The Physical Range of Majorana Neutrino Mixing Parameters

If neutrinos are Majorana fermions, the lepton mixing parameter space consists of six mixing parameters: three mixing angles and three CP-odd phases. A related issue concerns the physical range of the mixing parameters. What values should these take so that all physically distinguishable mixing scenarios are realized? We present a detailed discussion of the lepton mixing parameter space in the case of two and three active neutrinos, and in the case of three active and N sterile neutrinos. We emphasize that this question, which has been a source of confusion even among "neutrino" physicists, is connected to an unambiguous definition of the neutrino mass eigenstates. We find that all Majorana phases can always be constrained to lie between 0 and pi, and that all mixing angles can be chosen positive and at most less than or equal to pi/2 provided the Dirac phases are allowed to vary between -pi and pi. We illustrate our results with several examples. Finally, we point out that, in the case of new flavor-changing neutrino interactions, the lepton mixing parameter space may need to be enlarged. We properly qualify this statement, and offer concrete examples.Comment: 16 pages, 2 .eps figures, references added, minor typos correcte

Physics with Beam Tau-Neutrino Appearance at DUNE

We explore the capabilities of the upcoming Deep Underground Neutrino Experiment (DUNE) to measure $\nu_\tau$ charged-current interactions and the associated oscillation probability $P(\nu_\mu \to \nu_\tau)$ at its far detector, concentrating on how such results can be used to probe neutrino properties and interactions. DUNE has the potential to identify significantly more $\nu_\tau$ events than all existing experiments and can use this data sample to nontrivially test the three-massive-neutrinos paradigm by providing complementary measurements to those from the $\nu_e$ appearance and $\nu_\mu$ disappearance channels. We further discuss the sensitivity of the $\nu_\tau$ appearance channel to several hypotheses for the physics that may lurk beyond the three-massive-neutrinos paradigm: a non-unitary lepton mixing matrix, the $3+1$ light neutrinos hypothesis, and the existence of non-standard neutral-current neutrino interactions. Throughout, we also consider the relative benefits of the proposed high-energy tune of the Long-Baseline Neutrino Facility (LBNF) beam-line.Comment: 23 pages, 14 figures, 2 appendice

Neutrinos Have Mass - So What?

In this brief review, I discuss the new physics unveiled by neutrino oscillation experiments over the past several years, and discuss several attempts at understanding the mechanism behind neutrino masses and lepton mixing. It is fair to say that, while significant theoretical progress has been made, we are yet to construct a coherent picture that naturally explains non-zero, yet tiny, neutrino masses and the newly revealed, puzzling patterns of lepton mixing. I discuss what the challenges are, and point to the fact that more experimental input (from both neutrino and non-neutrino experiments) is dearly required - and that new data is expected to reveal, in the next several years, new information. Finally, I draw attention to the fact that neutrinos may have only just begun to reshape fundamental physics, given the fact that we are still to explain the LSND anomaly and because the neutrino oscillation phenomenon is ultimately sensitive to very small new-physics effects.Comment: invited brief review, 15 pages, 1 eps figure, typo corrected, reference adde

Low Temperature Static and Dynamic Behavior of the Two-Dimensional Easy-Axis Heisenberg Model

We apply the self-consistent harmonic approximation (SCHA) to study static and dynamic properties of the two-dimensional classical Heisenberg model with easy-axis anisotropy. The static properties obtained are magnetization and spin wave energy as functions of temperature, and the critical temperature as a function of the easy-axis anisotropy. We also calculate the dynamic correlation functions using the SCHA renormalized spin wave energy. Our analytical results, for both static properties and dynamic correlation functions, are compared to numerical simulation data combining cluster-Monte Carlo algorithms and Spin Dynamics. The comparison allows us to conclude that far below the transition temperature, where the SCHA is valid, spin waves are responsible for all relevant features observed in the numerical simulation data; topological excitations do not seem to contribute appreciably. For temperatures closer to the transition temperature, there are differences between the dynamic correlation functions from SCHA theory and Spin Dynamics; these may be due to the presence of domain walls and solitons.Comment: 12 pages, 14 figure

Vortex motion in a finite-size easy-plane ferromagnet and application to a nanodot

