The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model

Abstract

We use the chiral quark model to construct the complete O(p 2 ) weak ∆S = 1 chiral lagrangian via the bosonization of the ten relevant operators of the effective quark lagrangian. The chiral coefficients are given in terms of f π , the quark and gluon condensates and the scale-dependent NLO Wilson coefficients of the corresponding operators; in addition, they depend on the constituent quark mass M , a parameter characteristic of the model. All contributions of order N 2 c as well as N c and α s N c are included. The γ 5 -scheme dependence of the chiral coefficients, computed via dimensional regularization, and the Fierz transformation properties of the operator basis are discussed in detail. We apply our results to the evaluation of the hadronic matrix elements for the decays K → 2π, consistently including the renormalization induced by the meson loops. The effect of this renormalization is sizable and introduces a long-distance scale dependence that matches in the physical amplitudes the short-distance scale dependence of the Wilson coefficients.SISSA 43/95/EP September 1995 ‡ Permanent address:

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

“…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.…”

“…The last term in (16) corresponds to colour exchange between two currents and is genuinely non-factorizable.…”

“…Within the χQM one can include soft gluon contributions corresponding to the nonfactoralizable term in (16). One calculates soft gluon emision from the two coloured currents, and identify the product of two gluon field tensors with the gluon condensate < G 2 >.…”

“…One calculates soft gluon emision from the two coloured currents, and identify the product of two gluon field tensors with the gluon condensate < G 2 >. As an example [15,16]:…”

“…− Taipei [24]: Uses "generalized factorization" where scheme dependence is absorbed in effective Wilson coefficients. Non-factorizable contribtions in (16,27) are represented by a phenomenological parameter. − Valencia [25]: Special attention is put on FSI effects.…”