Study of variants for Monte Carlo generators of $τ\to 3πν$ decays

Low energy QCD (below 2 GeV) is a region of resonance dynamics, sometimes lacking satisfactory description as compared to precision of available experimental data. Hadronic $τ$ decays offer a probe for such energy regime. In general, predictions for decays are model dependent, with parameters fitted to experimental results. Parameterizations differ by amount of assumptions and theoretical requirements taken into account. Both model distributions and acquired data samples used for fits are results of complex effort. In this paper, we investigate main parameterizations of $τ$ decay matrix elements for the one- and three-prong channels of three-pion $τ$ decays. 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 results of models and experimental data. We present distributions from {\tt TAUOLA} Monte Carlo generation and semi-analytical calculation. These are necessary steps in development for fitting in as model-independent way as possible, and to explore multi-million event experimental data samples. This includes response of distributions to model variants, and/or numerical values of parameters. Interference effects of 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.

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