Anomalous decay and scattering processes of the eta meson

Abstract

We amend a recent dispersive analysis of the anomalous $\eta$ decay process $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ by the effects of the $a_2$ tensor meson, the lowest-lying resonance that can contribute in the $\pi \eta$ system. While the net effects on the measured decay spectrum are small, they may be more pronounced for the analogous ${\eta }^{\prime }$ decay. There are nonnegligible consequences for the $\eta$ transition form factor, which is an important quantity for the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment. We predict total and differential cross sections, as well as a marked forward-backward asymmetry, for the crossed process $\gamma {\pi }^{-}\to {\pi }^{-}\eta$ that could be measured in Primakoff reactions in the future.

12 pages, 11 figures; v2 matches version published in EPJC

References in corpus (15)

• Big-Bang Nucleosynthesis
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Towards a data-driven analysis of hadronic light-by-light scattering
• Dispersive analysis of omega --> 3pi and phi --> 3pi decays
• Dispersive analysis of the pion transition form factor
• Revisiting γγ->π^+π^- at low energies
• MO analysis of the high statistics Belle results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ with chiral constraints
• Extracting the chiral anomaly from gamma pi --> pi pi
• Odd and Even Partial Waves of $\eta {\pi }^{-}$ and ${\eta }^{\prime }{\pi }^{-}$ in ${\pi }^{-}p\to {\eta }^{(\prime )}{\pi }^{-}p$ at $191\text{GeV}/c$
• Measurement of the charged-pion polarisability
• The cusp effect in eta' --> eta pi pi decays
• Cross sections for low-energy ${\pi }^{-}\gamma$ reactions
• Tensor meson exchange at low energies
• Measurement of Γ(η-> π^+π^-γ)/Γ(η-> π^+π^-π^0) with the KLOE Detector
• Chiral corrections to ${\pi }^{-}\gamma \to 3\pi$ processes at low energies

Cited by in corpus (25)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• Asymptotic behavior of meson transition form factors
• Effects of $Z_b$ states and bottom meson loops on ${\rm Y}(4S)\to {\rm Y}(1S,2S){\pi }^{+}{\pi }^{-}$ transitions
• Nature of the $Y(4260)$: A light-quark perspective
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Strong Interaction Physics at the Luminosity Frontier with 22 GeV Electrons at Jefferson Lab
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Dispersive analysis of the Primakoff reaction $\gamma K\to K\pi$
• The $\eta \to {\gamma }^{\ast }{\gamma }^{\ast }$ transition form factor and the hadronic light-by-light $\eta$-pole contribution to the muon $g-2$ from lattice QCD
• The semileptonic decays ${\eta }^{(\prime )}\to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$ in the standard model
• Isospin-conserving hadronic decay of the $D_{s1}(2460)$ into $D_s{\pi }^{+}{\pi }^{-}$
• $C$ and $CP$ violation in effective field theories
• Dispersive analysis of the isospin breaking in the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $X(3872)\to J/\psi {\pi }^{+}{\pi }^0{\pi }^{-}$ decays
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• Revisit of tensor-meson nonet in resonance chiral theory
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Chromopolarizability of charmonium and $\pi \pi$ final state interaction revisited
• $CP$ violation in ${\eta }^{(\prime )}\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• $\varphi (2170)$ decaying to $\varphi \pi \pi$ and $\varphi K\bar{K}$
• Tests of Three-Flavor Chiral Perturbation Theory
• ${\eta }^{{(}^{\prime })}\to {\pi }^{+}{\pi }^{-}{\gamma }^{(\ast )}$ in large-$N_c$ chiral perturbation theory
• Understanding large localized CP violation in $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ using dispersive methods