$\omega-\rho$ Mixing and the $\omega\to\pi\pi\gamma$ Decay

In order to calculate the rho - omega mixing we extend the chiral couplings of the low-lying vector mesons in chiral perturbation theory to a lagrangian that contains two vector fields. We determine the momentum dependence of the two-point function and recover an earlier result for the on-shell expression. We discuss the off-shell behaviour of the mixing.

Based on the analysis of both Borel and Finite-Energy QCD sum rules, the inclusion of finite mesonic widths leads to a dramatic effect on the predictions for the momentum dependence of the rho-omega mixing matrix element. It is shown that the rho-omega mixing matrix element traditionally discussed in the literature, has the same sign and similar magnitude in the space-like region as its on-shell value. This contrasts the zero-width result where the mixing matrix element is ty...

The inclusion of the $\rho-\omega$ mixing effect is essential for a precise description of the pion electromagnetic form factor in the $e^+e^- \rightarrow \pi^+\pi^-$ process, which quantifies the two-pion contribution to the anomalous magnetic moment of the muon $a_\mu$. In this paper, we analyse the momentum dependence of the $\rho-\omega$ mixing by considering loop contributions at the next-to-leading order in the $1/N_C$ expansion within the framework of resonance chiral ...

An improved update of the structure and decays of $\rho^0$, $\omega$ and $\phi$ mesons based on a chiral SU(3) Lagrangian, including anomaly terms is presented. We demonstrate that a consistent and quantitatively successful description of both pion and kaon electromagnetic form factors can be achieved. We also discuss the $e^+e^- \to \pi^+ \pi^0 \pi^-$ cross section, the Dalitz decay $\omega \to \pi^0 \mu^+ \mu^-$ and aspects of $\rho^0 \omega$ and $\omega \phi$ mixing. Relat...

The role of higher meson resonances with spin 1 and 2 is investigated quantitatively in the decay processes of $\rho \to \pi^0\pi^0 \gamma$ and $\omega \to \pi^0 \pi^0 \gamma$. Among the higher resonances, we find that the $f_2(1270)$ tensor meson can give a nontrivial contribution especially to the $\omega \to \pi^0 \pi^0 \gamma$ decay process. When the $f_2$ contribution is combined with the processes involving the vector and scalar meson intermediate states, a good agreeme...

In this paper we improve and extend a recent analysis which showed that the rho-omega mixing amplitude cannot be unambiguously extracted from the pion electromagnetic form-factor in a model independent way. In particular, we focus on the argument that the extraction is sensitive to the presence of any intrinsic omega_I -> pi pi coupling. Our extended analysis confirms the original conclusion, with only minor, quantitative differences. The extracted mixing amplitude is shown t...

Starting from the Chiral Perturbation Theory Lagrangian, but keeping different masses for the charged and neutral mesons, and using a previously developed non-perturbative unitary scheme that generates the lightest meson-meson resonances, we construct K Kbar to K Kbar and K Kbar to pi+ pi- in the vector channel. This allows us to obtain the kaon-loop contribution to the phi-rho mixing and study the phi to pi+pi- decay. The dominant contribution to this decay comes from the ph...

Simulation methods for the decays $ B \to {\pi}^+ {\pi}^- V$, where $V$ is a $1^{--}$ vector-meson, are presented in detail. Emphasis is put on the use of the helicity formalism and the use of effective Lagrangians. We show the importance of ${{\rho}^{0}}-{\omega}$ mixing in enhancing the direct $CP$ violation (DCPV) when the pion-pion invariant mass is near the mass of the $\omega$.

We review the current status of rho-omega mixing and discuss its implication for our understanding of charge-symmetry breaking. In order to place this work in context we also review the photon-hadron coupling within the framework of vector meson dominance. This leads naturally to a discussion of the electromagnetic form-factor of the pion and of nuclear shadowing.

We study the radiative $\rho$, $\omega$ and $\phi$ decay into $\pi^0 \pi^0 \gamma$ and $\pi^0 \eta \gamma $ taking into account mechanisms in which there are two sequential vector-vector-pseudoscalar or axial-vector--vector--pseudoscalar steps followed by the coupling of a vector meson to the photon, considering the final state interaction of the two mesons. Other mechanisms in which two kaons are produced through the same sequential mechanisms or from vector meson decay into...