The Decays $K\to \pi {\ell }^{+}{\ell }^{-}$ beyond Leading Order in the Chiral Expansion

Abstract

We present a model-independent analysis of $K^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$ and $K_S\to {\pi }^0{\ell }^{+}{\ell }^{-}$ decays, including $K\to 3\pi$ unitarity corrections and a general decomposition of the dispersive amplitude. From the existing data on $K^{+}\to {\pi }^{+}{e}^{+}{e}^{-}$ we predict the ratio $R=B(K^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-})/B(K^{+}\to {\pi }^{+}{e}^{+}{e}^{-})$ to be larger than 0.23, in slight disagreement with the recent measurement $R=0.167\pm 0.036$. Consequences for the $K^{\pm }\to {\pi }^{\pm }{e}^{+}{e}^{-}$ charge asymmetries and for the $K_L\to {\pi }^0{e}^{+}{e}^{-}$ mode are also discussed.

18 pages, latex

Cited by in corpus (73)

• Secluded U(1) below the weak scale
• Kaon Decays in the Standard Model
• Flavor Physics in the Quark Sector
• Constraining Light Dark Matter with Low-Energy e+e- Colliders
• Rare and CP-Violating K and B Decays in the Littlest Higgs Model with T-Parity
• Muon g-2, Rare Kaon Decays, and Parity Violation from Dark Bosons
• Light-quark Loops in K->pi nu nu
• Search for the Rare Decay KL --> pi0 ee
• B, D and K decays
• FCNC portals to the dark sector
• Extracting short-distance physics from K_{L,S} -> pi0 e+ e- decays
• Constraints on scalar leptoquarks from lepton and kaon physics
• KL to pi0 e+ e- and KL to pi0 mu+ mu- : A binary star on the stage of flavor physics
• Rare Kaon Decays Revisited
• Lepton flavor (universality) violation in rare kaon decays
• Patterns of Flavour Violation in the Presence of a Fourth Generation of Quarks and Leptons
• New measurement of the K+- --> pi+-mu+mu- decay
• Precise measurement of the K+- --> pi+-e+e- decay
• A new measurement of the properties of the rare decay K -> pi+ e+ e-
• Rare Kaon Decays on the Lattice
• Observation of the rare decay Ks->pi0e+e-
• Observation of the rare decay K_S -> pi^0mu^+mu^-
• Prospects for Measurements with Strange Hadrons at LHCb
• Implications of a new particle from the HyperCP data on Σ^+ \to p μ^+ μ^-
• First exploratory calculation of the long-distance contributions to the rare kaon decays $K\to \pi {\ell }^{+}{\ell }^{-}$
• Prospects for a lattice computation of rare kaon decay amplitudes: $K\to \pi {\ell }^{+}{\ell }^{-}$ decays
• Observation of the Decay K- -> pi- mu+ mu- and Measurements of the Branching Ratios for K+/- -> pi+/- mu+ mu-
• Anatomy of kaon decays and prospects for lepton flavour universality violation
• Light vectors coupled to bosonic currents
• Searching for an invisible A' vector boson with DarkLight
• Developments in Rare Kaon Decay Physics
• Radiative corrections in K --> pi l+ l- decays
• Forward-backward Asymmetry in $K^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$
• Constraints on the new particle in ${\Sigma }^{+}\to p{\mu }^{+}{\mu }^{-}$
• Particle physics origin of the 5 MeV bump in the reactor antineutrino spectrum?
• The s ---> d gamma decay in and beyond the Standard Model
• The strange side of LHCb
• New physics in $s\to d$ semileptonic transitions: rare hyperon vs. kaon decays
• Unitarity corrections to K+ -> pi+ gamma l+l-
• On the amplitudes for the CP-conserving $K^{\pm }(K_S)\to {\pi }^{\pm }({\pi }^0){\ell }^{+}{\ell }^{-}$ rare decay modes
• Light, Long-Lived $B-L$ Gauge and Higgs Bosons at the DUNE Near Detector
• A measurement of the $K^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$ decay
• Rank-One Flavor Violation and B-meson anomalies
• Muon Decay Asymmetries from $K_L^0\to {\pi }^0{\mu }^{+}{\mu }^{-}$ Decays
• Beyond the Standard Model prospects for kaon physics at future experiments
• Running mass of the rho0 meson's implication for the dilepton mass spectrum and the mu+mu-/e+e- branching ratio in the K+ --> pi+l+l- decays
• Electromagnetic penguin operators and direct CP violation in K --> pi l^+ l^-
• Correlating New Physics Effects in Semileptonic $\Delta C=1$ and $\Delta S=1$ Processes
• Long-distance contribution to the forward-backward asymmetry in decays K+ --> pi+ l+ l-
• Precise determination of the branching ratio of the neutral-pion Dalitz decay
• $C$ and $CP$ violation in effective field theories
• $K\to \pi {\ell }^{+}{\ell }^{-}$ form factor in the Large-N${}_c$ and cut-off regularization method
• Closing in on the radiative weak chiral couplings
• SUSY contributions to the charge asymmetry in K^+- -> pi^+- l^+ l^- decays
• Tests of the Standard Model Using Muon Polarization Asymmetries in Kaon Decays
• Theory review on rare K decays: Standard Model and beyond
• Long-distance weak annihilation contribution to the $B^{\pm }\to ({\pi }^{\pm },K^{\pm }){\ell }^{+}{\ell }^{-}$ decays
• Recent progress in applying lattice QCD to kaon physics
• Studying the scale and q^2 dependence of K^+-->pi^+e^+e^- decay
• LAB observables for the muon polarization in K^+ --> π^+ μ^+ μ^-
• $(g-2{)}_{\mu }$ Versus $K\to \pi +E_{miss}$ Induced by the $(B-L{)}_{23}$ Boson
• ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$ decays within the standard model and beyond
• Correlations of $C$ and $CP$ violation in $\eta \to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$
• Theoretical overview of kaon decays
• Long-distance contribution to the muon-polarization asymmetry in K^+\to π^+ μμ
• On the electron-positron energy asymmetry in K_L --> pi0 e+ e-
• Rare Kaon Decays
• Radiative modes $K^{+}\to {\pi }^{+}{\gamma }^{\ast }{\gamma }^{(\ast )}$ and the $K^{+}\to {\pi }^{+}4e$ decay
• About one long-range contribution to K+ -> pi+ l+ l- decays
• Possible manifestation of the 2p pionium in particle physics processes
• Chiral Phenomenological Relations between Rates of Rare Radiative Decay of Kaon to Pion and leptons and the meson Formfactors
• $K\to \pi {\gamma }^{\ast }{\gamma }^{\ast }$ transitions at leading order and beyond
• CPV tests with rare kaon decays