Abstract
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 $$\tau $$ 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 $$\tau $$ decay matrix elements for the one- and three-prong channels of three-pion $$\tau $$ 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 $$3\pi \nu _\tau $$ modes, technical aspects of our study are relevant for all $$\tau $$ decay modes into three hadrons.
Highlights
Let us point out that there are various aspects of the work for construction of Monte Carlo, which need to be combined
Taking into account the Lorentz invariance and properties of weak couplings of the τ -lepton to an intermediate virtual W boson, the predictions still require four complex scalar functions Fi of three variables each. Such a parameterization of matrix elements is commonly used by τ decay Monte Carlo generators, e.g., by TAUOLA; and it exists since its beginning [2, 3]
18 Note: we present here only those parameters that are different as only those can introduce any discrepancies between CLEO publ. and TAUOLA CLEO
Summary
Let us point out that there are various aspects of the work for construction of Monte Carlo, which need to be combined. Taking into account the Lorentz invariance and properties of weak couplings of the τ -lepton to an intermediate virtual W boson, the predictions still require four complex scalar functions Fi of three variables each (see the definition later in the text) Such a parameterization of matrix elements is commonly used by τ decay Monte Carlo generators, e.g., by TAUOLA; and it exists since its beginning [2, 3]. For this task, we use mainly one-dimensional histograms; results of measurements in such a form are available from the CLEO but from the BaBar collaboration as well. We use mainly one-dimensional histograms; results of measurements in such a form are available from the CLEO but from the BaBar collaboration as well Such distributions were used to constrain the model parameters in many of our studies. For completeness some histograms of three-dimensional form are given in “Appendix C”
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