No Arabic abstract
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.
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.
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.
We study the scattering of neutrinos on polarized and unpolarized free nucleons, and also the polarization of recoil particles in these scatters. In contrast to electromagnetic processes, the parity-violating weak interaction gives rise to large spin asymmetries at leading order. Future polarization measurements could provide independent access to the proton axial structure and allow the first extraction of the pseudoscalar form factor from neutrino data without the conventional partially conserved axial current (PCAC) ansatz and assumptions about the pion-pole dominance. The pseudoscalar form factor can be accessed with precise measurements with muon (anti)neutrinos of a few hundreds $mathrm{MeV}$ of energy or with tau (anti)neutrinos. The axial form factor can be extracted from scattering measurements using accelerator neutrinos of all energies.
The $eta^prime$ transition form factor is reanalyzed in view of the recent BESIII first observation of the Dalitz decay $eta^primetogamma e^+e^-$ in both space- and time-like regions at low and intermediate energies using the Pade approximants method. The present analysis provides a suitable parameterization for reproducing the measured form factor in the whole energy region and allows to extract the corresponding low-energy parameters together with a prediction of its values at the origin, related to $Gamma_{eta^primetogammagamma}$, and the asymptotic limit. The $eta$-$eta^prime$ mixing is reassessed within a mixing scheme compatible with the large-$N_c$ chiral perturbation theory at next-to-leading order, with particular attention to the OZI-rule--violating parameters. The $J/psi$, $Ztoeta^{(prime)}gamma$ decays are also considered and predictions reported.