Cusps in K_L --> 3 pi decays

Abstract

The pion mass difference generates a pronounced cusp in K --> 3 pi decays, the strength of which is related to the pi pi S-wave scattering lengths. We apply an effective field theory framework developed earlier to evaluate the amplitudes for K_L --> 3 pi decays in a systematic manner, where the strictures imposed by analyticity and unitarity are respected automatically. The amplitudes for the decay eta --> 3 pi are also given.

15 pages, 3 figures, uses Elsevier style

References in corpus (27)

• ππscattering
• Spectrum and decays of kaonic hydrogen
• Ground-state energy of pionic hydrogen to one loop
• The pi pi S-wave scattering lengths
• Cusps in K --> 3 pi decays
• Virtual Photons in Low Energy pi-pi Scattering
• Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to $\pi \pi$ scattering
• High statistics measurement of Ke4 decay properties
• Determination of the a0-a2 pion scattering length from K->pi+ pi0 pi0 decay
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Pion-pion scattering and the K->3pi decay amplitudes
• Analysis and interpretation of new low-energy Pi-Pi scattering data
• Observation of a cusp-like structure in the pizero-pizero invariant mass distribution from K+- ==> pi+- pizero pizero decay and determination of the pi-pi scattering lengths
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• Decays of the pi+ pi- atom
• pi(-)p atom in ChPT: strong energy-level shift
• On the Lifetime of the pi+pi- Atom
• Numerical analysis of the pi+pi- atom lifetime in ChPT
• K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2
• The pion-nucleon scattering lengths from pionic deuterium
• Decay widths and energy shifts of pi pi and pi K atoms
• Isospin Breaking in $K\to 3\pi$ Decays III: Bremsstrahlung and Fit to Experiment
• Partial wave analysis of pbar-p to Lambdabar-Lambda
• Spectra and decays of pi pi and pi K atoms
• Isospin Breaking in $K\to 3\pi$ Decays II: Radiative Corrections
• Electromagnetic corrections to final state interactions in $K\to 3\pi$ decays

Cited by in corpus (39)

• Kaon Decays in the Standard Model
• Threshold cusps and triangle singularities in hadronic reactions
• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Resonance properties from the finite-volume energy spectrum
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• Electromagnetic corrections in eta --> 3 pi decays
• Radiative corrections in K --> 3 pi decays
• Analytical dispersive construction of $\eta \to 3\pi$ amplitude: First order in isospin breaking
• Isospin breaking in Kl4 decays
• Measurement of the Slope Parameter $\alpha$ for the $\eta \to 3{\pi }^0$ decay with the Crystal Ball detector at the Mainz Microtron (MAMI-C)
• Rescattering effects in eta {\to} 3pi decays
• Cusps in K --> 3pi decays: a theoretical framework
• Determination of the Dalitz plot parameter alpha for the decay eta->3pi^0 with the Crystal Ball at MAMI-B
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• The cusp effect in eta' --> eta pi pi decays
• Chiral Perturbation Theory: Introduction and Recent Results in the One-Nucleon Sector
• Dispersion relations for ${\eta }^{\prime }\to \eta \pi \pi$
• Measurement of the eta->3pi0 Dalitz Plot Distribution with the WASA Detector at COSY
• Predictions for the cusp in eta->3pi0 decay
• Extracting $\pi \pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions
• Visible narrow cusp structure in ${\Lambda }_c^{+}\to p{K}^{-}{\pi }^{+}$ enhanced by triangle singularity
• On the three-particle analog of the Lellouch-Lüscher formula
• Extraction of $ND$ scattering lengths from the ${\Lambda }_b\to {\pi }^{-}p{D}^0$ decay and properties of the ${\Sigma }_c(2800{)}^{+}$
• High-statistics measurement of the eta->3pi^0 decay at the Mainz Microtron
• Hadronic Atoms
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Dispersive representation of K -> 3 pi amplitudes and cusps
• The mass of the two lightest quarks
• Precision measurement of the matrix elements for $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $\eta \to {\pi }^0{\pi }^0{\pi }^0$ decays
• Measurement of the decay ${\eta }^{\prime }\to {\pi }^0{\pi }^0\eta$ at MAMI
• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory
• Evidence for the Cusp Effect in ${\eta }^{\prime }$ Decays into $\eta {\pi }^0{\pi }^0$
• Analysis of discrepancies in Dalitz plot parameters in eta to 3 pion decay
• Pion electroproduction in a nonrelativistic theory
• Pion photoproduction in a nonrelativistic theory
• Eta --> 3 pi and quark masses
• Electromagnetic effects in eta --> 3 pi
• Role of electromagnetic corrections in the $\pi \pi$ distributions of ${\psi }^{\prime }\to J/\psi \pi \pi$