Neutrino non-standard interactions as a portal to test flavour symmetries

Imposing non-Abelian discrete flavour symmetries to neutrino non-standard interactions (NSIs) is discussed for the first time. For definiteness, we choose $A_4$ as the flavour symmetry, which is subsequently broken to the residual symmetry $Z_2$ in the neutrino sector. We provide a general discussion on flavour structures of NSIs from higher-dimensional operators ($d\leqslant8$) without inducing unnecessary tree-level 4-charged-fermion interactions. Both $A_4$- and $Z_2$-motivated NSI textures are obtained. UV completions of higher-dimensional operators lead to extra experimental constraints on NSI textures. We study the implementation of matter-effect NSIs in DUNE from phenomenological point of view, and discover that DUNE can test $A_4$ with a high level of statistics. We also present exclusion limits of sum rules suggested by UV-complete models. Our result shows that the NSI effects, though predicted to be small for DUNE, could provide useful information that might extend our understanding of the flavour symmetry.