Neutrino Mass-squared Differences Research Articles

Upper bounds on lepton-number violating processes

We consider four lepton-number violating ($\mathrm{L\ensuremath{\llap{\not\;}}}$) processes: (a) neutrinoless double-beta decay $(0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta})$, (b) $\ensuremath{\Delta}L=2$ tau decays, (c) $\ensuremath{\Delta}L=2$ rare meson decays and (d) nuclear muon-positron conversion. In the absence of exotic $\mathrm{L\ensuremath{\llap{\not\;}}}$ interactions, the rates for these processes are determined by effective neutrino masses $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$, which can be related to the sum of light neutrino masses, the neutrino mass-squared differences, the neutrino mixing angles, a Dirac phase and two Majorana phases. We sample the experimentally allowed ranges of $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$ based on neutrino oscillation experiments as well as cosmological observations, and obtain a stringent upper bound $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}\ensuremath{\lesssim}0.14\text{ }\text{ }\mathrm{eV}$. We then calculate the allowed ranges for $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$ from the experimental rates of direct searches for the above $\ensuremath{\Delta}L=2$ processes. Comparing our calculated rates with the currently or soon available data, we find that only the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ experiment may be able to probe $⟨m{⟩}_{ee}$ with a sensitivity comparable to the current bound. Muon-positron conversion is next in sensitivity, while the limits of direct searches for the other $\ensuremath{\Delta}L=2$ processes are several orders of magnitude weaker than the current bounds on $⟨m{⟩}_{{\ensuremath{\ell}}_{1}{\ensuremath{\ell}}_{2}}$. Any positive signal in those direct searches would indicate new contributions to the $\mathrm{L\ensuremath{\llap{\not\;}}}$ interactions beyond those from three light Majorana neutrinos.

Neutrino Oscillations and Collider Test of the R-parity Violating Minimal Supergravity Model

We study the R-parity violating minimal supergravity models accounting for the observed neutrino masses and mixing, which can be tested in future collider experiments. The bi-large mixing can be explained by allowing five dominant tri-linear couplings $ \lambda'_{1,2,3}$ and $\lambda_{1,2}$. The desired ratio of the atmospheric and solar neutrino mass-squared differences can be obtained in a very limited parameter space where the tree-level contribution is tuned to be suppressed. In this allowed region, we quantify the correlation between the three neutrino mixing angles and the tri-linear R-parity violating couplings. Qualitatively, the relations $| \lambda'_1 | < | \lambda'_2| \sim | \lambda'_3|$, and $|\lambda_1| \sim |\lambda_2|$ are required by the large atmospheric neutrino mixing angle $\theta_{23}$ and the small angle $\theta_{13}$, and the large solar neutrino mixing angle $\theta_{12}$, respectively. Such a prediction on the couplings can be tested in the next linear colliders by observing the branching ratios of the lightest supersymmetric particle (LSP). For the stau or the neutralino LSP, the ratio $|\lambda_1|^2: |\lambda_2|^2: |\lambda_1|^2 + |\lambda_2|^2$ can be measured by establishing $Br(e\nu): Br(\mu\nu) : Br(\tau\nu)$ or $Br(\nu e^\pm \tau^\mp ): Br(\nu\mu^\pm\tau^\mp) : Br(\nu\tau^\pm\tau^\mp)$, respectively. The information on the couplings $\lambda'_i$ can be drawn by measuring $Br(l_i t \bar{b}) \propto |\lambda'_i|^2$ if the neutralino LSP is heavier than the top quark.

