Electromagnetic corrections in eta --> 3 pi decays

Abstract

We re-evaluate the electromagnetic corrections to eta --> 3 pi decays at next-to-leading order in the chiral expansion, arguing that effects of order e^2(m_u-m_d) disregarded so far are not negligible compared to other contributions of order e^2 times a light quark mass. Despite the appearance of the Coulomb pole in eta --> pi+ pi- pi0 and cusps in eta --> 3 pi0, the overall corrections remain small.

21 pages, 11 figures; references updated, version published in EPJC

References in corpus (14)

• Chiral perturbation theory
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Cusps in K --> 3 pi decays
• Effects of S-wave thresholds
• Radiative corrections in K --> 3 pi decays
• Cusps in K_L --> 3 pi decays
• Determination of the Dalitz plot parameter alpha for the decay eta->3pi^0 with the Crystal Ball at MAMI-B
• Matching Chiral Perturbation Theory and the Dispersive Representation of the Scalar Kpi Form Factor
• K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2
• Measurement of the Slope Parameter for the eta->3pi0 Decay in the pp->pp eta Reaction
• Soft-photon corrections in multi-body meson decays
• Detailed Study of the KL -> 3pi0 Dalitz Plot
• Electromagnetic low-energy constants in ChPT
• A note on the determination of light quark masses

Cited by in corpus (48)

• Review of lattice results concerning low energy particle physics
• Threshold cusps and triangle singularities in hadronic reactions
• Lattice QCD at the physical point: Simulation and analysis details
• Light Hadron Masses from Lattice QCD
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• Chiral expansions of the pi0 lifetime
• Analytical dispersive construction of $\eta \to 3\pi$ amplitude: First order in isospin breaking
• 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)
• Three-body Final State Interaction in $\eta \to 3\pi$
• Coupled-channel approach in hadron-hadron scattering
• Isospin violation in low-energy pion-nucleon scattering revisited
• The decay $\eta \to 3\pi$: study of the Dalitz plot and extraction of the quark mass ratio $Q$
• Rescattering effects in eta {\to} 3pi decays
• Extended chiral Khuri-Treiman formalism for $\eta \to 3\pi$ and the role of the $a_0(980)$, $f_0(980)$ resonances
• Novel approaches in Hadron Spectroscopy
• Measurement of the Matrix Elements for the Decays $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $\eta /{\eta }^{\prime }\to {\pi }^0{\pi }^0{\pi }^0$
• The cusp effect in eta' --> eta pi pi decays
• Three-body final state interaction in $\eta \to 3\pi$ updated
• Dispersion relations for ${\eta }^{\prime }\to \eta \pi \pi$
• Measurement of the eta->3pi0 Dalitz Plot Distribution with the WASA Detector at COSY
• Extracting $\pi \pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions
• Measurement of the $\eta \to 3{\pi }^0$ slope parameter $\alpha$ with the KLOE detector
• Measurement of the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ Dalitz plot distribution
• Quark-mass dependence in $\omega \to 3\pi$ decays
• What can we learn about light-meson interactions at electron-positron colliders?
• Solving integral equations in $\eta \to 3\pi$
• Patterns of CP violation from mirror symmetry breaking in the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ Dalitz plot
• An overview of $\eta$ and ${\eta }^{\prime }$ decays at BESIII
• $\eta$ and ${\eta }^{\prime }$ Physics at BES-III
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Patterns of $C$- and $CP$-violation in hadronic $\eta$ and ${\eta }^{\prime }$ three-body decays
• The mass of the two lightest quarks
• eta and eta' Physics at MAMI
• 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
• Isospin-Breaking quark condensates in Chiral Perturbation Theory
• Constraints on low energy QCD parameters from $\eta \to 3\pi$ and $\pi \pi$ scattering
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Evidence for the Cusp Effect in ${\eta }^{\prime }$ Decays into $\eta {\pi }^0{\pi }^0$
• Status of chiral perturbation theory for light mesons
• Study of $\eta$-meson Decays at KLOE/KLOE-2
• Constraints on 3-flavor QCD order parameters from eta to pi+pi-pi0 decay width
• Eta --> 3 pi and quark masses
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• Electromagnetic effects in eta --> 3 pi
• Role of electromagnetic corrections in the $\pi \pi$ distributions of ${\psi }^{\prime }\to J/\psi \pi \pi$
• Novel method for determining the light quark mass ratio using ${\eta }^{\prime }\to \eta \pi \pi$ decays