Off-shell Behavior of the $\pi -\eta$ Mixing Amplitude

Abstract

We extend a recent calculation of the momentum dependence of the $\rho -\omega$ mixing amplitude to the pseudoscalar sector. The $\pi -\eta$ mixing amplitude is calculated in a hadronic model where the mixing is driven by the neutron-proton mass difference. Closed-form analytic expressions are presented in terms of a few nucleon-meson parameters. The observed momentum dependence of the mixing amplitude is strong enough as to question earlier calculations of charge-symmetry-breaking observables based on the on-shell assumption. The momentum dependence of the $\pi -\eta$ amplitude is, however, practically identical to the one recently predicted for $\rho -\omega$ mixing. Hence, in this model, the ratio of pseudoscalar to vector mixing amplitudes is, to a good approximation, a constant solely determined from nucleon-meson coupling constants. Furthermore, by selecting these parameters in accordance with charge-symmetry-conserving data and SU(3)-flavor symmetry, we reproduce the momentum dependence of the $\pi -\eta$ mixing amplitude predicted from chiral perturbation theory. Alternatively, one can use chiral-perturbation-theory results to set stringent limits on the value of the $NN\eta$ coupling constant.

13 pages, Latex with Revtex, 3 postscript figures (not included) available on request, SCRI-030893

References in corpus (1)

• The Momentum Dependence of the $\rho -\omega$ Mixing Amplitude in a Hadronic Model

Cited by in corpus (25)

• Photo- and Electroproduction of Eta Mesons
• Constraints on the momentum dependence of rho-omega mixing
• A new $N^{\ast }(1675)$ resonance in the $\gamma N\to \eta N$ reaction
• $\eta$ photoproduction on the quasi-free nucleons in the chiral quark model
• Study of π^{-}p \to ηn at low energies in a chiral constituent quark model
• On the Coupling of the $\eta$ Meson to the Nucleon
• The $\eta NN$ coupling constant
• Comments on differential cross section of phi-meson photoproduction at threshold
• Photoproduction of phi meson off deuteron near threshold
• The Mixed-Isospin Vector Current Correlator in Chiral Perturbation Theory and QCD Sum Rules
• Two Model-Independent Results for the Momentum Dependence of Rho-Omega Mixing
• Quasifree Eta Photoproduction from Nuclei
• Pionic dispersion relations in the presence of a weak magnetic field
• Comparison of Chiral Perturbation Theory and QCD Sum Rule Results for Pseudoscalar Isoscalar-Isovector Mixing
• Isospin-Violating Meson-Nucleon Vertices as an Alternate Mechanism of Charge-Symmetry Breaking
• Pi- Eta Mixing from QCD Sum Rules
• An isotopic effect in phi photoproduction at a few GeV
• On eta-pi mixing close to the eta-Helium threshold
• Combined analysis of the ${\pi }^{-}p\to K^0\Lambda$, $\eta n$ reactions in a chiral quark model
• Tri-meson-mixing of $\pi$-$\eta$-${\eta }^{\prime }$ and $\rho$-$\omega$-$\varphi$ in the light-cone quark model
• Isospin mode splitting and mixing in asymmetric nuclear matter
• The Okamoto-Nolen-Schiffer anomaly without rho-omega mixing
• Nucleon-Nucleon interaction, charge symmetry breaking and renormalization
• ${\rho }^0-\omega$ mixing in the presence of a weak magnetic field
• $\pi$-$\eta$ mixing and charge symmetry violating NN potential in matter