Two Model-Independent Results for the Momentum Dependence of Rho-Omega Mixing

Abstract

Two model-independent results on the momentum-dependence of $\rho$-$\omega$ mixing are described. First, an explicit choice of interpolating fields for the vector mesons is displayed for which both the mixing in the propagator and the isospin-breaking at the nucleon-vector meson vertices (and hence also the one-vector-meson-exchange contribution to NN charge symmetry breaking) vanish identically at $q^2=0$. Second, it is shown, using the constraints of unitarity and analyticity on the spectral function of the vector meson propagator, that there is no possible choice of interpolating fields for the ${\rho }^0$, ${\omega }^0$ mesons such that, with the $\rho \omega$ element of the propagator defined by ${\Delta }_{\mu \nu }^{\rho \omega }(q^2)=(g_{\mu \nu }-q_{\mu }{q}_{\nu }/q^2)$$\theta (q^2)/(q^2-m_{\rho }^2)(q^2-m_{\omega }^2)$, $\theta (q^2)$ is independent of momentum. It follows that the standard treatment of charge symmetry breaking in few-body systems cannot be interpreted as arising from any realizable effective meson-baryon Lagrangian and must, therefore, be considered purely phenomenological in content.

14 pages, uses REVTEX Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-35.T189.ps

References in corpus (12)

• The Momentum Dependence of the $\rho -\omega$ Mixing Amplitude in a Hadronic Model
• Constraints on the momentum dependence of rho-omega mixing
• The Off Shell $\rho$-$\omega$ Mixing in the QCD Sum Rules
• Charge-Symmetry Breaking, Rho-Omega Mixing and the Quark Propagator
• Charge symmetry breaking via rho-omega mixing from model quark-gluon dynamics
• Compton Scattering by a Pion and off--Shell Effects
• Off-shell Behavior of the $\pi -\eta$ Mixing Amplitude
• $q^2$-Dependence of Meson Mixing in Few-Body Charge Symmetry Breaking: ${\pi }^o-\eta$ Mixing to One Loop in Chiral Perturbation Theory
• The Mixed-Isospin Vector Current Correlator in Chiral Perturbation Theory and QCD Sum Rules
• Comparison of Chiral Perturbation Theory and QCD Sum Rule Results for Pseudoscalar Isoscalar-Isovector Mixing
• Modelling the Off-Shell Dependence of ${\pi }^o-\eta$ Mixing with Quark Loops
• Pi- Eta Mixing from QCD Sum Rules

Cited by in corpus (11)

• Effective chiral Lagrangians for spin-1 mesons
• Radiative Decays, Nonet Symmetry and SU(3) Breaking
• Analysis of rho-omega interference in the pion form-factor
• Matter induced rho-omega mixing
• Rho-Omega Mixing via QCD Sum Rules with Finite Mesonic Widths
• Isospin Breaking and $\omega$->$\pi \pi$ Decay
• Investigating $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ decay process within QCD sum rule approach
• Semileptonic Decay of $D_s^{+}\to {\pi }^0{\ell }^{+}{\nu }_{\ell }$ Via Neutral Meson Mixing
• The Okamoto-Nolen-Schiffer anomaly without rho-omega mixing
• Vector Meson Mixing and Charge Symmetry Violation
• $\rho -\omega$ Mixing at High Temperature and Density