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Register a new userA study of $rho-omega$ mixing in resonance chiral theory
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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.
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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.
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.
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.
We present a calculation of the $eta$-$eta$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $eta$-$eta$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the $eta$-$eta$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and $mathcal{O}(N_c p^6)$ contact terms.
We calculate the momentum dependence of the $rho^0-omega$ mixing amplitude in vacuum with vector nucleon-nucleon interaction in presence of a constant homogeneous weak magnetic field background. The mixing amplitude is generated by the nucleon-nucleon ($NN$) interaction and thus driven by the neutron-proton mass difference along with a constant magnetic field. We find a significant effect of magnetic field on the mixing amplitude. We also calculate the Charge symmetry violating (CSV) $NN$ potential induced by the magnetic field dependent mixing amplitude. The presence of the magnetic field influences the $NN$ potential substantially which can have important consequences in highly magnetized astrophysical compact objects, such as magnetars. The most important observation of this work is that the mixing amplitude is non-zero, leading to positive contribute to the CSV potential if the proton and neutron masses are taken to be equal.
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