improved RI-SMOM schemes that differ from traditional methods.

Contribution

It introduces and validates new RI-SMOM renormalisation schemes for $ abla F=2$ operators, improving upon the standard RI-MOM approach for BSM kaon mixing calculations.

Findings

RI-SMOM Z-factors agree well after MS conversion

Significant differences found between RI-SMOM and RI-MOM schemes

Renormalisation procedure impacts cross-collaboration discrepancies

Abstract

We compute the renormalisation factors (Z-matrices) of the $\Delta F=2$ four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf=2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to MS, the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.