Abstract: We formulate an alternative approach based on unitarity triangles to describe neutrino oscillations in presence of non-standard interactions (NSI). Using perturbation theory, we derive the expression for the oscillation probability in case of NSI and cast it in terms of the three independent parameters of the leptonic unitarity triangle (LUT). The form invariance of the probability expression (even in presence of new physics scenario as long as the mixing matrix is unitary) facilitates a neat geometric view of neutrino oscillations in terms of LUT. We examine the regime of validity of perturbative expansions in the NSI case and make comparisons with approximate expressions existing in literature. We uncover some interesting dependencies on NSI terms while studying the evolution of LUT parameters and the Jarlskog invariant. Interestingly, the geometric approach based on LUT allows us to express the oscillation probabilities for a given pair of neutrino flavours in terms of only three (and not four) degrees of freedom which are related to the geometric properties (sides and angles) of the triangle. Moreover, the LUT parameters are invariant under rephasing transformations and independent of the parameterization adopted.

Abstract: Motivated by the recent XENON1T results, we explore various new physics models that can be discovered through searches for electron recoils in O(keV)-threshold direct-detection experiments. First, we consider the absorption of axion-like particles, dark photons, and scalars, either as dark matter relics or being produced directly in the Sun. In the latter case, we find that keV mass bosons produced in the Sun provide an adequate fit to the data but are excluded by stellar cooling constraints. We address this tension by introducing a novel Chameleon-like axion model, which can explain the excess while evading the stellar bounds. We find that absorption of bosonic dark matter provides a viable explanation for the excess only if the dark matter is a dark photon or an axion. In the latter case, photophobic axion couplings are necessary to avoid X-ray constraints. Second, we analyze models of dark matter-electron scattering to determine which models might explain the excess. Standard scattering of dark matter with electrons is generically in conflict with data from lower-threshold experiments. Momentum-dependent interactions with a heavy mediator can fit the data with dark matter mass heavier than a GeV but are generically in tension with collider constraints. Next, we consider dark matter consisting of two (or more) states that have a small mass splitting. The exothermic (down)scattering of the heavier state to the lighter state can fit the data for keV mass splittings. Finally, we consider a subcomponent of dark matter that is accelerated by scattering off cosmic rays, finding that dark matter interacting though an O(100 keV)-mass mediator can fit the data. The cross sections required in this scenario are, however, typically challenged by complementary probes of the light mediator. Throughout our study, we implement an unbinned Monte Carlo analysis and use an improved energy reconstruction of the XENON1T events.