Additional Isospin-Breaking Effects in \epsilon^\prime/\epsilon

TL;DR

This paper investigates additional isospin-breaking effects, specifically from u-d quark mass differences, and finds they can significantly increase the theoretical estimate of  extprime/8 extprime by up to a factor of two.

Contribution

It introduces a new isospin-violating effect from quark mass differences in the gluonic penguin operator's hadronization, expanding the understanding of 8 extprime/8 extprime calculations.

Findings

Additional isospin violation can double 8 extprime/8 extprime estimates.

The effect arises from u-d quark mass differences in gluonic penguin hadronization.

Model-dependent analysis shows potential for larger theoretical predictions.

Abstract

In the analysis of \epsilon^\prime/\epsilon it has been traditional to consider the isospin-breaking effects arising from electroweak-penguin contributions and from \pi^0-\eta and \pi^0-\eta^\prime mixing, yet additional isospin-violating effects exist. In particular, we study the isospin violation which arises from the u-d quark mass difference in the hadronization of the gluonic penguin operator, engendering contributions of an effective \Delta I=3/2 character. Using chiral perturbation theory and the factorization approximation for the hadronic matrix elements, we find within a specific model for the low-energy constants that we can readily accommodate an increase in \epsilon^\prime/\epsilon by a factor of two.