Varepsilon '/varepsilon in the Standard Model at the Dawn of the 2020s

Jason Aebischer,Andrzej J. Buras,Christoph Bobeth

doi:10.1140/epjc/s10052-020-8267-1

Abstract

We reanalyse the ratio varepsilon '/varepsilon in the Standard Model (SM) using most recent hadronic matrix elements from the RBC-UKQCD collaboration in combination with most important NNLO QCD corrections to electroweak penguin contributions and the isospin-breaking corrections. We illustrate the importance of the latter by using their latest estimate from chiral perturbation theory (ChPT) based on the octet approximation for lowest-lying mesons and a very recent estimate in the nonet scheme that takes into account the contribution of eta _0. We find (varepsilon '/varepsilon )^{(8)}_text {SM} = (17.4 pm 6.1) times 10^{-4} and (varepsilon '/varepsilon )^{(9)}_text {SM} = (13.9 pm 5.2) times 10^{-4}, respectively. Despite a very good agreement with the measured value (varepsilon '/varepsilon )_text {exp} = (16.6 pm 2.3) times 10^{-4}, the large error in (varepsilon '/varepsilon )_text {SM} still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for (varepsilon '/varepsilon )_text {BSM} valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters B_6^{(1/2)}(mu ) and B_8^{(3/2)}(mu ) at the mu -scales used by the RBC-UKQCD collaboration and at lower scales mathcal {O}(1, text {GeV}) used by ChPT and Dual QCD (DQCD). We present semi-analytic formulae for (varepsilon '/varepsilon )_text {SM} in terms of these parameters and hat{Omega }_text {eff} that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the mathcal {O}(alpha _{text {em}}) contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at mathcal {O}(alpha _{text {em}}) in the present analyses of varepsilon '/varepsilon .

Highlights

Lattice QCD, lead by the RBC-UKQCD LQCD collaboration
Our final result for ε /ε in (5) differs significantly from the one of the RBC-UKQCD collaboration but in view of large uncertainties in both results they are in agreement with each other and with experiment
Still it would be important to clarify whether the QCD dynamics enhancing the parameter B6(1/2) over unity in LQCD and in Chiral Perturbation theory (ChPT) is the same

Summary

Preliminaries

Note that aEWP contains the I = 0 and I = 2 contributions of the EWPs at the scales (μ0, μ2) = (4.006, 3.0) GeV, where the QCDP matrix elements for I = 2 are zero because the lattice calculation is done in the isospin limit. These hierarchies are strongly counteracted by those present in the Wilson coefficients yi at the two scales μ0 = 4.006 GeV and μ2 = 3.0 GeV, where we evaluate Im A0 and Im A2, respectively This is illustrated by the following semi-analytic results of ε /ε that include the NNLO QCD corrections to EWPs [24].

BSM master formula

Summary and outlook

B Wilson coefficients

Findings

C Isospin-breaking RG effects