Master formula for ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model

Abstract

We present for the first time a master formula for ${\epsilon }^{\prime }/\epsilon$, the ratio probing direct CP violation in $K\to \pi \pi$ decays, valid in any theory beyond the Standard Model (BSM). The formula makes use of hadronic matrix elements of BSM operators calculated recently in the Dual QCD approach and the ones of the SM operators from lattice QCD. We emphasize the large impact of several scalar and tensor BSM operators in the context of the emerging ${\epsilon }^{\prime }/\epsilon$ anomaly. We have implemented the results in the open source code flavio.

Comments: 6 pages, 1 table. v3: signs in table I corrected. arXiv admin note: text overlap with arXiv:1808.00466