Resolve the appropriate hidden gauge-group rank

Determine whether the hidden confining gauge theory should be modeled with gauge rank N_c=2 or N_c=4, and quantify the resulting change in the Wess–Zumino–Witten 3-to-2 rate and the lower bound on the portal scale.

Background

The numerical analysis adopts N_c=2 for the confining Sp(N_c) dark gauge theory. The gauge rank enters the Wess–Zumino–Witten 3-to-2 rate through an overall factor, and consequently affects the portal-scale floor required for the 3-to-2 process to dominate over pi pi -> aa.

The paper explicitly identifies the choice between N_c=2 and N_c=4 as unresolved and states that it changes the relevant rate and floor by a factor of four. Resolving this issue would reduce the model’s residual normalization uncertainty and clarify the surviving parameter space.

References

Moreover the choice $N_c=2$ against $N_c=4$ remains an unresolved convention, and it shifts $\braket{\sigma v2}_{3\to2}$ and the floor of Table~\ref{tab: floor} by a factor of four.

— Relocating the SIMP Miracle in the Axion Portal  (2609.11254 - Thongyoi et al., 10 Sep 2026) in Section 9, Conclusions, paragraph beginning “Several limitations should be stated”