We describe non-standard contributions to semileptonic processes in a model independent way in terms of an SU (2) L × U (1) Y invariant effective lagrangian at the weak scale, from which we derive the low-energy effective lagrangian governing muon and beta decays. We find that the deviation from Cabibbo universality, ∆ CKM ≡ |V ud | 2 + |V us | 2 + |V ub | 2 − 1, receives contributions from four effective operators. The phenomenological bound ∆ CKM = (−1 ± 6) × 10 −4 provides strong constraints on all four operators, corresponding to an effective scale Λ > 11 TeV (90% CL). Depending on the operator, this constraint is at the same level or better then the Z pole observables. Conversely, precision electroweak constraints alone would allow universality violations as large as ∆ CKM = −0.01 (90% CL). An observed ∆ CKM = 0 at this level could be explained in terms of a single four-fermion operator which is relatively poorly constrained by electroweak precision measurements.

We survey 129 lepton number violating effective operators, consistent with the minimal Standard Model gauge group and particle content, of mass dimension up to and including eleven. Upon requiring that each one radiatively generates the observed neutrino masses, we extract an associated characteristic cutoff energy scale which we use to calculate other observable manifestations of these operators for a number of current and future experimental probes, concentrating on lepton number violating phenomena. These include searches for neutrinoless double-beta decay and rare meson, lepton, and gauge boson decays. We also consider searches at hadron/lepton collider facilities in anticipation of the LHC and the future ILC. We find that some operators are already disfavored by current data, while more are ripe to be probed by next-generation experiments. We also find that our current understanding of lepton mixing disfavors a subset of higher dimensional operators. While neutrinoless double-beta decay is the most promising signature of lepton number violation for the majority of operators, a handful is best probed by other means. We argue that a combination of constraints from various independent experimental sources will help to pinpoint the "correct" model of neutrino mass, or at least aid in narrowing down the set of possibilities.

The Standard Model augmented by the presence of gauge-singlet right-handed neutrinos proves to be an ideal scenario for accommodating nonzero neutrino masses. Among the new parameters of this "New Standard Model" are right-handed neutrino Majorana masses M . Theoretical prejudice points to M much larger than the electroweak symmetry breaking scale, but it has recently been emphasized that all M values are technically natural and should be explored. Indeed, M around 1 − 10 eV can accommodate an elegant oscillation solution to the LSND anomaly, while other M values lead to several observable consequences. We consider the phenomenology of low energy (M 1 keV) seesaw scenarios. By exploring such a framework with three right-handed neutrinos, we can consistently fit all oscillation data -including those from LSND -while partially addressing several astrophysical puzzles, including anomalous pulsar kicks, heavy element nucleosynthesis in supernovae, and the existence of warm dark matter. Furthermore, low-energy seesaws -regardless of their relation to the LSND anomaly -can also be tested by future tritium beta-decay experiments, neutrinoless double-beta decay searches, and other observables. We estimate the sensitivity of such probes to M .

Is the relatively isolated member of the neutrino mass spectrum heavier or lighter than the two closely-spaced members? This question -the character of the neutrino mass hierarchy -is of great theoretical interest. All previously identified experiments for addressing it via neutrino oscillations require that the currently unknown size of the Ue3 element of the leptonic mixing matrix (parameterized by the unknown θ13 mixing angle) be sufficiently large, and will utterly fail in the limit θ13 → 0. For this reason, we explore alternative oscillation approaches that would still succeed even if θ13 vanishes. We identify several alternatives that require neither a nonzero |Ue3| nor the presence of significant matter effects. All include multiple percent-level neutrino oscillation measurements, usually involving muon-neutrino (or antineutrino) disappearance and very long baselines. We comment on the degree of promise that these alternative approaches show.

The addition of gauge singlet fermions to the Standard Model Lagrangian renders the neutrinos massive and allows one to explain all that is experimentally known about neutrino masses and lepton mixing by varying the values of the Majorana mass parameters M for the gauge singlets and the neutrino Yukawa couplings λ. Here we explore the region of parameter space where M values are much smaller than the neutrino Dirac masses λv. In this region, neutrinos are pseudo-Dirac fermions. We find that current solar data constrain M values to be less than at least 10 −9 eV, and discuss the sensitivity of future experiments to tiny gauge singlet fermion masses. We also discuss a useful basis for analyzing pseudo-Dirac neutrino mixing effects. In particular, we identify a simple relationship between elements of M and the induced enlarged mixing matrix and new mass-squared differences. These allow one to directly relate bounds on the new mass-squared differences to bounds on the singlet fermion Majorana masses.