Created attachment 867 [details]
The energy fraction of the tau that is passed to the hadrons for the tau -> pi0 pi- nutau decay mode

When simulating hadronic tau decays, the G4PhaseSpaceDecayChannel is used. However, when looking at PDG [1] and the theory [2] for tau hadronic decays, it seems like the vast majority of the hadronic tau decays are through a resonance. For example, the decay mode tau -> pi0 pi- nutau is in reality tau -> rho(770) nutau -> pi0 pi- nutau. When simulating an n-body decay and ignoring the resonance, the hadronic energy is typically overestimated. This can be seen in the attached figure, where the total energy fraction of the hadronic decay products is compared between the Tauola tau decay simulation library [3] and Geant4.

To resolve this, a similar decay simulation as the one used in Tauola could be implemented in Geant4. In the mean time however, would it be possible to add a note to the documentation that the energy distributions of hadronic tau decays are incorrect?

I have also implemented a Tauola integration into Geant4 [4], such that all tau decays are handled by Tauola. This is similar to the Pythia8 integration that currently exists as an example in Geant4 [5]. I can open a pull request to merge this integration into Geant4 as an additional example, if that would be of interest to the Geant4 development team?

References:
[1] Sw. Banerjee and A. Lusiani. τ branching fractions, 2022. URL https://pdg.lbl.gov/2023/reviews/rpp2023-rev-tau-branching-fractions.pdf.
[2] B.K. Bullock, K. Hagiwara, and A.D. Martin. Tau polarization and its correlations as a probe of new physics. Nuclear Physics B, 395(3):499–533, 1993. ISSN 0550-3213. doi: https://doi.org/10.1016/0550-3213(93)90045-Q. URL https://www.sciencedirect.com/science/article/pii/055032139390045Q.
[3] M. Chrzaszcz, T. Przedzinski, Z. Was, and J. Zaremba. Tauola of τ lepton decays—framework for hadronic currents, matrix elements and anomalous decays. Computer Physics Communications, 232:220–236, 2018. ISSN 0010-4655. doi:https://doi.org/10.1016/j.cpc.2018.05.017. URL https://www.sciencedirect.com/science/article/pii/S0010465518301802.
[4] S. Thor. tauoladecayer, 2024. URL https://github.com/simonthor/tau-polarization-icecube/tree/main/learn-geant4/tauoladecayer
[5] J. Yarba. Example py8decayer, 2021. URL https://geant4-userdoc.web.cern.ch/Doxygen/examples_doc/html/Examplepy8decayer.html.