Study of variants for Monte Carlo generators of τ→3πν decays

Low energy QCD (below 2 GeV) is a region of resonance dynamics, sometimes lacking a satisfactory description as compared to the precision of available experimental data. Hadronic τ decays offer a probe for such an energy regime. In general, the predictions for decays are model dependent, with parameters fitted to experimental results. The parameterizations differ by the amount of assumptions and theoretical requirements taken into account. Both model distributions and acquired data samples used for the fits are the results of a complex effort. In this paper, we investigate the main parameterizations of τ decay matrix elements for the one- and three-prong channels of three-pion τ decays. The differences in analytical forms of the currents and resulting distributions used for comparison with the experimental data are studied. We use invariant mass spectra of all possible pion pairs and the whole three-pion system. Also three-dimensional histograms spanned over all distinct squared invariant masses are used to represent the results of models and experimental data. We present distributions from TAUOLA Monte Carlo generation and a semi-analytical calculation. These are necessary steps in the development for fitting in an as model-independent way as possible, and to explore multi-million event experimental data samples. This includes the response of distributions to model variants, and/or numerical values of the parameters. The interference effects of the currents' parts are also studied. For technical purposes, weighted events are introduced. Even though we focus on 3πν_τ modes, technical aspects of our study are relevant for all τ decay modes into three hadrons