${\pi }^0$-$\eta$-${\eta }^{\prime }$ mixing from $V\to P\gamma$ and $P\to V\gamma$ decays

Abstract

An enhanced phenomenological model that includes isospin-symmetry breaking is presented in this letter. The model is then used in a number of statistical fits to the most recent experimental data for the radiative transitions $VP\gamma$ ($V=\rho$, $K^{\ast }$, $\omega$, $\varphi$ and $P=\pi$, $K$, $\eta$, ${\eta }^{\prime }$) and estimations for the mixing angles amongst the three pseudoscalar states with vanishing third-component of isospin are obtained. The quality of the performed fits is good, e.g. ${\chi }_{\text{min}}^2/\text{d.o.f}=1.9$. The current experimental uncertainties allow for isospin symmetry violations with a confidence level of approximately $2.5\sigma$.

arXiv comment10 pages, 3 tables

References in corpus (26)

• Mixing and Decay Constants of Pseudoscalar Mesons
• Quark structure of pseudoscalar mesons
• Mixing and Decay Constants of Pseudoscalar Mesons: The Sequel
• Large N_c in chiral perturbation theory
• On the 1/N expansion in chiral perturbation theory
• Phenomenological Evidence for the Gluon Content of $\eta$ and ${\eta }^{\prime }$
• Study of the eta-eta' system in the two mixing angle scheme
• Effective Hadron Dynamics: From Meson Masses to the Proton Spin Puzzle
• The $\eta -{\eta }^{\prime }$ Mixing Angle Revisited
• A global fit to determine the pseudoscalar mixing angle and the gluonium content of the eta' meson
• eta - eta prime Mixing -From electromagnetic transitions to weak decays of charm and beauty hadrons
• Radiative Decays, Nonet Symmetry and SU(3) Breaking
• Mixing of eta-eta' Mesons in J/psi Decays into a Vector and a Pseudoscalar Meson
• The ${\eta }^{\prime }$ transition form factor from space- and time-like experimental data
• ηand η' transition form factors from rational approximants
• The eta transition form factor from space- and time-like experimental data
• Implications of eta-etaprime mixing for the decay eta->3 pi
• Predictions on the second-class current decays ${\tau }^{-}\to {\pi }^{-}{\eta }^{(\prime )}{\nu }_{\tau }$
• Mixing of Pseudoscalar Mesons
• Radiative VPgamma transitions and eta-eta' mixing
• Phenomenological evidence for the energy dependence of the $\eta -{\eta }^{\prime }$ mixing angle
• Isospin symmetry breaking through pi^0 - eta -eta' mixing
• J/psi->VP decays and the quark and gluon content of the eta and eta'
• Interpolation Formulas for the Eta-Gamma and Eta'-Gamma Transition Form Factors
• $\eta$-${\eta }^{\prime }$ Mixing in Large-$N_c$ Chiral Perturbation Theory
• Mixing and decay constants of pseudoscalar mesons: Octet-singlet vs. quark flavor basis

Cited by in corpus (14)

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• A theoretical analysis of the doubly radiative decays ${\eta }^{(\prime )}\to {\pi }^0\gamma \gamma$ and ${\eta }^{\prime }\to \eta \gamma \gamma$
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• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• New-physics signatures via $CP$ violation in ${\eta }^{(\prime )}\to {\pi }^0{\mu }^{+}{\mu }^{-}$ and ${\eta }^{\prime }\to \eta {\mu }^{+}{\mu }^{-}$ decays
• Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball
• State mixing and masses of the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons from $n_f=1+1+1$ lattice QCD+QED
• Role of the $\rho (1450)$ in low-energy observables from an analysis in the meson dominance approach
• Improved measurement of the branching fraction of $h_c\to \gamma {\eta }^{\prime }/\eta$ and search for $h_c\to \gamma {\pi }^0$
• Leptophobic dark photon interpretation of the ${\eta }^{\left(\prime \right)}\to {\pi }^0\left(\eta \right)\gamma \gamma$ puzzle
• QCD analysis of the $P$-wave charmonium electromagnetic Dalitz decays $h_c\to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$
• Contribution of exclusive $({\pi }^0{\pi }^0,{\pi }^0\eta ,\eta \eta )\gamma$ channels to the leading order HVP of the muon $g-2$
• Improved measurement of $\eta /{\eta }^{\prime }$ mixing in $B_{(s)}^0\to J/\psi {\eta }^{(\prime )}$ decays
• ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay induced by QED one-loop effects