at O(p4) in the chiral expansion

Abstract

After updating the determination of the combination of Kobayashi-Maskawa elements Im V td V * ts according to our new estimate of the parameter B K , we study the CP -violating ratio ε ′ /ε by means of hadronic matrix elements computed to O(p 4 ) in the chiral expansion. It is the first time that this order in chiral perturbation theory is included. We also discuss the relevance of some O(p 2 ) terms that are generally neglected in the calculation of the electroweak penguin matrix elements. The most important effect of this improved analysis is the substantial reduction (20%) of the leading electroweak penguin matrix element and accordingly a reduced cancelation between the electroweak and gluon penguin contributions. The ratio ε ′ /ε is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find ε ′ /ε = 1.7+1.4 −1.0 × 10 −3 . Values positive and of the order of 10 −3 are therefore preferred.

Combined analysis of the unitarity triangle and CP violation in the Standard Model

“…3, we display the individual contributions of each operator to the prediction of ε ′ /ε using matrix elements computed on the lattice, as explained in the next section. Qualitatively, very similar results are obtained also in other approaches [10,13,14]. There is a general consensus that the largest contributions to ε ′ /ε are those coming from Q 6 and Q 8 , with opposite sign, and sizeable contributions may come from Q 4 , Q 5 and Q 9 in the presence of large cancellations between Q 6 and Q 8 , i.e.…”

“…We also make a critical comparison with previous calculations of the Rome group [4]- [6], with the recent estimates of ref. [13] and with results obtained in other approaches such as the χQM [9,10] and the 1/N expansion [14,20]. Some general remarks are necessary before entering a more detailed discussion.…”

“…[21,22], where only the V CKM constraints were considered, or with the analyses of refs. [9,10] and [14,20], where the input values and errors of the V CKM parameters used in the study of ε ′ /ε were taken elsewhere. With respect to the recent study of ref.…”

Theoretical Estimate(s) of the CP-Violating Quantity ɛ′/ɛ in K → 2π decays

“…These are used as input to estimate ε ′ /ε , and we got [18] a result close to the one which later became the world average Re ε ′ /ε = (19 ± 2.4) × 10 −4 , based on results from 1992 at CERN and FNAL, and the last years run at FNAL (KTeV) [19] and CERN (NA48) [20]. Our ("Trieste group") estimate is shown together with other theoretical estimates in Fig.…”

“…For precice statements about numerical values, I refer to the cited papers. The strength of our approach [16,17,18] is that all contributions are calculated systematically up to O(p 4 ) in the chiral expansion. The weakness is its model dependence, which it shares more or less with other estimates.…”