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Register a new userRadiative VPgamma transitions and eta-eta mixing
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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 $phi_P=(37.7pm 2.4)^circ$.
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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 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.
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.
Recently CLEO has studied the radiative decay of $Upsilon$ into $eta$ and an upper limit for the decay has been determined. Confronting with this upper limit,most of theoretical predictions for the decay fails. After briefly reviewing these predictions we re-examine the decay by separating nonperturbative effect related to the quarkonium and that related to $eta$ or $eta$, in which the later is parameterized by distribution amplitudes of gluons in $eta$. With this factorization approach we obtain theoretical predictions which are in agreement with experiment. Uncertainties in our predictions are discussed. The possibly largest uncertainties are from relativistic corrections for $J/Psi$ and the value of the charm quark mass. We argue that the effect of these uncertainties can be reduced by using quarkonium masses instead of using quark masses. An example of the reduction is shown with an attempt to explain the violation of the famous 14% rule in radiative decays of charmonia.
It has been realized for a long time that knowing the eta and eta wave functions in terms of quark and gluon components probes our understanding of non-perturbative QCD dynamics. Great effort has been given to this challenge -- yet no clear picture has emerged even with the most recent KLOE data. We point out which measurements would be most helpful in arriving at a more definite conclusion. A better knowledge of these wave functions will significantly help to disentangle the weight of different decay subprocesses in semi-leptonic decays of D^+, D_s^+ and B^+ mesons. The resulting insights will be instrumental in treating even non-leptonic B transitions involving $eta$ and $eta^{prime}$ and their CP asymmetries; thus they can sharpen the case for or against New Physics intervening there.
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