On Non-Unitary Lepton Mixing and Neutrino Mass Observables

There are three observables related to neutrino mass, namely the kinematic mass in direct searches, the effective mass in neutrino-less double beta decay, and the sum of neutrino masses in cosmology. In the limit of exactly degenerate neutrinos there are very simple relations between those observables, and we calculate corrections due to non-zero mass splitting. We discuss how the possible non-unitarity of the lepton mixing matrix may modify these relations and find in particular that corrections due to non-unitarity can exceed the corrections due to mass splitting. We furthermore investigate constraints from neutrino-less double beta decay on mass and mixing parameters of heavy neutrinos in the type I see-saw mechanism. There are constraints from assuming that heavy neutrinos are exchanged, and constraints from assuming light neutrino exchange, which arise from an exact see-saw relation. The latter has its origin in the unitarity violation arising in see-saw scenarios. We illustrate that the limits from the latter approach are much stronger. The drastic impact on inverse neutrino-less double beta decay (e e -> W W) is studied. We furthermore discuss neutrino mixing in case there is one or more light sterile neutrino. Neutrino oscillation probabilities for long baseline neutrino oscillation experiments are considered, and the analogy to general non-unitarity phenomenology, such as zero-distance effects, is pointed out.Comment: 16 pages, 2 figures. To appear in PL

Getting Information on |U_{e3}|^2 from Neutrino-less Double Beta Decay

We consider the possibility to gain information on the lepton mixing matrix element |U_{e3}| from an improved experimental limit on the effective neutrino mass governing neutrino-less double beta decay. We show that typically a lower limit on |U_{e3}| can be set. Furthermore, we give the values of the sum of neutrino masses and |U_{e3}| which are allowed and forbidden by an experimental upper limit on the effective mass. Alternative explanations for neutrino-less double beta decay or Dirac neutrinos would be required if future measurements showed that the values lie in the respective regions. Moreover, we argue that a measurement of |U_{e3}| from neutrino-less double beta decay is very difficult due to the expected errors on the effective mass and the oscillation parameters.Comment: 17 pages, 7 figures; Comments and references added; to appear in AHEP (Advances in High Energy Physics

Reducing \theta_13 to 9 degrees

We propose to consider the possibility that the observed value of $\theta_{13}$ is not the result of a correction from an initially vanishing value, but rather the result of a correction from an initially larger value. As an explicit example of this approach, we consider analytically and numerically well-known CKM-like charged lepton corrections to a neutrino diagonalization matrix that corresponds to a certain mixing scheme. Usually this results in generating $\theta_{13} = 9^\circ$ from zero. We note here, however, that 9 is not only given by $0 + 9$, but also by $18 - 9$. Hence, the extreme case of an initial value of 18 degrees, reduced by charged lepton corrections to 9 degrees, is possible. For some cases under study new sum rules for the mixing parameters, and correlations with CP phases are found.Comment: 11 pages, 6 figure

Neutrinoless Double Beta Decay

We review the potential to probe new physics with neutrinoless double beta decay $(A,Z) \to (A,Z+2) + 2 e^-$. Both the standard long-range light neutrino mechanism as well as short-range mechanisms mediated by heavy particles are discussed. We also stress aspects of the connection to lepton number violation at colliders and the implications for baryogenesis.Comment: Review prepared for the NJP focus issue on "Neutrino Physics". 23 pages, 10 figure

Sterile Neutrino Anarchy

Lepton mixing, which requires physics beyond the Standard Model, is surprisingly compatible with a minimal, symmetryless and unbiased approach, called anarchy. This contrasts with highly involved flavor symmetry models. On the other hand, hints for light sterile neutrinos have emerged from a variety of independent experiments and observations. If confirmed, their existence would represent a groundbreaking discovery, calling for a theoretical interpretation. We discuss anarchy in the two-neutrino eV-scale seesaw framework. The distributions of mixing angles and masses according to anarchy are in agreement with global fits for the active and sterile neutrino parameters. Our minimal and economical scenario predicts the absence of neutrinoless double beta decay and one vanishing neutrino mass, and can therefore be tested in future experiments.Comment: 4 pages, 4 figures, matches published versio

Fits to SO(10) Grand Unified Models

We perform numerical fits of Grand Unified Models based on SO(10), using various combinations of 10-, 120- and 126-dimensional Higgs representations. Both the supersymmetric and non-supersymmetric versions are fitted, as well as both possible neutrino mass orderings. In contrast to most previous works, we perform the fits at the weak scale, i.e. we use RG evolution from the GUT scale, at which the GUT-relations between the various Yukawa coupling matrices hold, down to the weak scale. In addition, the right-handed neutrinos of the seesaw mechanism are integrated out one by one in the RG running. Other new features are the inclusion of recent results on the reactor neutrino mixing angle and the Higgs mass (in the non-SUSY case). As expected from vacuum stability considerations, the low Higgs mass and the large top-quark Yukawa coupling cause some pressure on the fits. A lower top-quark mass, as sometimes argued to be the result of a more consistent extraction from experimental results, can relieve this pressure and improve the fits. We give predictions for neutrino masses, including the effective one for neutrinoless double beta decay, as well as the atmospheric neutrino mixing angle and the leptonic CP phase for neutrino oscillations.Comment: 40 pages, 2 figures. Published versio

Gauged L_mu - L_tau Symmetry at the Electroweak Scale

The extension of the Standard Model by a spontaneously broken abelian gauge group based on the L(mu)-L(tau) lepton number can resolve the longstanding discrepancy between experimental and theoretical values for the magnetic moment of the muon. It furthermore naturally generates mu-tau symmetric lepton mixing, introduces neutrino non-standard interactions, and the associated gauge boson Z' serves as a mediator to the right-handed neutrino sector. A detailed fit to electroweak data is performed to identify the allowed values for the mass of Z' and its mixing with the Standard Model Z. An economical new scalar sector is constructed that spontaneously breaks the new symmetry and leads to experimental consequences such as lepton flavor violation and collider signatures. Furthermore we discuss the non-abelian extension to an SU(2)', particularly the neutrino sector.Comment: 22 pages, 7 figures; matches published versio