Abstract: We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point tau = i, where modular invariant theories possess a residual Z(4) invariance. In this region the breaking of Z(4) can be fully described by the spurion epsilon approximate to tau – i, that flips its sign under Z(4). Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the Z(4) symmetry at tau = i, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of vertical bar epsilon vertical bar. We present examples where this mechanism is a key ingredient to successfully implement an hierarchical spectrum in the lepton sector, even in the presence of a non-minimal Kahler potential.

Abstract: We discuss the systematic decomposition of all dimension-7 (d = 7) lepton number violating operators. These d = 7 operators produce momentum enhanced contributions to the long-range part of the 0 nu beta beta decay amplitude and thus are severely constrained by existing half-live limits. In our list of possible models one can find contributions to the long-range amplitude discussed previously in the literature, such as the left-right symmetric model or scalar leptoquarks, as well as some new models not considered before. The d = 7 operators generate Majorana neutrino mass terms either at tree-level, 1-loop or 2-loop level. We systematically compare constraints derived from the mass mechanism to those derived from the long-range 0 nu beta beta decay amplitude and classify our list of models accordingly. We also study one particular example decomposition, which produces neutrino masses at 2-loop level, can fit oscillation data and yields a large contribution to the long-range 0 nu beta beta decay amplitude, in some detail.

Abstract: We evaluate the probability of future neutrino oscillation facilities to discover leptonic CP violation and/or measure the neutrino mass hierarchy. We study how this probability is affected by positive or negative hints for these observables to be found at T2K and NO nu A. We consider the following facilities: LBNE; T2HK; and the 10 GeV Neutrino Factory (NF10), and show how their discovery probabilities change with the running time of T2K and NO nu A conditioned to their results. We find that, if after 15 years T2K and NO nu A have not observed a 90% CL hint of CP violation, then LBNE and T2HK have less than a 10% chance of achieving a 5 sigma discovery, whereas NF10 still has a similar to 40% chance to do so. Conversely, if T2K and NO nu A have an early 90% CL hint in 5 years from now, T2HK has a rather large chance to achieve a 5 sigma CP violation discovery (75% or 55%, depending on whether the mass hierarchy is known or not). This is to be compared with the 90% (30%) probability that NF10 (LBNE) would have to observe the same signal at 5 sigma. A hierarchy measurement at 5 sigma is achievable at both LBNE and NF10 with more than 90% probability, irrespectively of the outcome of T2K and NO nu A. We also find that if LBNE or a similar very long baseline super-beam is the only next generation facility to be built, then it is very useful to continue running T2K and NO nu A (or at least T2K) beyond their original schedule in order to increase the CP violation discovery chances, given their complementarity.

Abstract: We explore how well reactor antineutrino experiments can constrain or measure the loss of quantum coherence in neutrino oscillations. We assume that decoherence effects are encoded in the size of the neutrino wave-packet, sigma. We find that the current experiments Daya Bay and the Reactor Experiment for Neutrino Oscillation (RENO) already constrain sigma >1.0x10(-4) nm and estimate that future data from the Jiangmen Underground Neutrino Observatory (JUNO) would be sensitive to sigma <2.1x10(-3) nm. If the effects of loss of coherence are within the sensitivity of JUNO, we expect sigma to be measured with good precision. The discovery of nontrivial decoherence effects in JUNO would indicate that our understanding of the coherence of neutrino sources is, at least, incomplete.

Abstract: We explore the potential of several Neutrino Factory (NF) setups to constrain, discover and measure new physics effects due to Non-Standard Interactions (NSI) in propagation through Earth matter. We first study the impact of NSI in the measurement of theta(13): we find that these could be large due to strong correlations of theta(13) with NSI parameters in the golden channel, and the inclusion of a detector at the magic baseline is crucial in order to reduce them as much as possible. We present, then, the sensitivity of the considered NF setups to the NSI parameters, paying special attention to correlations arising between them and the standard oscillation parameters, when all NSI parameters are introduced at once. Off-diagonal NSI parameters could be tested down to the level of 10(-3), whereas the diagonal combinations (epsilon(ee) – epsilon(tau tau)) and (epsilon(mu mu) – epsilon(tau tau)) can be tested down to 10(-1) and 10(-2), respectively. The possibilities of observing CP violation in this context are also explored, by presenting a first scan of the CP discovery potential of the NF setups to the phases phi(e mu), phi(e tau) and delta. We study separately the case where CP violation comes only from non-standard sources, and the case where it is entangled with the standard source, delta. In case delta turns out to be CP conserving, the interesting possibility of observing CP violation for reasonably small values of the NSI parameters emerges.