Determine the proton-model distribution of the theta100 test statistic

Determine whether applying the test statistic used by the Telescope Array composition analysis to multiple simulations of a proton ultra-high-energy-cosmic-ray model yields a substantial probability of measuring a theta100 value far from the model prediction.

Background

The paper critiques an earlier analysis that compares an observed theta100 value with a single value calculated for a particular ultra-high-energy-cosmic-ray model. The authors argue that a valid model test requires the distribution of the test statistic under repeated simulations of the model rather than a single model value.

The unresolved issue is whether proton-model realizations can produce theta100 values substantially different from the nominal prediction with non-negligible probability. Resolving this would establish whether the earlier analysis genuinely excludes a pure-proton composition.

References

It might be that, for example, when one applies the TS to different simulations of a proton UHECR model, one will find out that there is actually a decent chance of measuring a \theta_{100} that is very far from the model value.

— The high entropy of the UHECR arrival direction distribution favors a light composition  (2608.17801 - Strasman et al., 18 Aug 2026) in Section 5, Comparison to previous works