$K\rightarrow \pi\pi e^+e^-$ decays and chiral low-energy constants

Abstract

The branching ratios of the measured decay K L → π + π − e + e − and of the still unmeasured decay

K +→π + π 0 e + e −: a novel short-distance probe

“…The numbers in Eq. (1.3) were found by numerically integrating over the phase space using arbitrary kinematical variables [18]. One of the conclusions of the present work is that an improvement can be obtained by studying the Dalitz plot with a specific set of kinematical variables, namely T * c and E * γ (the kinetic energies of the charged pion and the photon, respectively, in the kaon rest frame) and the dilepton invariant mass q 2 .…”

“…The expressions for M(K + → π + π 0 ) and the direct emission piece (electric and magnetic) can be systematically computed using Chiral Perturbation Theory (ChPT) [18]. To leading order and neglecting isospin-violating effects they read, 1…”

“…These different contributions were studied in considerable detail in Ref. [18]. In particular, one finds the following rate for the branching ratios: These numbers clarify how hard one must work to extract dynamical information from this decay: much like with K ± → π ± π 0 γ, one needs to fight the dominant Bremsstrahlung contribution.…”

Standard Model prediction and new physics tests for $ {D^0}\to h_1^{+}h_2^{-}{\ell^{+}}{\ell^{-}}\left( {h=\pi, K;\ell =e,\mu } \right) $

“…Similar contributions have been studied in the B → K * (Kπ)l + l − decay [24]. The situation is in sharp contrast with what one encounters in kaon 4-body decays [25][26][27] at least in two aspects: (i) in Ke4 decays the energy range is always far below resonance thresholds. As a result, Bremsstrahlung is overwhelmingly dominant; and (ii) additionally, the kaon direct emission contribution can be estimated in chiral perturbation theory.…”

Different approaches to calculate the $$K^{\pm }\rightarrow \pi ^{\pm }\pi ^0e^+e^-$$ K ± → π ± π 0 e + e - decay width

“…1). The solid theoretical base for this decay was developed in [7], where the DE contribution was calculated up to the next-to-leading order (up to O( p 4 )) in ChPT.…”