Radiative corrections in K --> 3 pi decays

Abstract

We investigate radiative corrections to K --> 3 pi decays. In particular, we extend the non-relativistic framework developed recently to include real and virtual photons and show that, in a well-defined power counting scheme, the results reproduce corrections obtained in the relativistic calculation. Real photons are included exactly, beyond the soft-photon approximation, and we compare the result with the latter. The singularities generated by pionium near threshold are investigated, and a region is identified where standard perturbation theory in the fine structure constant alpha may be applied. We expect that the formulae provided allow one to extract S-wave pi pi scattering lengths from the cusp effect in these decays with high precision.

57 pages, 17 figures

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Cited by in corpus (41)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Kaon Decays in the Standard Model
• Threshold cusps and triangle singularities in hadronic reactions
• Roy-Steiner-equation analysis of pion-nucleon scattering
• Electromagnetic corrections in eta --> 3 pi decays
• Determination of the S-wave pi pi scattering lengths from a study of K+- -> pi+- pi0 pi0 decays
• Isospin breaking in Kl4 decays
• Experiments with K-Meson Decays
• Isospin breaking in the pion-nucleon scattering lengths
• Isospin violation in low-energy pion-nucleon scattering revisited
• Rescattering effects in eta {\to} 3pi decays
• Cusps in K --> 3pi decays: a theoretical framework
• The branching ratio $\omega \to {\pi }^{+}{\pi }^{-}$ revisited
• 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
• Extracting $\pi \pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions
• Predictions for the cusp in eta->3pi0 decay
• On the three-particle analog of the Lellouch-Lüscher formula
• Radiative corrections in K --> pi l+ l- decays
• Solving integral equations in $\eta \to 3\pi$
• What can we learn about light-meson interactions at electron-positron colliders?
• Chiral corrections to ${\pi }^{-}\gamma \to 3\pi$ processes at low energies
• Hadronic Atoms
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Empirical parameterization of the K+- -> pi+- pi0 pi0 decay Dalitz plot
• 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
• Radiative corrections in $K_{e4}$ decay
• Evidence for the Cusp Effect in ${\eta }^{\prime }$ Decays into $\eta {\pi }^0{\pi }^0$
• Pion electroproduction in a nonrelativistic theory
• Pion photoproduction in a nonrelativistic theory
• Final state interaction in kaons decays
• Feasibility of perturbative generation of bound-states from resonances or virtual states
• Eta --> 3 pi and quark masses
• DAFNE and KLOE-2
• Status of chiral perturbation theory
• Cusps in eta' --> eta pi 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