Resolve the tied-branch flavon scale and relic-ALP constraints

Determine the flavon scale selected by the relic-abundance condition in the condensate-tied axion-portal SIMP realization, then determine the corresponding ALP lifetime against decaying-relic bounds and the ALP photon coupling against the supernova constraint for a sub-MeV ALP, in order to establish whether this branch is excluded.

Background

In the condensate-tied realization, the ALP mass is generated solely by the dark condensate, giving a very light ALP relative to the dark pion. The contact interaction then makes the conversion process pi pi -> aa efficient, while the resulting ALP population can remain as a relic comparable to the dark-matter abundance. The authors’ coupled calculation does not reach the observed relic abundance throughout the decoupled regime, but they do not regard this as a definitive exclusion because the flavon scale and the associated ALP decay phenomenology have not yet been fully determined.

The unresolved calculation is therefore needed to decide whether the tied branch is genuinely ruled out: the flavon scale must be fixed using the corrected energy-injection treatment, after which the ALP lifetime must be compared with bounds on decaying relics and the photon coupling must be tested against the supernova limit in the short-lifetime regime.