Relocating the SIMP Miracle in the Axion Portal

Abstract: In the strongly interacting massive particle (SIMP) scenario, dark matter is a pseudo-Nambu--Goldstone boson whose abundance is set by a three-to-two Wess--Zumino--Witten process. We study this scenario in an axion portal and find that the kinetic contact the canonical mechanism assumes is excluded by bounds on sub-GeV axion-like particles (ALPs). The dark sector then freezes out at its own temperature, so the relic abundance no longer fixes the self-interaction cross section but predicts the portal coupling instead. Moreover, the portal operator is Hermitian and even in the ALP field, so no trilinear ALP--pion coupling arises. The contact term then drives $ππ\to aa$ with nothing to cancel against it, and we find the conversion four orders of magnitude faster than a trilinear estimate gives. This disfavours the minimal realisation in which the dark condensate alone generates the ALP mass. The realisation that survives instead makes the ALP slightly heavier than the dark pion. Matching the observed abundance then fixes the flavon vacuum expectation value at $V_φ\simeq 1.1\times10^{10} \ {\rm GeV}$ and leaves the dark scale open over more than an order of magnitude. The decay $K<sup>+\toπ<sup>+a$ requires the flavon to charge the leptons alone. The model then predicts a dark matter self-interaction of $0.20\,{\rm cm<sup>2/g}$ at a dark pion mass of $140\ {\rm MeV}$, in a window running from $82$ to $169 \ {\rm MeV}$. The predictive power of the SIMP framework is therefore not lost but relocated, from the self-interaction to the flavon scale.