epsilon'/epsilon at the NLO: 10 Years Later

TL;DR

This paper revisits the calculation of the CP-violating ratio epsilon'/epsilon within the Standard Model, incorporating recent experimental and theoretical updates to refine the understanding of hadronic matrix elements and their implications for CP violation.

Contribution

It provides a new analysis of epsilon'/epsilon at NLO using updated parameters, estimating the hadronic matrix element R_6 and comparing it with large-N_c approaches.

Findings

Estimated R_6=1.23+-0.16 from current epsilon'/epsilon data

Found <Q_6>_0^NDR(m_c) ~ -0.8 <Q_8>_2^NDR(m_c)

Compared results with large-N_c approaches showing R_6 ~ R_8

Abstract

During the last four years several parameters relevant for the analysis of the CP-violating ratio epsilon'/epsilon improved and/or changed significantly. In particular, the experimental value of epsilon'/epsilon and the strange quark mass decreased, the uncertainty in the CKM factor has been reduced, and for a value of the hadronic matrix element of the dominant electroweak penguin operator Q_8, some consensus has been reached among several theory groups. In view of this situation, ten years after the first analyses of epsilon'/epsilon at the next-to-leading order, we reconsider the analysis of epsilon'/epsilon within the SM and investigate what can be said about the hadronic Q_6 matrix element of the dominant QCD penguin operator on the basis of the present experimental value of epsilon'/epsilon and todays values of all other parameters. Employing a conservative range for the reduced electroweak penguin matrix element R_8=1.0+-0.2 from lattice QCD, and present values for all other input parameters, on the basis of the current world average for epsilon'/epsilon, we obtain the reduced hadronic matrix element of the dominant QCD penguin operator R_6=1.23+-0.16 implying <Q_6>_0^NDR(m_c) ~ -0.8 <Q_8>_2^NDR(m_c). We compare these results with those obtained in large-N_c approaches in which generally R_6 ~ R_8 and <Q_6>_0^NDR(m_c) is chirally suppressed relatively to <Q_8>_2^NDR(m_c). We present the correlation between R_6 and R_8 that is implied by the data on epsilon'/epsilon provided new physics contributions to epsilon'/epsilon can be neglected.