Abstract: We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry Gf, and HS be the subgroup of Gf that remains unbroken under a generic vacuum expectation value < S >; we show that the EFT Lagrangian constructed from the spurion analysis saturates the EFT Lagrangian without the spurions but restricted to HS invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of HS invariants in the EFT without the spurions, demonstrating the saturation theorem. Motivated by phenomenological connections, we provide linearly independent spurion polynomials for selected lepton flavor covariants. A supplementary material file supplies , a Mathematica notebook that provides functions for computing general Hilbert series of invariants and covariants of compact classical groups. It presents examples demonstrating the use of the code, including the Hilbert series for our MLFV scenarios.

Abstract: The discovery of neutrino masses has revealed a new flavour sector in the Standard Model. Just like the quark flavour sector, it contains a seed of CP violation, resulting in an asymmetric behaviour of matter and antimatter. It is argued that this new source of leptonic CP violation may be discovered in more precise neutrino oscillation experiments involving neutrino beams with energies in the GeV range that will be sent to distances of a few thousand kilometres.

Abstract: We present an extension of the Casas-Ibarra parametrization that applies to all possible Majorana neutrino mass models. This framework allows us to systematically identify minimal models, defined as those with the smallest number of free parameters. We further analyze the phenomenologically relevant combination of the Yukawa matrix, y dagger y, and show that in certain scenarios it exhibits an unexpected reduction in the number of free parameters, depending on just one real degree of freedom. Finally, the application of our results is illustrated in specific models, which can be tested or falsified due to their definite experimental predictions in heavy neutrino and charged lepton flavor violating decays.

Abstract: The origin of neutrino masses and the nature of dark matter are two in most pressing open questions in modern astro-particle physics. We consider here the possibility that these two problems are related, and review some theoretical scenarios which offer common solutions. A simple possibility is that the dark matter particle emerges in minimal realizations of the seesaw mechanism, as in the majoron and sterile neutrino scenarios. We present the theoretical motivation for both models and discuss their phenomenology, confronting the predictions of these scenarios with cosmological and astrophysical observations. Finally, we discuss the possibility that the stability of dark matter originates from a flavor symmetry of the leptonic sector. We review a proposal based on an A(4) flavor symmetry.

Abstract: A new algorithm is developed to identify the flavour of neutral B mesons at production in pp collisions by utilising all tracks from the hadronisation process. The algorithm is calibrated separately for B-0 and B-s(0) mesons using B-0 -> J/psi K+pi(-) and B-s(0) -> D-s(-)pi(+) decays from pp collision data collected by the LHCb experiment at a centre-of-mass energy of 13TeV. This new algorithm improves the tagging power by 35% for B-0 mesons and 20% for B-0 s mesons when compared to the combined performance of the existing LHCb flavour-tagging algorithms.