Abstract
As an important step towards a complete next-to-leading (NLO) QCD analysis of the ratio ε′/ε 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.
Highlights
On the other hand there is no consensus on the size of the QCDP contribution, which originates on the one hand in different estimates of the hadronic matrix elements of QCDP operators and on the other hand in the estimate of isospin-breaking effects that suppress the QCDP contributions
As an important step towards a complete next-to-leading (NLO) QCD analysis of the ratio ε /ε within the Standard Model Effective Field Theory (SMEFT), we present for the first time the next-to-leading order (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
The importance of a given contribution to ε /ε will eventually depend on the size of Wilson coefficients (WCs) at the electroweak scale and this will depend on NP scenario considered
Summary
On the other hand there is no consensus on the size of the QCDP contribution, which originates on the one hand in different estimates of the hadronic matrix elements of QCDP operators and on the other hand in the estimate of isospin-breaking effects that suppress the QCDP contributions. A similar result is found using ChPT [7], but as discussed in [1] it is a numerical coincidence in view of the smaller estimate of EWP contributions by these authors relative to LQCD, and a different estimate of isospin-breaking corrections. As argued on the basis of the DQCD approach [6] in [1, 12] the values of ε /ε in the SM in the ballpark of 5 × 10−4 are still possible This situation motivated various authors already for many years to perform analyses of ε /ε in various extensions of the SM with the goal to identify which models could allow for significant contributions to ε /ε taking existing constraints from other processes into account. As proposed in [14], it is useful to write ε /ε as a sum of the SM and BSM contributions, ε= ε
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