Cusps in K --> 3 pi decays

Abstract

The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave pi pi scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.

14 pages, 3 figures, uses Elsevier style

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Cited by in corpus (75)

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• Threshold cusps and triangle singularities in hadronic reactions
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• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Resonance properties from the finite-volume energy spectrum
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• Chiral perturbation theory
• Search for direct CP violating charge asymmetries in $K^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ and $K^{\pm }\to {\pi }^{\pm }{\pi }^0{\pi }^0$ decays
• Interpretation of structure in the di-$J/\psi$ spectrum
• Effects of S-wave thresholds
• Electromagnetic corrections in eta --> 3 pi decays
• Radiative corrections in K --> 3 pi decays
• Determination of the S-wave pi pi scattering lengths from a study of K+- -> pi+- pi0 pi0 decays
• Matrix elements of unstable states
• Analytical dispersive construction of $\eta \to 3\pi$ amplitude: First order in isospin breaking
• Isospin breaking in Kl4 decays
• Experiments with K-Meson Decays
• Cusps in K_L --> 3 pi decays
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Rescattering effects in eta {\to} 3pi decays
• Cusps in K --> 3pi decays: a theoretical framework
• Determination of $\pi \pi$ scattering lengths from measurement of ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Measurement of the Matrix Elements for the Decays $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $\eta /{\eta }^{\prime }\to {\pi }^0{\pi }^0{\pi }^0$
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Chiral Perturbation Theory: Introduction and Recent Results in the One-Nucleon Sector
• The cusp effect in eta' --> eta pi pi decays
• Dispersion relations for ${\eta }^{\prime }\to \eta \pi \pi$
• K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2
• Measurement of the eta->3pi0 Dalitz Plot Distribution with the WASA Detector at COSY
• Finite volume corrections to the binding energy of the X(3872)
• The $B\to K^{\ast }$ form factors on the lattice
• Extracting $\pi \pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions
• Predictions for the cusp in eta->3pi0 decay
• Visible narrow cusp structure in ${\Lambda }_c^{+}\to p{K}^{-}{\pi }^{+}$ enhanced by triangle singularity
• Soft-photon corrections in multi-body meson decays
• Dispersion representations and anomalous singularities of the triangle diagram
• Considerations on the Schmid theorem for triangle singularities
• Measurement of the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ Dalitz plot distribution
• Topological susceptibility on the lattice and the three-flavour quark condensate
• On the three-particle analog of the Lellouch-Lüscher formula
• What can we learn about light-meson interactions at electron-positron colliders?
• Measurement of the matrix elements for the decays ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to \eta {\pi }^0{\pi }^0$
• Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
• Particle-dimer approach for the Roper resonance in a finite volume
• Electromagnetic corrections to final state interactions in $K\to 3\pi$ decays
• Determining the chiral condensate from the distribution of the winding number beyond topological susceptibility
• Extraction of $ND$ scattering lengths from the ${\Lambda }_b\to {\pi }^{-}p{D}^0$ decay and properties of the ${\Sigma }_c(2800{)}^{+}$
• Hadronic Atoms
• Nucleon in a periodic magnetic field
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Isospin breaking in the phases of the Ke4 form factors
• Empirical parameterization of the K+- -> pi+- pi0 pi0 decay Dalitz plot
• Resonances in an external field: the 1+1 dimensional case
• The mass of the two lightest quarks
• Dispersive representation of K -> 3 pi amplitudes and cusps
• Measurement of the decay ${\eta }^{\prime }\to {\pi }^0{\pi }^0\eta$ at MAMI
• Effects of Final State Interactions on Landau Singularities
• Nucleon in a periodic magnetic field: Finite-volume aspects
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Evidence for the Cusp Effect in ${\eta }^{\prime }$ Decays into $\eta {\pi }^0{\pi }^0$
• The isospin symmetry breaking effects in $K_{e4}$ decays
• The electromagnetic effects in $K_{e4}$ decay
• Pion photoproduction in a nonrelativistic theory
• Pion electroproduction in a nonrelativistic theory
• Final state interaction in kaons decays
• Status of chiral perturbation theory
• Analytic Properties of Triangle Feynman Diagrams in Quantum Field Theory
• DAFNE and KLOE-2
• Cusps in eta' --> eta pi pi decays
• Measuring the a0-a2 pion scattering lengths through K to 3 pi decays
• Role of electromagnetic corrections in the $\pi \pi$ distributions of ${\psi }^{\prime }\to J/\psi \pi \pi$
• Electromagnetic effects in eta --> 3 pi