Related papers: The $\Delta I = 1/2$ Selection Rule

I review a recent attempt to reproduce the isospin $I= 0$ and 2 amplitudes for the decay of a kaon into two pions by estimating the relevant hadronic matrix elements in the chiral quark model. The results are parametrized in terms of the…

We calculate the hadronic matrix elements to $O(p^4)$ in the chiral expansion for the ($\Delta S =1$) $K^0 \to 2 \pi$ decays and the ($\Delta S=2$) $\bar K^0$-$K^0$ oscillation. This is done within the framework of the chiral quark model.…

The $K\to\pi\pi$ decay amplitudes are studied within the framework of generalized factorization in which the effective Wilson coefficients are gauge-invariant, renormalization-scale and -scheme independent while factorization is applied to…

I discuss the role of the Delta I = 1/2 selection rule in K -> pi pi decays for the theoretical calculations of eps'/eps. Lacking reliable ``first principle'' calculations, phenomenological approaches may help in understanding correlations…

We calculate $\Delta I = 3/2$ kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to $a^{-1} = 1.3$ GeV. We employ the Lellouch and L\"uscher formula and its extention…

The $\Delta I=1/2$ rule and direct CP violation $\epsilon'/\epsilon$ in kaon decays are studied within the framework of the effective Hamiltonian approach in conjunction with generalized factorization for hadronic matrix elements. We…

We present a new analysis of the Delta I = 1/2 rule in K --> pi pi decays and the B_K parameter. We use the 1/N_c expansion within the effective chiral lagrangian for pseudoscalar mesons and compute the hadronic matrix elements at leading…

We report on the progress of our ongoing project to quantify the role of the charm quark in the non-leptonic decay of a kaon into two pions. The effect of its associated mass scale in the dynamics underlying the \Delta I = 1/2 rule can be…

We discuss a new estimate of $\varepsilon '/\varepsilon$ in the kaon system. The present approach is based on the evaluation of the hadronic matrix elements of the \mbox{$\Delta S =1$} effective quark lagrangian by means of the chiral quark…

We study the scaling of kaon decay amplitudes with the number of colours, $N_c$, in a theory with four degenerate flavours, $N_f=4$. In this scenario, two current-current operators, $Q^\pm$, mediate $\Delta S=1$ transitions, such as the two…

The weak decay of the kaon to two pions is studied within the NJL Model. Using the standard effective weak Hamiltonian, both the decay amplitude arising from an intermediate state \sigma-meson and the direct decay amplitude are calculated.…

We study the $\Delta I = 1/2$ rule for kaon decays and the $B_K$ parameter for $K^0 - {\bar K}^0$ mixing in a dual 5-dimensional holographic QCD model. We perform, in the chiral limit, computations of the relevant four-point current-current…

I : Chiral Perturbation Theory is introduced and its applications to semileptonic and nonleptonic kaon decays are discussed. II: The method of large $N_c$ is used to calculate $K\to\pi\pi$ nonleptonic matrix elements, in particular the…

We present new results for the amplitude $A_2$ for a kaon to decay into two pions with isospin $I=2$: Re$A_2 = 1.50(4)_\mathrm{stat}(14)_\mathrm{syst}\times 10^{-8}$ GeV; Im$A_2 = -6.99(20)_\mathrm{stat}(84)_\mathrm{syst}\times 10^{-13}$…

The low energy dynamics of QCD is investigated with special attention paid to the matching between QCD and chiral perturbation theory(ChPT), and also to some useful algebraic chiral operator relations which survive even when we include…

The $\Delta I=1/2$ rule and direct CP violation $\epsilon'/\epsilon$ in kaon decays are studied within the framework of the effective Hamiltonian approach in conjunction with generalized factorization for hadronic matrix elements.

This article gives details of our proposal to replace ordinary chiral $SU(3)_L\times SU(3)_R$ perturbation theory $\chi$PT$_3$ by 3-flavor chiral-scale perturbation theory $\chi$PT$_\sigma$. In $\chi$PT$_\sigma$, amplitudes are expanded at…

The Delta I = 3/2 K to Pi Pi decay amplitude is calculated on RBC/UKQCD 32^3 x 64, L_s=32 dynamical lattices with 2+1 flavors of domain wall fermions using the DSDR and Iwasaki gauge action. The calculation is performed with a single pion…

We present our results for the on-shell Delta I = 3/2 kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to 1/a = 1.31 GeV in the quenched approximation. The on-shell…

The \Delta I = 3/2 K to pi pi decay amplitude is calculated on RBC/UKQCD 32^3 times 64, L_s=32 dynamical lattices with 2+1 flavours of domain wall fermions using the Dislocation Suppressing Determinant Ratio and Iwasaki gauge action. The…