The QCD axion, a fascinating hypothetical particle proposed about 50 years ago, might hold the key to explaining one of the universe’s lingering mysteries: why strong interactions don't seem to break CP symmetry. Perhaps more importantly, it remains one of the most exciting dark matter candidates. 

Precise nuclear physics theories and models are playing an increasingly important role in neutrino physics. While this has long been recognized in low-energy neutrino experiments, recent advances in accelerator-based neutrino oscillation studies have further highlighted the importance of nuclear many-body effects. Modern experiments such as T2K and NOvA require accurate simulations of nucleon correlations, a necessity that will persist in future experiments like ORCA and IceCube-Upgrade, DUNE, and Hyper-Kamiokande.

Motivated by the phenomenology of MOND, we propose a theory based on a fundamental non Abelian Yang-Mills gauge field with gravitational coupling constant (a "graviphoton") emerging in a regime of weak acceleration, i.e. below the MOND acceleration scale. Using the formalism of the effective field theory and invoking a mechanism of gravitational polarization of the dark matter medium, we show that generic solutions of this theory reproduce the deep MOND limit without having to introduce in an ad hoc way an arbitrary function in the action.