In this paper we document the modifications introduced to the previous version of the resonance chiral Lagrangian current [Phys. Rev. D 86, 113008 (2012)] of the ${$\tau${}}^{\ifmmode\pm\else\textpm\fi{}}$\rightarrow${}{$\pi${}}^{\ifmmode\pm\else\textpm\fi{}}{$\pi${}}^{\ifmmode\pm\else\textpm\fi{}}{$\pi${}}^{$\mp${}}{$\nu${}}_{$\tau${}}$ decay which enable the one-dimensional distributions measured by the BABAR Collaboration to be well modeled. The main change required to model the data is the addition of the $$\sigma${}$ resonance. Systematic errors, theoretical and experimental ones, limitations due to fits of one-dimensional distributions only, and resulting difficulties and statistical/systematic errors for fitted parameters are addressed. The current and fitting environment is ready for comparisons with the fully exclusive experimental data. The present result for ${$\tau${}}^{\ifmmode\pm\else\textpm\fi{}}$\rightarrow${}{$\pi${}}^{\ifmmode\pm\else\textpm\fi{}}{$\pi${}}^{\ifmmode\pm\else\textpm\fi{}}{$\pi${}}^{$\mp${}}{$\nu${}}_{$\tau${}}$ is encouraging for work on other $$\tau${}$ decay modes and resonance chiral Lagrangian based currents.

In the present paper we describe the set of form factors for hadronic $\tau${} decays based on Resonance Chiral Theory. The technical implementation of the form factors in fortran code is also explained. It is shown how it can be installed into the TAUOLA Monte~Carlo program. Then it is rather easy to implement into software environments of not only Belle and BABAR collaborations but also for fortran and C++ applications of LHC. The description of the current for each $\tau${} decay mode is complemented with technical numerical tests. The set is ready for fits, paramxers to be used in fits are explained. Arrangements to work with the experimental data not requiring unfolding are prepared. Hadronic currents, ready for confrontation with the $\tau${} decay data, but not yet ready for the general use, cover more than 88% of hadronic $\tau${} decay width.

We have developed a phenomenological approach which describes very well the $\pi${}0, $\eta${} and $\eta${}$'${} meson production in the two-photon interactions. The simultaneous description of the $\pi${}0, $\eta${} and $\eta${}$'${} meson two-photon form factors is consistent with data in the spacelike region, with the exception of the $\pi${}0 BABAR data. The obtained form factors are implemented in the event generator EKHARA and the simulated cross sections are presented. Uncertainties in the measured form factors coming from the model dependence in Monte~Carlo simulations are studied. The model predictions for the form factor slopes at the origin are given and the high-Q2 limit is also discussed.

We study—at leading order in the large number of colors expansion and within the resonance chiral theory framework—the odd-intrinsic-parity $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}({\pi }^0,\eta )$ cross sections in the energy regime populated by hadron resonances, namely $3m_{\pi }\lesssim E\lesssim 2\mathrm{GeV}$. In addition, we implement our results in the Monte Carlo generator phokhara 7.0 and we simulate hadron production through the radiative return method.