Review Paper. Neutrino masses, mixing and oscillations

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Bilenky S. M. 2004Review Paper. Neutrino masses, mixing and oscillationsProc. R. Soc. Lond. A.460403–443http://doi.org/10.1098/rspa.2003.1263SectionRestricted accessReview Paper. Neutrino masses, mixing and oscillations S. M. Bilenky S. M. Bilenky Joint Institute for Nuclear Research, Dubna 141980, Russia Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria 1 and Dipartimento di Fisica Teorica, Universitá di Torino, 10125 Torino, Italy Google Scholar Find this author on PubMed Search for more papers by this author S. M. Bilenky S. M. Bilenky Joint Institute for Nuclear Research, Dubna 141980, Russia Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria 1 and Dipartimento di Fisica Teorica, Universitá di Torino, 10125 Torino, Italy Google Scholar Find this author on PubMed Search for more papers by this author Published:08 February 2004https://doi.org/10.1098/rspa.2003.1263AbstractNeutrino mixing and the basics of neutrino oscillations in a vacuum and in matter are considered. Recent evidence in favour of neutrino oscillations, obtained in the Super–Kamiokande, Sudbury Neutrino Observatory (SNO), Kamioka liquid–scintillator anti–neutrino detector (KamLAND) and other neutrino experiments, is discussed. Neutrino oscillations in the solar and atmospheric ranges of the neutrino mass-squared differences are considered in the framework of the minimal scheme with the mixing of three massive neutrinos. Results of the tritium β–decay experiments and experiments on the search for neutrinoless double β–decay are briefly discussed. Next Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Pismak Y and Shakhova O (2021) Neutrino Oscillations in the Model of Interaction of Spinor Fields with Zero-Range Potential Concentrated on a Plane, Symmetry, 10.3390/sym13112180, 13:11, (2180) Nanni L (2020) Production of tachyonic neutrino in matter, Journal of Physics Communications, 10.1088/2399-6528/ab7056, 4:2, (025003), Online publication date: 1-Feb-2020. Naumov D and Naumov V (2020) Quantum Field Theory of Neutrino Oscillations, Physics of Particles and Nuclei, 10.1134/S1063779620010050, 51:1, (1-106), Online publication date: 1-Jan-2020. Moreno G and Zamora-Saa J (2016) Rare meson decays with three pairs of quasidegenerate heavy neutrinos, Physical Review D, 10.1103/PhysRevD.94.093005, 94:9 Tomaschitz R (2013) Mass generation in the aether: Neutrino oscillations and massive gauge fields, Physics Letters A, 10.1016/j.physleta.2013.02.028, 377:13, (945-951), Online publication date: 1-May-2013. Lobanov A and Studenikin A (2004) Neutrino self-polarization effect in matter, Physics Letters B, 10.1016/j.physletb.2004.09.037, 601:3-4, (171-175), Online publication date: 1-Nov-2004. Dvornikov M and Studenikin A (2004) Electromagnetic form factors of a massive neutrino, Journal of Experimental and Theoretical Physics, 10.1134/1.1800181, 99:2, (254-269), Online publication date: 1-Aug-2004. This Issue08 February 2004Volume 460Issue 2042 Article InformationDOI:https://doi.org/10.1098/rspa.2003.1263Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/02/2004Published in print08/02/2004 License: Citations and impact KeywordsNeutrinoless Double β–DecayNeutrino OscillationsNeutrino Masses

One-loop corrections to the seesaw mechanism in the multi-Higgs-doublet standard model

We consider the lepton sector of the standard model and allow for an arbitrary number of Higgs doublets and, moreover, for the presence of right-handed neutrino singlets which enable the seesaw mechanism. In this framework, we identify and calculate the dominant one-loop radiative corrections to the tree-level mass matrix of the light neutrinos. The interesting feature is that both the tree-level and the one-loop contributions to the light-neutrino mass matrix are quadratic in the Yukawa couplings, with the effect that the one-loop contribution is smaller than the tree-level one mainly because of the one-loop factor (16π2)−1. We also point out the possibility of generating radiatively—in this framework—the ratio of solar over atmospheric neutrino mass-squared differences, as needed for the large-mixing-angle MSW solution of the solar-neutrino problem.

Back reaction of Einstein’s gravitational waves as the origin of natal pulsar kicks

At the early core bounce of a supernova collapse rapid convective overturn along with gradients in density and temperature in the neutrino-decoupling zone drives anisotropic neutrino flux. If then active-to-sterile $({\ensuremath{\nu}}_{\overline{\ensuremath{\tau}},\overline{\ensuremath{\mu}}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{s})$ neutrino oscillations in the dense core take place, gravitational radiation should be emitted the entire oscillation length. Since the oscillation feeds mass energy up into (or drains it from) the new species, the large neutrino mass-squared difference ${(10}^{4}$ ${\mathrm{eV}}^{2}\ensuremath{\lesssim}\ensuremath{\Delta}{m}^{2}\ensuremath{\lesssim}{10}^{8}$ ${\mathrm{eV}}^{2})$ implies that a huge amount of energy is released as gravity waves. This gravitational waves luminosity is larger than the one from either neutrino convection and cooling or perturbed matter distributions. I identify the back-reaction force (mass and current multipoles) of the gravitational wave burst generated over the oscillation time scale as the pulsar thruster.

