Current neutrino experiments are measuring the neutrino mixing parameters with an unprecedented accuracy. The upcoming generation of neutrino experiments will be sensitive to subdominant oscillation effects that can give information on the yet-unknown neutrino parameters: the Dirac CP-violating phase, the mass ordering and the octant of $\theta_{23}$. Determining the exact values of neutrino mass and mixing parameters is crucial to test neutrino models and flavor symmetries designed to predict these neutrino parameters. In the first part of this review, we summarize the current status of the neutrino oscillation parameter determination. We consider the most recent data from all solar experiments and the atmospheric data from Super-Kamiokande, IceCube and ANTARES. We also implement the data from the reactor neutrino experiments KamLAND, Daya Bay, RENO and Double Chooz as well as the long baseline neutrino data from MINOS, T2K and NOvA. If in addition to the standard interactions, neutrinos have subdominant yet-unknown Non-Standard Interactions (NSI) with matter fields, extracting the values of these parameters will suffer from new degeneracies and ambiguities. We review such effects and formulate the conditions on the NSI parameters under which the precision measurement of neutrino oscillation parameters can be distorted. Like standard weak interactions, the non-standard interaction can be categorized into two groups: Charged Current (CC) NSI and Neutral Current (NC) NSI. Our focus will be mainly on neutral current NSI because it is possible to build a class of models that give rise to sizeable NC NSI with discernible effects on neutrino oscillation. These models are based on new $U(1)$ gauge symmetry with a gauge boson of mass $\lesssim 10$~MeV. The UV complete model should be of course electroweak invariant which in general implies that along with neutrinos, charged fermions also acquire new interactions on which there are strong bounds. We enumerate the bounds that already exist on the electroweak symmetric models and demonstrate that it is possible to build viable models avoiding all these bounds. In the end, we review methods to test these models and suggest approaches to break the degeneracies in deriving neutrino mass parameters caused by NSI.

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Neutrino oscillations and Non-Standard Interactions

The Majorana nature of neutrinos is strongly motivated from the theoretical and phenomenological point of view. A plethora of neutrino mass models, known collectively as Seesaw models, exist that could generate both a viable neutrino mass spectrum and mixing pattern. They can also lead to rich, new phenomenology, including lepton number non-conservation as well as new particles, that may be observable at collider experiments. It is therefore vital to search for such new phenomena and the mass scale associated with neutrino mass generation at high energy colliders. In this review, we consider a number of representative Seesaw scenarios as phenomenological benchmarks, including the characteristic Type I, II, and III Seesaw mechanisms, their extensions and hybridizations, as well as radiative constructions. We present new and updated predictions for analyses featuring lepton number violation and expected coverage in the theory parameter space at current and future colliders. We emphasize new production and decay channels, their phenomenological relevance and treatment across different facilities in $e^+e^-$, $e^-p$ and $pp$ collisions, as well as the available Monte Carlo tools available for studying Seesaw partners in collider environments.

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Lepton Number Violation: Seesaw Models and Their Collider Tests

Flavor structures of charged fermions and massive neutrinos

Large, nonstandard neutrino self-interactions have been shown to resolve the $\ensuremath{\sim}4\ensuremath{\sigma}$ tension in Hubble constant measurements and a milder tension in the amplitude of matter fluctuations. We demonstrate that interactions of the necessary size imply the existence of a force carrier with a large neutrino coupling ($g{10}^{\ensuremath{-}4}$) and mass in the keV--100 MeV range. This mediator is subject to stringent cosmological and laboratory bounds, and we find that nearly all realizations of such a particle are excluded by existing data unless it carries spin 0 and couples almost exclusively to $\ensuremath{\tau}$-flavored neutrinos. Furthermore, we find that the light neutrinos must be Majorana particles, and that a UV-complete model requires a nonminimal mechanism to simultaneously generate neutrino masses and appreciable self-interactions.

Constraining the Self-Interacting Neutrino Interpretation of the Hubble Tension

Charged lepton flavour violating transitions would be a clear signal of new physics beyond the Standard Model. Their search has been carried out in a variety of channels, the most sensitive being those involving a muon: however no positive evidence has been found so far. The MEG experiment has recently set the best limit on such processes by investigating the existence of the $\mu \to e\gamma$ decay. In the next decade several experiments are planned to pursue the search for $\mu \to e\gamma$, $\mu \to eee$, $\mu \to e$ conversion in nuclei, as well as on processes involving the $\tau$, to an unprecedented level of precision. In this review we want to give a pedagogical introduction on the theoretical motivations for such searches as well as on the experimental aspects upon which they are based.

Charged Lepton Flavour Violation: An Experimental and Theoretical Introduction

A plausible explanation for the lightness of neutrino masses is that neutrinos are massless at tree level, with their mass (typically Majorana) being generated radiatively at one or more loops. The new couplings, together with the suppression coming from the loop factors, imply that the new degrees of freedom cannot be too heavy (they are typically at the TeV scale). Therefore, in these models there are no large mass hierarchies and they can be tested using different searches, making their detailed phenomenological study very appealing. In particular, the new particles can be searched for at colliders and generically induce signals in lepton-flavor and lepton-number violating processes (in the case of Majorana neutrinos), which are not independent from reproducing correctly the neutrino masses and mixings. The main focus of the review is on Majorana neutrinos. We order the allowed theory space from three different perspectives: (i) using an effective operator approach to lepton number violation, (ii) by the number of loops at which the Weinberg operator is generated, (iii) within a given loop order, by the possible irreducible topologies. We also discuss in more detail some popular radiative models which involve qualitatively different features, revisiting their most important phenomenological implications. Finally, we list some promising avenues to pursue.

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From the Trees to the Forest: A Review of Radiative Neutrino Mass Models

This work studies the case where dark matter emerges from a complex scalar field charged under aU (1) global symmetry, which is spontaneously broken. The analysis considers different explicit symmetry breaking terms, motivated by discrete symmetries, and the results show that in some regions of the parameter space these scenarios may be distinguished by combining different observables, such as direct detection and collider signatures. It is also discussed the case where the stabilising symmetry could be spontaneously broken.

Juan Herrero García

Papers

From the Trees to the Forest: A Review of Radiative Neutrino Mass Models

Dark matter from a complex scalar singlet and and preservation of its stabilising symmetry