dorsal/arxiv
View SchemaOff-shell Behavior of the $\pi\!-\!\eta$ Mixing Amplitude
| Authors | J. Piekarewicz |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9303005 |
| URL | https://arxiv.org/abs/nucl-th/9303005 |
| DOI | 10.1103/PhysRevC.48.1555 |
| Journal | Phys.Rev.C48:1555-1561,1993 |
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.
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"abstract": "We extend a recent calculation of the momentum dependence of the\n$\\rho-\\omega$ mixing amplitude to the pseudoscalar sector. The $\\pi\\!-\\!\\eta$\nmixing amplitude is calculated in a hadronic model where the mixing is driven\nby the neutron-proton mass difference. Closed-form analytic expressions are\npresented in terms of a few nucleon-meson parameters. The observed momentum\ndependence of the mixing amplitude is strong enough as to question earlier\ncalculations of charge-symmetry-breaking observables based on the on-shell\nassumption. The momentum dependence of the $\\pi\\!-\\!\\eta$ amplitude is,\nhowever, practically identical to the one recently predicted for $\\rho-\\omega$\nmixing. Hence, in this model, the ratio of pseudoscalar to vector mixing\namplitudes is, to a good approximation, a constant solely determined from\nnucleon-meson coupling constants. Furthermore, by selecting these parameters in\naccordance with charge-symmetry-conserving data and SU(3)-flavor symmetry, we\nreproduce the momentum dependence of the $\\pi\\!-\\!\\eta$ mixing amplitude\npredicted from chiral perturbation theory. Alternatively, one can use\nchiral-perturbation-theory results to set stringent limits on the value of the\n$NN\\eta$ coupling constant.",
"arxiv_id": "nucl-th/9303005",
"authors": [
"J. Piekarewicz"
],
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"doi": "10.1103/PhysRevC.48.1555",
"journal_ref": "Phys.Rev.C48:1555-1561,1993",
"title": "Off-shell Behavior of the $\\pi\\!-\\!\\eta$ Mixing Amplitude",
"url": "https://arxiv.org/abs/nucl-th/9303005"
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