On epsilon_K beyond lowest order in the Operator Product Expansion

TL;DR

This paper investigates the long-distance contributions to the CP-violating parameter epsilon_K in K0-K0bar mixing, highlighting the importance of including effects on both the absorptive and dispersive parts, which refines the theoretical estimate.

Contribution

It demonstrates that considering long-distance contributions to both Im(Gamma_12) and Im(M_12) reduces the estimated impact on epsilon_K, providing a more consistent theoretical framework.

Findings

LD contributions to Im(M_12) are significant and must be included.

Including these contributions reduces the estimated LD impact on epsilon_K from -6.0% to -3.6%.

The overall correction factor kappa_epsilon is determined to be 0.94 +/- 0.02.

Abstract

We analyse the structure of long distance (LD) contributions to the CP-violating parameter epsilon_K, that generally affect both the absorptive (Gamma_12) and the dispersive (M_12) parts of the K0 -- K0bar mixing amplitude. We point out that, in a consistent framework, in addition to LD contributions to Im(Gamma_12), estimated recently by two of us, also LD contributions to Im(M_12) have to be taken into account. Estimating the latter contributions the impact of LD effects on epsilon_K is significantly reduced (from -6.0 % to -3.6 %). The overall effect of LD corrections and of the superweak phase being different from 45 degrees is summarised by the multiplicative factor kappa_epsilon = 0.94 +/- 0.02.