Majorana neutrinos, neutrino mass spectrum,CPviolation, and neutrinoless double β decay. II. Mixing of four neutrinos

Assuming four-neutrino mixing and massive Majorana neutrinos, we study the implications of neutrino oscillation solutions of the solar and atmospheric neutrino problems, of the results of the Liquid Scintillation Neutrino Detector (LSND) experiment and of the constraints on neutrino oscillations, obtained in reactor and accelerator experiments, for the predictions of the effective Majorana mass in neutrinoless double beta $((\ensuremath{\beta}\ensuremath{\beta}{)}_{0\ensuremath{\nu}}\ensuremath{-})$ decay, |〈m〉|. All four-neutrino mass spectra compatible with the existing neutrino mass and oscillation data are considered: $2+2A,B$ and $3+1A,B,C.$ The general case of CP nonconservation is investigated. The predicted values of |〈m〉| depend strongly on the value of the lightest neutrino mass ${m}_{1},$ on the type of the neutrino mass spectrum, on the LSND neutrino mass-squared difference $\ensuremath{\Delta}{m}_{\mathrm{SBL}}^{2},$ on the solution of the solar neutrino problem, as well as on the values of the three Majorana CP-violating phases, present in the lepton mixing matrix. If CP invariance holds, |〈m〉| is very sensitive to the values of the relative CP parities of the massive Majorana neutrinos. We also analyze in detail the question of whether a measurement of $|〈m〉|\ensuremath{\gtrsim}0.01\mathrm{eV}$ in the next generation of $(\ensuremath{\beta}\ensuremath{\beta}{)}_{0\ensuremath{\nu}}$-decay experiments (NEMO3, CUORE, EXO, and GENIUS), combined with the data from the solar, atmospheric, reactor and accelerator neutrino oscillation experiments and from the future neutrino mass ${}^{3}\mathrm{H}$ \ensuremath{\beta}-decay experiment KATRIN would allow us, and under what conditions, (i) to determine the absolute values of the neutrino masses and thus the neutrino mass spectrum, and (ii) to establish the existence of CP violation in the lepton sector. We have pointed out, in particular, that the $2+2A$ and $3+1A$ spectra can be critically tested by the KATRIN experiment. The latter, in particular, can provide information on the value of the lightest neutrino mass ${m}_{1}$ in the cases of the spectra $2+2A,$ $3+1A,$ $3+1B,$ and $3+1C.$ For these neutrino mass spectra there exists a direct relation between |〈m〉| or ${m}_{1}$ and the neutrino mass measured in ${}^{3}\mathrm{H}$ \ensuremath{\beta} decay, ${m}_{{\ensuremath{\nu}}_{e}},$ and the measurement of $|〈m〉|\ensuremath{\gtrsim}0.01\mathrm{eV}$ and of ${m}_{{\ensuremath{\nu}}_{e}}\ensuremath{\gtrsim}0.4\mathrm{eV}$ will provide the unique possibility to determine the absolute values of all four neutrino masses and to obtain information on CP violation in the lepton sector.

Spontaneous breaking of flavor symmetry and naturalness of nearly degenerate neutrino masses and bi-maximal mixing

The gauge model with $SO(3)_{F}$ flavor symmetry and three Higgs triplets is studied. We show how the intriguing nearly degenerate neutrino mass and bi-maximal mixing scenario comes out naturally after spontaneous breaking of the symmetry. The hierarchy between the neutrino mass-squared differences, which is needed for reconciling both solar and atmospheric neutrino data, is naturally resulted from an approximate permutation symmetry. The model can also lead to interesting phenomena on lepton-flavor violations via the $SO(3)_{F}$ gauge interactions.

SO(3) gauge model for neutrino masses and oscillations

I mainly describe neutrino masses and oscillations in the gauge model with SO(3) F lepton flavor symmetry and with two Higgs triplets. It is shown how the maximal mixing between v μ and v τ neutrinos comes out naturally after spontaneous breaking of the symmetry. The nearly two-flavor mixing scenario is resulted naturally from an approximate permutation symmetry between the two Higgs triplets. The hierarchy between the neutrino mass-squared differences, which is needed for reconciling both solar and atmospheric neutrino data, leads to an almost maximal mixing between v e and v μ neutrinos. Thus the model favors the intriguing bi-maximal mixing scenario. The three Majorana neutrino masses are allowed to be nearly degenerate and large enough to play a significant cosmological role. The model can also lead to interesting phenomena on lepton-flavor violations via the SO(3) F gauge interactions.

