The decay $\eta \to 3\pi$: study of the Dalitz plot and extraction of the quark mass ratio $Q$

Abstract

The $\eta \to 3\pi$ amplitude is sensitive to the quark mass difference $m_u-m_d$ and offers a unique way to determine the quark mass ratio $Q^2\equiv (m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$ from experiment. We calculate the amplitude dispersively and fit the KLOE data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Our representation of the transition amplitude implies $Q=22.0\pm 0.7$.

5 pages, 1 figure, v2 = published version. Slightly shorter and with minor changes

References in corpus (4)

• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Rescattering effects in eta {\to} 3pi decays
• Measurement of the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ Dalitz plot distribution

Cited by in corpus (21)

• Kaon electromagnetic form factors in dispersion theory
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Novel approaches in Hadron Spectroscopy
• Multi-${\pi }^{+}$ systems in finite volume
• Modeling few-body resonances in finite volume
• Theoretical analysis of the $\gamma \gamma \to {\pi }^0\eta$ process
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• Visualizing resonances in finite volume
• Khuri-Treiman equations for $3\pi$ decays of particles with spin
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Analysis of rescattering effects in $3\pi$ final states
• Patterns of $C$- and $CP$-violation in hadronic $\eta$ and ${\eta }^{\prime }$ three-body decays
• Precision measurement of the matrix elements for $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $\eta \to {\pi }^0{\pi }^0{\pi }^0$ decays
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Ratios of the light quark masses: Cubic curve vs ellipse
• Khuri-Treiman analysis of $J/\psi \to {\pi }^{+}{\pi }^{-}{\pi }^0$
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• $a_1$ properties in hadronic tau decays
• Novel method for determining the light quark mass ratio using ${\eta }^{\prime }\to \eta \pi \pi$ decays
• Light Meson Physics at BESIII