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

In terms of effective field theory and mixed propagator approach, we show that there is a larger hidden effect of isospin breaking in $\rho^0\to\pi^0\gamma$ decay due to an $\omega$ exchange, $\rho^0\to\omega\to\pi^0\gamma$. The branching ratio is predicted as $B(\rho^0\to\pi^0\gamma)=(11.67\pm 2.0)\times 10^{-4}$, which is much larger than Partcile Data Group's datum $(6.8\pm 1.7)\times 10^{-4}$ and one of charged mode, $B(\rho^\pm\to\pi^\pm\gamma)=(4.5\pm 0.5)\times 10^{-4}...

The BESIII Collaboration has recently reported a new resonance structure in the cross-section analyses of the $e^+e^- \to \rho\pi$ and $e^+e^- \to \rho(1450)\pi$ processes, displaying characteristics akin to an $\omega$-meson. However, its measured mass, $M = 2119 \pm 11 \pm 15 \, \text{MeV}$, significantly deviates from the predictions of the unquenched relativized potential model for conventional $\omega$ vector meson spectroscopy. To address this discrepancy, we propose a ...

The momemtum dependence of the off-shell $\rho$-$\omega$ mixing amplitude is calculated through a two-quark loop diagram, using non-perturbative meson-quark vertex functions for the $\rho$ and $\omega$ mesons, as well as non-perturbative quark propagators. Both these quantities are generated self-consistently through an interlinked BSE-cum-SDE approach with a 3D support for the BSE kernel with two basic constants which are pre- checked against a wide cross section of both mes...

We study $\omega\to\pi^+\pi^-$ decay up to including all orders of the chiral expansion and one-loop level of mesons in formlism of chiral constituent quark model. This G-parity forbidden decay is caused by $m_u\neq m_d$ and electromagnetic interaction of mesons. We illustrate that in the formlism both nonresonant contact interaction and $\rho$ resonance exchange contribute to this process, and the contribution from $\rho$ resonance exchange is dominant. We obtain that transi...

We study the $CP$ asymmetry of $B^\pm\to \omega K^\pm$ with the inclusion of the $\rho-\omega$ mixing mechanism. It is shown that the $CP$ asymmetry of $B^\pm\to\omega K^\pm$ experimentally measured ($A_{CP}^{\text{exp}}$) and conventionally defined ($A_{CP}^{\text{con}}$) are in fact different, which relation can be illustrated as $A_{CP}^{\text{exp}}=A_{CP}^{\text{con}}+\Delta A_{CP}^{\rho\omega}$, with $\Delta A_{CP}^{\rho\omega}$ the $\rho-\omega$ mixing contribution to $...

Using the close relationship between the low--energy constants of chiral perturbation theory and the chiral invariant interactions of the vector meson resonances with the pseudoscalar mesons, we investigate the process $\rho^0 \ra \pi^+ \pi^- \gamma$. Compared with the contribution from the pure bremsstrahlung mechanism, we find an enhancement of the decay rate near the endpoint of the photon energy spectrum. Such a particular shape of the differential decay rate has indeed b...

We re-examine 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 -> 2pi coupling. Our extended analysis confirms the original conclusion, with only minor, quantitative differences. The extracted mixing amplitude is shown to be sensitiv...

The complementarity between Chiral Perturbation Theory and the Linear Sigma Model in the scalar channel is exploited to study $\pi^0\pi^0$ production in $\rho$ and $\omega$ radiative decays, where the effects of a low mass scalar resonance $\sigma(500)$ should manifest. The recently reported data on $\rho\to\pi^0\pi^0\gamma$ seem to require the contribution of a low mass and moderately narrow $\sigma(500)$. The properties of this controversial state could be fixed by improvin...

The problem of $\rho$- and $\omega$- mesons contributions to the background for $\eta \to \pi^0 e^+e^-$ decay and to the asymmetries in the decays $\eta \to \pi^+\pi^-\pi^0$ and $\eta \to \pi^+\pi^-\gamma$ is considered.

Dalitz decays of $\omega$ and $\rho$ mesons, $\omega\to \pi^0\gamma^*\to\pi^0 e^+e^-$ and $\rho^0\to \pi^0\gamma^*\to\pi^0 e^+e^-$, produced in $pp$ collisions are calculated within a covariant effective meson-nucleon theory. We argue that the $\omega$ transition form factor $F_{\omega\to \pi^0\gamma^*}$ is experimentally accessible in a fairly model independent way in the reaction $pp \to pp \pi^0 e^+ e^-$ for invariant masses of the $\pi^0 e^+ e^-$ subsystem near the $\omeg...