BSM Master Formula for $\varepsilon'/\varepsilon$ in the WET Basis at NLO in QCD

TL;DR

This paper derives a comprehensive NLO master formula for the BSM contribution to the $ ext{Re}(rac{ ext{ε}'}{ ext{ε}})$ ratio within the SMEFT framework, integrating Wilson coefficients, hadronic matrix elements, and QCD effects.

Contribution

It provides the first NLO master formula for BSM effects on $ ext{ε}'/ ext{ε}$ in the WET basis, connecting SMEFT Wilson coefficients to hadronic matrix elements at the electroweak scale.

Findings

Includes NLO QCD effects and threshold corrections.

Uses Dual QCD and lattice QCD for matrix elements.

Provides a tool for precise BSM analysis of $ ext{ε}'/ ext{ε}$.

Abstract

As an important step towards a complete next-to-leading order (NLO) QCD analysis of the ratio $\varepsilon'/\varepsilon$ within the Standard Model Effective Field Theory (SMEFT), we present for the first time the NLO master formula for the BSM part of this ratio expressed in terms of the Wilson coefficients of all contributing operators evaluated at the electroweak scale. To this end we use the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. The relevant hadronic matrix elements of BSM operators at the electroweak scale are taken from Dual QCD approach and the SM ones from lattice QCD. It includes the renormalization group evolution and quark-flavour threshold effects at NLO in QCD from hadronic scales, at which these matrix elements have been calculated, to the electroweak scale.