The Deep Underground Neutrino Experiment (DUNE) will be a world-class neutrino observatory and nucleon decay detector designed to answer fundamental questions about the nature of elementary particles and their role in the universe.

In this paper we study an SU(5) × A 5 flavour model which exhibits a neutrino mass sum rule and golden ratio mixing in the neutrino sector which is corrected from the charged lepton Yukawa couplings. We give the full renormalisable superpotential for the model which breaks SU(5) and A 5 after integrating out heavy messenger fields and minimising the scalar potential. The mass sum rule allows for both mass orderings but we will show that inverted ordering is not valid in this setup. For normal ordering we find the lightest neutrino to have a mass of about 10-50 meV, and all leptonic mixing angles in agreement with experiment. Parameter best-fit (±1σ) 3σ range θ PMNS 12 in • 33.48 +0.77 −0.74 31.30 → 35.90 θ PMNS 13 in • 8.52 +0.20 −0.21 7.87 → 9.11 θ PMNS 23 in • 42.2 +0.1 −0.1 ⊕ 49.4 +1.6 −2.0 38.4 → 53.3 δ PMNS in • 251 +67 −59 0 → 360 ∆m 2 21 in 10 −5 eV 2 7.50 +0.19 −0.17 7.03 → 8.09 ∆m 2 31 in 10 −3 eV 2 (NH) 2.458 +0.002 −0.002 2.325 → 2.599 ∆m 2 32 in 10 −3 eV 2 (IH) −2.448 +0.047 −0.047 −2.590 → −2.307Table 1: The best-fit values and the 3σ ranges for the parameters taken from [8]. There are two minima for θ PMNS 23. The first one corresponds to the normal hierarchy whereas the second one corresponds to the inverted hierarchy.

Neutrino oscillations in matter provide a unique probe of new physics. Leveraging the advent of neutrino appearance data from NOvA and T2K in recent years, we investigate the presence of CP-violating neutrino non-standard interactions in the oscillation data. We first show how to very simply approximate the expected NSI parameters to resolve differences between two long-baseline appearance experiments analytically. Then, by combining recent NOvA and T2K data, we find a tantalizing hint of CP-violating NSI preferring a new complex phase that is close to maximal: φeµ or φeτ ≈ 3π/2 with | eµ| or | eτ | ∼ 0.2. We then compare the results from long-baseline data to constraints from IceCube and COHERENT.

Correlations between light neutrino observables are arguably the strongest predictions of lepton flavour models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles. A subclass of these correlations are neutrino mass sum rules, which connect the three (complex) light neutrino mass eigenvalues among each other. This connection constrains both the light neutrino mass scale and the Majorana phases, so that mass sum rules generically lead to a nonzero value of the lightest neutrino mass and to distinct predictions for the effective mass probed in neutrinoless double beta decay. However, in nearly all cases known, the neutrino mass sum rules are not exact and receive corrections from various sources. We introduce a formalism to handle these corrections perturbatively in a model-independent manner, which overcomes issues present in earlier approaches. Our ansatz allows us to quantify the modification of the predictions derived from neutrino mass sum rules. We show that, in most cases, the predictions are fairly stable: while small quantitative changes can appear, they are generally rather mild. We therefore establish the predictivity of neutrino mass sum rules on a level far more general than previously known.

Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. After a discussion of the types of corrections that could possibly appear and elucidating on the theory behind neutrino mass sum rules, we estimate and explicitly compute the impact of radiative corrections, as these appear in general and thus hold for whole groups of models. We discuss all neutrino mass sum rules currently present in the literature, which together have realisations in more than 50 explicit neutrino flavour models. We find that, while the effect of the renormalisation group running can be visible, the qualitative features do not change. This finding strongly backs up the solidity of the predictions derived in the literature, and it thus marks a very important step in deriving testable and reliable predictions from neutrino flavour models.