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In this work, we calculate the branching ratios for the $eta(eta)rightarrowbar{ell}ell$ decays, where $ell = e,mu$. These processes have tiny rates in the standard model due to spin flip, loop, and electromagnetic suppression, for what they could be sensitive to New Physics effects. In order to provide a reliable input for the Standard Model, we exploit the general analytical properties of the amplitude. For that purpose, we invoke the machinery of Canterbury approximants, which provides a systematic description of the underlying hadronic physics in a data-driven fashion. Given the current experimental discrepancies, we discuss in detail the role of the resonant region and comment on the reliability of $chi$PT calculations. Finally, we discuss the kind of new physics which we think would be relevant to account for them.
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We present our model-independent and data-driven method to describe pseudoscalar meson transition form factors in the space- and (low-energy) time-like regions. The method is general and conforms a toolkit applicable to any other form factor, of one and two variables, with the potential to include both high- and low-energy QCD constraints altogether. The method makes use of analyticity and unitary properties of form factors, it is simple, systematic and can be improved upon by including new data. In the present discussion, the method is used to show the impact of experimental data for precision calculations in the low-energy sector of the Standard Model. In particular, due to its relevance for New Physics searches, we have considered the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon (the pseudoscalar exchange contribution), the pseudoscalar decays into lepton pairs, and the determination of the mixing parameters of the $eta$ and $eta$ system. For all of them we provide the most updated results in a data-driven manner.
A search for rare lepton decays of the eta meson was performed using the WASA detector at CELSIUS. Two candidates for double Dalitz decay eta->e+e-e+e- events are reported with a background of 1.3+/-0.2 events. This allows to set an upper limit to the branching ratio of 9.7E-5 (90% CL). The branching ratio for the decay eta->e+e-gamma is determined to (7.8+/-0.5 stat+/-0.8 syst)E-3. An upper limit (90% CL) for the branching ratio for the eta->e+e- decay is 2.7E-5 and a limit for the sum of the eta->mu+mu-mu+mu- and eta->pi+pi-mu+mu- decays is 3.6E-4.
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.
Motivated by recent measurements of the radiative decay rates of the emph{P}-wave spin singlet charmonium $h_c$ to the light meson $eta$ or $eta^prime$ by the BESIII Collaboration, we investigate the decay rates of these channels at order $alpha alpha_s^4$. The photon is radiated mainly from charm quark pairs in the lowest order Feynman diagrams, since the diagrams where a photon radiated from light quarks are suppressed by $alpha_s$ or the relative charm quark velocity $v$, due to Charge parity conservation. The form factors of two gluons to $eta$ or $eta^prime$ are employed, which are the major mechanism for $eta$ and $eta^prime$ productions. $eta(eta^prime)$ is treated as a light cone object when we consider that the parent charmonium mass is much heavier than that of the final light meson. We obtain the branching ratio ${cal B}(h_cto gammaeta^prime) = (1.94^{+0.70}_{-0.51})times 10^{-3}$ in the nonrelativistic QCD approach, which is in agreement with the BESIII measurement. The prediction of the branching ratio of $h_cto gammaeta$ is also within the range of experimental error after including the larger uncertainty of the total decay width $Gamma_{h_c}$. The applications of these formulae to the radiative decays to $eta(eta^prime)$ of the emph{P}-wave spin singlet bottomonium $h_b(nP)$ are presented. These studies will shed some light on the $eta - eta^prime$ mixing effects, the flavor SU(3) symmetry breaking, as well as the nonperturbative dynamics of charmonium and bottomonium.
The hadronic decays eta, eta-prime -> 3 pi and eta-prime -> eta pi pi are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving s- and p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. Very good overall agreement with currently available data on decay widths and spectral shapes is achieved.
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