$\eta$ and $\eta '$ transition form factors from rational approximants

Abstract

The η and η transition form factors in the space-like region are analyzed at low and intermediate energies in a model-independent way through the use of rational approximants. The slope and curvature parameters of the form factors as well as their values at zero and infinity are extracted from experimental data. The impact of these results on the mixing parameters of the η-η system and the pseudoscalar-exchange contributions to the hadronic light-by-light scattering part of the anomalous magnetic moment aµ are also discussed.

Predictions on the second-class current decaysτ−→π−η(′)<

“…In Refs. [19,20] we have also provided a short review of the theory as applied to the computation of the vector and scalar K − η ( ) form factors describing the decays…”

“…The so-called dispersive representation has been wide and successfully employed to describe lots of phenomena and in particular data on exclusive hadronic tau decays [16,17,18,19,20,21,22,30,69,70] 11 . Unfortunately, for the π − η ( ) decay modes there is a lack of experimental data either on the phase shifts or the decays spectra.…”

“…Previous theoretical analysis estimated the branching ratio to be of the order of 10 −5 and within the range 10 −8 to 10 −6 for the π − η and π − η modes, respectively. In this work, we revisit these processes benefited from our previous experiences in describing dimeson τ decays data [16,17,18,19,20,21,22]. Here, the main subject of our study is the theoretical construction of the participant vector and scalar form factors.…”