Rare kaon decays in the 1/N c-expansion

The average action is a new tool for investigating spontaneous symmetry breaking in elementary particle theory and statistical mechanics beyond the validity of standard perturbation theory. The aim of this work is to provide techniques for an investigation of models with fermions and scalars by means of the average potential. In the phase with spontaneous symmetry breaking, the inner region of the average potential becomes flat as the averaging extends over infinite volume and the average potential becomes flat as the averaging extends over infinite volume and the average potential approaches the convex effective potential. Fermion fluctuations in this region necessitate a calculation of the fermion determinant in a spin wave background. We also compute the fermionic contribution to the wave function renormalization in the scalar kinetic term.     

Two-loop calculations in QCD and the ΔI = 1/2 rule in non-leptonic weak decays

Two-gluon-exchange corrections to the effective operators of the Wilson expansion of the product of two currents have been calculated in order to find the g⁴-term of the γ-function. Next to leading order contribution increases the ratio of ΔI = 1/2 to ΔI = 1/2, 3/2 amplitudes, obtained from leading order.     

Nonleptonic kaon decays and nonperturbative QCD effects in chiral-bag model

The instanton induced-term, proposed by Konishi and Ranfone [1] was introduced in the chiral-bag model based analysis ofK→2π decays. Almost perfect fit of the experimental data was possible with the induced-term coefficient \(\tilde C_1 \cong 1,4\) . However, this conclusion, which is appreciably larger than the rough theoretical estimate [1] (which was \(\tilde C_1 = 0.15\) m _s /μ) depends on the approximation used in the theoretical approach.     

Recent results on kaon decays by the NA48/2 experiment at CERN

The NA48/2 experiment reports the first observation of the rare decay K^± → π^±π⁰e⁺e^?, based on about 2000 candidates from 2003 data. The preliminary branching ratio in the full kinematic region is \(\mathcal {B}(K^{\pm } \to \pi ^{\pm }\pi ^{0}e^{+}e^{-})=(4.06\pm 0.17)\cdot 10^{-6}\). A sample of 4.687 × 10⁶\(K^{\pm }\to \pi ^{\pm }{\pi ^{0}_{D}}\) events collected in 2003/4 is analyzed to search for the dark photon (\(A^{\prime }\)) via the decay chain K^± → π^±π⁰, \(\pi ^{0}\to \gamma A^{\prime }\), \(A^{\prime }\to e^{+}e^{-}\). No signal is observed, limits in the plane mixing parameter ε² versus its mass \(m_{A^{\prime }}\) are reported.     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

A comment on octet enhancement in the ΔI=1/2 rule

We apply vacuum background fields method to correct the coefficient functions of theO ₊ andO _? operators in ΔS=1 effective weak Hamiltonian responsible forK→2π decays. The additional relative octet enhancement factor of 2–3 is obtained by accounting for the gluon condensate corrections if the scale parameterπ ²x is set below 1 GeV₂.     

Comments on CP, T and CPT violation in neutral kaon decays

We comment on CP, T and CPT violation in the light of interesting new data from the CPLEAR and KTeV Collaborations on neutral kaon decay asymmetries. Other recent data from the CPLEAR experiment, constraining possible violations of CPT and the ΔS=ΔQ rule, exclude the possibility that the semileptonic-decay asymmetry A_T measured by CPLEAR could be solely due to CPT violation, confirming that their data constitute direct evidence for T violation. The CP-violating asymmetry in K_L→e⁻e⁺π⁻π⁺ recently measured by the KTeV Collaboration does not by itself provide direct evidence for T violation, but we use it to place new bounds on CPT violation.     

Electromagnetic final-state interactions in the leptonic decays of the neutral kaon (I) Kℓ3 mode

We present a calculation of the Coulomb final-state interaction effects in the decays K_L → π ℓ^±V_ℓ. Specifically we investigate the charge asymmetry and the transverse polarization of the charged lepton. We consider the effects of possible ΔQ = −ΔS amplitudes and the q² dependence of the form factors. The variation of the effects over the Dalitz plot is discussed and many numerical results are given.     

A measurement of the KL-KS mass difference from the charge asymmetry in semi-leptonic kaon decays

The change asymmetry in semi-leptonic kaon decays has been measured as a function of the kaon lifetime. High statistics data of K_e3⁰ and K_μ3⁰ decay modes agree with each other and with the general expectation of the CP violation phenomenology together with the ΔS?ΔQ rule. The K_L-K_S mass difference obtained is Δm = (0.533 ± 0.004) × 10¹⁰ s^?1.