On the contribution of electromagnetic penguins to ϵ′
Stephen R. Sharpe · Physics Letters B · 1987
I discuss the importance of the electromagnetic penguin (EMP) contribution to ϵ′. I confirm the corrections to earlier calculations found by Buras and Gerard (BG). Incorporating these corrections, I calculate the Wilson coefficients of the EMP operators using the full anomalous dimension matrices, and also using the large- N (number of colors) approach of BG. I disagree with BG on the coefficient of the EMP operator dominant at large N : my result is of opposite sign and smaller in magnitude. This means that for large N the EMP contribution increases ϵ′, but by less than 1%. I also find that this Wilson coefficient is poorly estimated in the large- N approach. I agree with the BG result for the coefficient of the EMP operator subdominant at large N . This coefficient is large, and is well estimated using the large- N anomalous dimension matrices. I emphasize that the crucial factor determining the EMP contribution to ϵ′ is the size of the hadronic matrix elements of the subdominant EMP operator. Though suppressed at large N , it increases ϵ′ by 5–20% if one assumes vacuum insertion approximation, and by up to 100% if one uses the results from a recent lattice calculation.