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Register a new userMixing and decays of rho- and omega-mesons
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Ya. I. Azimov
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Isospin violating mixing of rho- and omega-mesons is reconsidered in terms of propagators. Its influence on various pairs of (rho^0,omega)-decays to the same final states is demonstrated. Some of them, (rho^0,omega)topi^+pi^- and (rho^0,omega)topi^0gamma, have been earlier discussed in the literature, others (e.g., (rho^0,omega)toetagamma and (rho^0,omega)to e^+e^-) are new in this context. Changes in partial widths for all the decay pairs are shown to be correlated. The set of present experimental data, though yet inconclusive, provides some limits for the direct (rhoomega)-coupling and indirectly supports enhancement of rho^0topi^0gamma in comparison with rho^{pm}topi^{pm}gamma, though not so large as in some previous estimates.
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Influence of the isospin-violating (rho^0, omega)-mixing is discussed for any pair of decays of rho^0, omega into the same final state. It is demonstrated, in analogy to the CP-violation in neutral kaon decays, that isospin violation can manifest itself in various forms: direct violation in amplitudes and/or violation due to mixing. In addition to the known decays (rho^0, omega)topi^+pi^- and (rho^0, omega)topi^0gamma, the pair of decays to e^+e^- and the whole set of radiative decays with participation of rho^0, omega (in initial or final states) are shown to be also useful and perspective for studies. Existing data on these decays agree with the universal character of the mixing parameter and indirectly support enhancement of rho^0topi^0gamma in respect to rho^{pm}topi^{pm}gamma. Future precise measurements will allow to separate different forms of isospin violation and elucidate their mechanisms.
The strong and electromagnetic corrections to $rho-omega$ mixing are calculated using a SU(2) version of resonance chiral theory up to next-to-leading orders in $1/N_C$ expansion, respectively. Up to our accuracy, the effect of the momentum dependence of $rho-omega$ mixing is incorporated due to the inclusion of loop contributions. We analyze the impact of $rho-omega$ mixing on the pion vector form factor by performing numerical fit to the data extracted from $e^+e^-rightarrow pi^+pi^-$ and $taurightarrow u_{tau}2pi$, while the decay width of $omegarightarrow pi^+pi^-$ is taken into account as a constraint. It is found that the momentum dependence is significant in a good description of the experimental data. In addition, based on the fitted values of the involved parameters, we analyze the decay width of $omega rightarrow pi^+pi^-$, which turns out to be highly dominated by the $rho-omega$ mixing effect.
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.
We study the $CP$ asymmetry of $B^pmto omega K^pm$ with the inclusion of the $rho-omega$ mixing mechanism. It is shown that the $CP$ asymmetry of $B^pmtoomega K^pm$ experimentally measured ($A_{CP}^{text{exp}}$) and conventionally defined ($A_{CP}^{text{con}}$) are in fact different, which relation can be illustrated as $A_{CP}^{text{exp}}=A_{CP}^{text{con}}+Delta A_{CP}^{rhoomega}$, with $Delta A_{CP}^{rhoomega}$ the $rho-omega$ mixing contribution to $A_{CP}^{text{exp}}$. $A_{CP}^{text{exp}}$ is in fact the regional $CP$ asymmetry of $B^pmtopi^+pi^-pi^0 K^pm$ when the invariant mass of the three pions lies in the vicinity of the $omega$ resonance. The numerical value of $Delta A_{CP}^{rhoomega}$ is extracted from the experimental data of $B^pmtopi^+pi^-K^pm$ and is found to be comparable with $A_{CP}^{text{exp}}$, hence, nonnegligible. The conventionally defined $CP$ asymmetry, $A_{CP}^{text{con}}$, is obtained from the values of $A_{CP}^{text{exp}}$ and $Delta A_{CP}^{rhoomega}$, and is compared with the theoretical calculations in the literature.
The investigation in the work of the reaction electron-positron to omega and pi0 mesons in the 3P0 nonrelativistic quark model reveals that the reaction electron-positron to omega and pi0 mesons process at the energy region from the omega and pi mesons threshold to 2.0 GeV is dominated by the two-step process in which the primary quark-antiquark pair first forms rho and rho mesons and then the vector mesons decay into omega and pi. With rho(1450) and rho(1700) mainly in 2S and 1D states respectively, the experimental data for the cross section of the reaction electron-positron to omega and pi0 mesons are well produced in the 3P0 quark model. The work supports the argument that rho(1450) is mainly a 2S meson and rho(1700) a 1D meson.
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