The strong isospin-breaking correction for the gluonic penguin contribution to ε′/ε at next-to-leading order in the chiral expansion

Abstract

The strong isospin-breaking correction Ωst, which appears in estimates of the standard model value for the direct CP-violating ratio ε′/ε, is evaluated to next-to-leading order (NLO) in the chiral expansion using chiral perturbation theory. The relevant linear combinations of the unknown NLO CP-odd weak low-energy constants (LEC’s) which, in combination with one-loop and strong LEC contributions, are required for a complete determination at this order, are estimated using two different models. It is found that, to NLO, Ωst=0.08±0.05, significantly reduced from the “standard” value, 0.25±0.08, employed in recent analyses. The potentially significant numerical impact of this decrease on standard model predictions for ε′/ε, associated with the decreased cancellation between gluonic penguin and electroweak penguin contributions, is also discussed.