Coupling QCD-scale axion-like particles to gluons

We present a novel data-driven method for determining the hadronic interaction strengths of axion-like particles (ALPs) with QCD-scale masses. Using our method, it is possible to calculate the hadronic production and decay rates of ALPs, along with many of the largest ALP decay branching fractions to exclusive final states. To illustrate the impact on QCD-scale ALP phenomenology, we consider the scenario where the ALP-gluon coupling is dominant over the ALP coupling to photons, electroweak bosons, and all fermions for $m_{\pi} \lesssim m_a \lesssim 3$ GeV. We emphasize, however, that our method can easily be generalized to any set of ALP couplings to SM particles. Finally, using the approach developed here, we provide calculations for the branching fractions of $\eta_c \to VV$ decays, i.e. $\eta_c$ decays into two vector mesons, which are consistent with the known experimental values.