Constraints on the coupling with photons of heavy axion-like-particles from Globular Clusters

We update the globular cluster bound on massive ($m_a$ up to a few 100 keV) axion-like particles (ALP) interacting with photons. The production of such particles in the stellar core is dominated by the Primakoff $\gamma + Ze\to Ze +a$ and by the photon coalescence process $\gamma+\gamma\to a$. The latter, which is predominant at high masses, was not included in previous estimations. Consequently, our result strengthens the previous constraints considerably, especially for $m_a \gtrsim 50$ keV. The combined constraints from Globular Cluster stars, SN 1987A, and beam-dump experiments leave a small triangularly shaped region open in the parameter space around $m_a \sim 0.5-1\,$ MeV and $g_{a\gamma} \sim 10^{-5}$ GeV$^{-1}$. This is informally known as the ALP "cosmological triangle" since it can be excluded only using standard cosmological arguments. As we shall discuss, however, there are viable cosmological models that are compatible with axion-like particles with parameters in such region. We also discuss possibilities to explore the cosmological triangle experimentally in upcoming accelerator experiments.