Matter effects in four-neutrino mixing

The evidence in favor of neutrino oscillations implies the existence of at least three independent neutrino mass-squared differences. If the Liquid Scintillation Neutrino Detector (LSND) results are confirmed, transitions into active and sterile neutrinos can take place simultaneously for both solar and atmospheric neutrinos. In this paper we present a formalism for the calculation of the transition probabilities into active and sterile neutrinos for solar ${\ensuremath{\nu}}_{e}\mathrm{'}\mathrm{s}$ and atmospheric ${\ensuremath{\nu}}_{\ensuremath{\mu}}\mathrm{'}\mathrm{s},$ taking into account the matter effects in the Sun and in the Earth. We find that the solar neutrino transition probabilities depend on just one single additional parameter compared to that of the standard two-generation analysis, while for atmospheric neutrinos two additional mixing angles are necessary to analyze the data in addition to those of the usual two-generation analysis.

A redetermination of the neutrino mass-squared difference in tri-maximal mixing with terrestrial matter effects

We re-fit for the neutrino mass-squared difference Δm 2 in the threefold maximal (i.e. tri-maximal) mixing scenario using recent CHOOZ and SUPER-K data, taking account of matter effects in the Earth. While matter effects have little influence on reactor experiments and proposed long-baseline accelerator experiments with L ≲ 1000 km, they are highly significant for atmospheric experiments, suppressing naturally ν e mixing and enhancing ν μ − ν τ mixing, so as to effectively remove the experimental distinction between threefold maximal and twofold maximal ν μ − ν τ mixing. Threefold maximal mixing is fully consistent with the CHOOZ and SUPER-K data and the best-fit value for the neutrino mass-squared difference is Δm 2≃(0.98± 0.30 0.23)×10 −3 eV 2.

Further evidence for threefold maximal lepton mixing and a hierarchical spectrum of neutrino mass-squared differences

The phenomenological case for threefold maximal lepton mixing is strengthened by more detailed comparison with existing data. The atmospheric neutrino data are self-consistent and in good agreement with the threefold maximal mixing prediction R = 2 3 ( χ 2 DOF = 4.3 5 , CL = 51%). Including partially-contained event data, the zenith angle dependence also points to threefold maximal mixing, ruling out a range of mixing schemes, including that of Fritzsch and Xing. Accounting for de facto uncertainties in solar neutrino fluxes, the solar neutrino data (including HOMESTAKE) are shown to be consistent with threefold maximal mixing ( χ 2 DOF = 5.1 3 , CL = 16%), as is the upper limit from the LSND appearance experiment. Detailed predictions for forthcoming long-base-line reactor and accelerator experiments are presented.

Effects of random density fluctuations on matter-enhanced neutrino flavor transitions in supernovas and implications for supernova dynamics and nucleosynthesis.

We calculate the effects of random density fluctuations on two-neutrino flavor transformations (${\nu}_{\tau(\mu)} \rightleftharpoons {\nu}_e$) in the post-core-bounce supernova environment. In particular, we follow numerically the flavor evolution of neutrino states propagating through a stochastic field of density fluctuations. We examine the approach to neutrino flavor depolarization, and study the effects of this phenomenon in both the early shock reheating epoch and the later r-process nucleosynthesis epoch. Our results suggest that significant fluctuation-induced neutrino flavor depolarization effects occur in these environments only when the zero-order (without density fluctautions) evolution of the neutrino states includes adiabatic propagation through resonances (mass level crossings). In the shock reheating epoch, depolarization effects from fluctuations with amplitudes larger than 0.05% of the local matter density can cause an increase in the heating rate of the material behind the shock compared to the case with no neutrino flavor transformation - but this corresponds to a significant decrease in this quantity relative to the case with adiabatic neutrino transformation. If r-process nucleosynthesis is to occur during the late stages of supernova evolution, then the requirement of neutron-rich conditions excludes a region of neutrino mass-squared difference and vacuum mixing angle ($\delta m^2,\ \sin^22\theta$) parameter space for neutrino flavor transformation. We find that in the presence of stochastic fluctuations, this excluded region is not significantly altered even for random fluctuations with an amplitude of 1% of the local matter density.