Neutrino Lorentz invariance violation and ultralight axion-like dark matter searches at the European Spallation Source

The dark matter conundrum stands out as one of the central challenges to understand in both particle physics and cosmology. The ultralight axion-like particle (UALP) is an appealing dark matter candidate that can be searched for in neutrino oscillation experiments. In this work, we examine the interaction among neutrinos and a UALP; such interaction might induce violations of the Lorentz and $CPT$ symmetries. We assess the sensitivity to both the isotropic $CPT-$odd Standard Model Extension (SME) coefficients $(a_L{)}^T$ and effective neutrino-UALP couplings $\tilde{g}$ at the next-to-next generation neutrino oscillation experiment at the European Spallation Source (ESS).