We study the motion of a non-planar vortex in a circular easy-plane ferromagnet, which imitates a magnetic nanodot. Analysis was done using numerical simulations and a new collective variable theory which includes the coupling of Goldstone-like mode with the vortex center. Without magnetic field the vortex follows a spiral orbit which we calculate. When a rotating in-plane magnetic field is included, the vortex tends to a stable limit cycle which exists in a significant range of field amplitude B and frequency $\omega$ for a given system size L. For a fixed $\omega$, the radius R of the orbital motion is proportional to L while the orbital frequency $\Omega$ varies as 1/L and is significantly smaller than $\omega$. Since the limit cycle is caused by the interplay between the magnetization and the vortex motion, the internal mode is essential in the collective variable theory which then gives the correct estimate and dependency for the orbit radius $R\sim B L/\omega$. Using this simple theory we indicate how an ac magnetic field can be used to control vortices observed in real magnetic nanodots.Comment: 15 pages (RevTeX), 14 figures (eps

Parameterizing Majorana Neutrino Couplings in the Higgs Sector

Nonzero masses for the active neutrinos - regardless of their nature or origin - arise only after electroweak symmetry breaking. We discuss the parameterization of neutrino couplings to a Higgs sector consisting of one SU(2)_L scalar doublet and one SU(2)_L scalar triplet, and allow for right-handed neutrinos whose Majorana mass parameters arise from the vacuum expectation value of a Standard Model scalar singlet. If the neutrinos are Majorana fermions, all Yukawa couplings can be expressed as functions of the neutrino mass eigenvalues and a subset of the elements of the neutrino mixing matrix. In the mass basis, the Yukawa couplings are, in general, not diagonal. This is to be contrasted to the case of charged-fermions or Dirac neutrinos, where couplings to the Higgs-boson are diagonal in the mass basis and proportional only to the fermion masses. Nonetheless, all physically distinguishable parameters can be reached if all neutrino masses are constrained to be positive, all mixing angles constrained to lie in the first quadrant (theta in [0,pi/2]), and all Majorana phases to lie in the first two quadrants (phi in [0,pi]), as long as all Dirac phases vary within the entire unit circle (delta in [0,2pi}). We discuss several concrete examples and comment on the Casas-Ibarra parameterization for the neutrino Yukawa couplings in the case of the type-I Seesaw Lagrangian.Comment: 13 pages, 2 eps figure

On The Decaying-Sterile Neutrino Solution to the Electron (Anti)Neutrino Appearance Anomalies

We explore the hypothesis that the unexplained data from LSND and MiniBooNE are evidence for a new, heavy neutrino mass-eigenstate that mixes with the muon-type neutrino and decays into an electron-type neutrino and a new, very light scalar particle. We consider two different decay scenarios, one with Majorana neutrinos, one with Dirac neutrinos; both fit the data equally well. We find a reasonable, albeit not excellent, fit to the data of MiniBooNE and LSND. The decaying-sterile-neutrino hypothesis, however, cleanly evades constraints from disappearance searches and precision measurements of leptonic meson decays, as long as $1~{\rm MeV}\gtrsim m_4\gtrsim 10$~keV. The SBN program at Fermilab should be able to definitively test the decaying-sterile-neutrino hypothesis.Comment: This version v2 has been accepted for publication in JHEP. The changes from previous version are: inclusion of the data from KARMEN in the analysis, a new subsection about the sensitivity of SBN to nonzero decay effects, an new appendix describing the details of MiniBooNE analysis, additional references and some other minor change

Deviation of Atmospheric Mixing from Maximal and Structure in the Leptonic Flavor Sector

I attempt to quantify how far from maximal one should expect the atmospheric mixing angle to be given a neutrino mass-matrix that leads, at zeroth order, to a nu_3 mass-eigenstate that is 0% nu_e, 50% nu_mu, and 50% nu_tau. This is done by assuming that the solar mass-squared difference is induced by an "anarchical" first order perturbation, an approach than can naturally lead to experimentally allowed values for all oscillation parameters. In particular, both |cos 2theta_atm| (the measure for the deviation of atmospheric mixing from maximal) and |U_e3| are of order sqrt(Delta m^2_sol/Delta m^2_atm) in the case of a normal neutrino mass-hierarchy, or of order Delta m^2_sol/Delta m^2_atm in the case of an inverted one. Hence, if any of the textures analyzed here has anything to do with reality, next-generation neutrino experiments can see a nonzero cos 2theta_atm in the case of a normal mass-hierarchy, while in the case of an inverted mass-hierarchy only neutrino factories should be able to see a deviation of sin^2 2theta_atm from 1.Comment: 12 pages, no figures, references and acknowledgments adde