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Register a new userSelect physics solution via $eta$-$eta$ mixing
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Kai Zhu
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A novel and simple method is proposed to select the physics solution in the decays of $Y(4230) to eta J/psi$ and $Y(4230) to eta J/psi$, where multiple solutions have been reported in the experimental measurements. Based on an $eta$-$eta$ mixing analysis, unique solutions are determined for the two measurements, respectively. Furthermore, this analysis also indicates $Y(4230)$ would not contain substantial $sbar{s}$ quark component.
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We have revisited glueball mixing with the pseudoscalar mesons in the MIT bag model scheme. The calculation has been performed in the spherical cavity approximation to the bag using two different fermion propagators, the cavity and the free propagators. We obtain a very small probability of mixing for the eta at the level of $0.04-0.1% and a bigger for the eta at the level of 4-12%. Our results differ from previous calculations in the same scheme but seem to agree with the experimental analysis. We discuss the origin of our difference which stems from the treatment of our time integrations.
A value for the $eta$-$eta^prime$ mixing angle is extracted from the data on $VPgamma$ transitions using simple quark-model ideas. The set of data covers {it all} possible radiative transitions between the pseudoscalar and vector meson nonets. Two main ingredients of the model are the introduction of flavour-dependent overlaps for the various $qbar{q}$ wave functions and the use of the quark-flavour basis to describe the $eta$-$eta^prime$ system. In this basis the mixing angle is found to be $phi_P=(37.7pm 2.4)^circ$.
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 present a lattice QCD computation of $eta$ and $eta^prime$ masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for the eta mass 551(8)(6) MeV (first error statistical, second systematic) and the eta mass 1006(54)(38)(+61) MeV (third error from our method) are in excellent agreement with experiment. Our data show that the mixing in the quark flavour basis can be described by a single mixing angle of 46(1)(3) degree indicating that the eta is mainly a flavour singlet state.
The mixing of $eta-eta$ or $eta-eta-G$ is of a great theoretical interest, because it concerns many aspects of the underlying dynamics and hadronic structure of pseudoscalar mesons and glueball. Determining the mixing parameters by fitting data is by no means trivial. In order to extract the mixing parameters from the available processes where hadrons are involved, theoretical evaluation of hadronic matrix elements is necessary. Therefore model-dependence is somehow unavoidable. In fact, it is impossible to extract the mixing angle from a unique experiment because the model parameters must be obtained by fitting other experiments. Recently $BR(Dtoeta+bar l+ u_l)$ and $BR(D_stoeta(eta)+bar l+ u_l)$ have been measured, thus we are able to determine the $eta-eta$ mixing solely from the semileptonic decays of D-mesons where contamination from the final state interactions is absent. Thus we hope that the model-dependence of the extraction can be somehow alleviated. Once $BR(Dtoeta+bar l+ u_l)$ is measured, we can further determine all the mixing parameters for $eta-eta-G$. As more data are accumulated, the determination will be more accurate. In this work, we obtain the transition matrix elements of $D_{(s)}to eta^{(prime)}$ using the light-front quark model whose feasibility and reasonability for such processes have been tested.
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