Rare kaon decays revisited

Abstract

We present an updated discussion of K → πll decays in a combined framework of chiral perturbation theory and Large-Nc QCD, which assumes the dominance of a minimal narrow resonance structure in the invariant mass dependence of thell pair. The proposed picture reproduces very well, both the experimental K + → π + e + e − decay rate and the invariant e + e − mass spectrum. The predicted Br(KS → π 0 e + e − ) is, within errors, consistent with the recently reported result from the NA48 collaboration. Predictions for the K → π µ + µ − modes are also obtained. We find that the resulting interference between the direct and indirect CP-violation amplitudes in KL → π 0 e + e − is constructive.

Precise measurement of the K±→π±e+e− decay

“…The obtained |f 0 |, a + and b + are in agreement with the only previous measurement [8]. The obtained values ofw and β are in fair agreement with the fit of the data points [8] performed by the authors of [4] (the value of M ρ = 0.77549 GeV/c 2 [14] is used in our fit; using M ρ = 0.7711 GeV/c 2 as in [4] leads to a central value of β = 3.27, which improves agreement with [4]). The measured parameter M a is consistent with the nominal mass of the a 0 (980) resonance, while M ρ is a few % lower than the nominal ρ(770) mass [14].…”

“…Combined framework of ChPT and large-N c QCD [4]: the form factor is parameterized as W (z) ≡ W (w, β, z) with free parameters (w, β), see also the Appendix. …”

“…The paper [4] that formulates one of the considered models does not contain the full definition for the form factor f V (z): the function χ(z) appearing in the Eq. …”

“…The flavour-changing neutral current process K ± → π ± e + e − , induced at one-loop level in the Standard Model and highly suppressed by the GIM mechanism [1], is of particular interest. The K ± → π ± l + l − processes have been described by the Chiral Perturbation Theory (ChPT) [2]; several models predicting the form factor characterizing the dilepton invariant mass spectrum, and thus the decay rate, have been proposed [3,4,5].…”

Phenomenology of a very light scalar (100 MeV < m h < 10 GeV) mixing with the SM Higgs

“…The NA48/2 collaboration has measured Br(K ± → π ± µ + µ − ) = (9.62±0.25)×10 −8 [60], in good agreement with the theoretical predictions (8.7±2.8)×10 −8 and (12±3)×10 −8 [61,62]. To derive limits on sin 2 ρ we assume that a πµµ vertex is reconstructed if the h → µ + µ − .…”