The Relevance of the Dipole Penguin Operators in ǫ′/ǫ

The standard model contribution to ǫ/ǫ of the magneticand electric-dipole penguin operators Q11 = gs 16π ms s̄ σμνt G a (1− γ5) d and Q12 = eQd 16π ms s̄ σμνF μν(1− γ5) d is discussed. While the electromagnetic penguin Q12 seems to have a vanishingly small matrix element, we find that the gluonic dipole operator Q11 may give a contribution to ǫ/ǫ comparable to that of other operators so far considered, and should therefore be consistently included in the analysis. CERN-TH.7097/93 SISSA 174/93/EP December 1993, revised March 1994. 1. The determination of the ∆S = 1, CP -violating parameter ǫ/ǫ in neutral kaon decays has attracted considerable experimental and theoretical interest (for a complete list of references see, for instance, ref. [1]). The possibility of drastic cancellations among QCDand electroweak-induced operators [2], occurring for large values of the top quark mass, has spurred new and more accurate theoretical investigations [3, 4]. On the experimental side, the present sensitivity of 1 part in 10 [5] is not conclusive and an effort in improving it by one order of magnitude is under way. The theoretical framework for the study of ǫ/ǫ is the effective field theory. The local Hamiltonian for ∆S = 1 transitions can be written, for μ < mc, as [3] H = GF √ 2 λu ∑