A new estimate of ε′/ε

Abstract

We discuss direct CP violation in the standard model by giving a new estimate of ε ′ /ε in kaon decays. Our analysis is based on the evaluation of the hadronic matrix elements of the ∆S = 1 effective quark lagrangian by means of the chiral quark model, with the inclusion of meson one-loop renormalization and NLO Wilson coefficients. Our estimate is fully consistent with the ∆I = 1/2 selection rule in K → ππ decays which is well reproduced within the same framework. By varying all parameters in the allowed ranges and, in particular, taking the quark condensate-which is the major source of uncertainty-between (−200 MeV) 3 and (−280 MeV) 3 we findAssuming for the quark condensate the improved PCAC result qq = −(221 ± 17 MeV) 3 and fixing ΛQCD to its central value, we find the more restrictive predictionwhere the central value is defined as the average over the allowed values of Im λ t in the first and second quadrants. In these estimates the relevant mixing parameter Im λ t is selfconsistently obtained from ε and we take m pole t = 180 ± 12 GeV. Our result is, to a very good approximation, renormalization-scale and γ 5 -scheme independent.

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

“…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.…”

“…Note that, in refs. [9,10], the calculations are performed using dimensional regularization in which quadratic divergences do not appear. We suggest to repeat the calculation of the relevant matrix elements with the χQM using a hard cutoff to show the stability of the results with respect to the change of regularization scheme and verify the possible presence of quadratic divergences.…”

Theoretical status of

“…A complete control of the scheme dependence at this order is expected to be possible [25]. In the large-N c limit one has B (14) showing that the corrections to the large N c limit are indeed reasonably small, as expected in [24,15,16] The chiral quark model [27,28] calculates all Bparameters in terms of three model parameters, which are determined from Re A 0 and Re A 2 . It includes chiral corrections up to O(p 4 ).…”

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

“…Other possible operators of dimension 5 or 6 exist, but give small contributions within the SM [11,12]. However, it has been stated that higher dimensional operators will become relevant [13] if the renormalization (separation) scale µ is chosen to low [8].…”