On the determination of nonleptonic kaon decays from K→π matrix elements

Abstract

The coupling constants of the order p 2 low-energy weak effective lagrangian can be determined from the K → π and K → 0 weak matrix elements, choosing degenerate quark masses for the first of these. However, for typical values of quark masses in Lattice QCD computations, next-to-leading O(p 4 ) corrections are too large to be ignored, and will need to be included in future analyses. Here we provide the complete O(p 4 ) expressions for these matrix elements obtained from Chiral Perturbation Theory, valid for partially quenched QCD with N degenerate sea quarks. Quenched QCD corresponds to the special case N = 0. We also discuss the role of the η meson in some detail, and we give numerical examples of the size of chiral logarithms.

Chiral limit prediction for ε′/K/εK at NLO in 1/Nc

“…Including again the two known higher order CHPT corrections to this result, we obtain our final number for ε ′ K /ε K in (24). Notice however, as discussed in Section 5, that most of the higher order CHPT corrections are actually unknown and as remarked in several recent work they could affect numerically the Standard Model value of ε ′ K /ε K significantly [12,43,44].…”

“…This procedure is unambiguous. One can use also K → π and K → vacuum transitions form lattice simulations to predict the lowest order CHPT couplings [15,23,24].…”

“…This would be very interesting. Of course, one also wants to predict the ∆I = 1/2 enhancement ratio Re a 2 /Re a 0 but K → π calculations look more straightforward in the lattice at present [24].…”

Light hadron weak matrix elements

“…In the second study, it is one-loop corrections to the matrix elements of the (8, 1) and (27, 1) operators for K → π transitions at rest with degenerate s and d quarks and for K → 0 with m s = m d , and the relation of these matrix elements to K → ππ amplitudes, which are studied in pqχPT [38]. Not surprisingly, they find that K → π and K → 0 amplitudes are not sufficient to determine all O p 4 couplings required to obtain K → ππ matrix elements at this order.…”

Lattice extraction ofK→ππamplitudes to next-to-leading order in partially quenched and in full chiral perturbation theory

“…The Minkowski space propagators for the flavor diagonal elements of Φ are given by analytically continuing the Euclidean expression in [30] …”