Short-Baseline Electron Neutrino Disappearance, Tritium Beta Decay and Neutrinoless Double-Beta Decay

We consider the interpretation of the MiniBooNE low-energy anomaly and the Gallium radioactive source experiments anomaly in terms of short-baseline electron neutrino disappearance in the framework of 3+1 four-neutrino mixing schemes. The separate fits of MiniBooNE and Gallium data are highly compatible, with close best-fit values of the effective oscillation parameters Delta m^2 and sin^2 2 theta. The combined fit gives Delta m^2 >~ 0.1 eV^2 and 0.11 < sin^2 2 theta < 0.48 at 2 sigma. We consider also the data of the Bugey and Chooz reactor antineutrino oscillation experiments and the limits on the effective electron antineutrino mass in beta-decay obtained in the Mainz and Troitsk Tritium experiments. The fit of the data of these experiments limits the value of sin^2 2 theta below 0.10 at 2 sigma. Considering the tension between the neutrino MiniBooNE and Gallium data and the antineutrino reactor and Tritium data as a statistical fluctuation, we perform a combined fit which gives Delta m^2 \simeq 2 eV and 0.01 < sin^2 2 theta < 0.13 at 2 sigma. Assuming a hierarchy of masses m_1, m_2, m_3 << m_4, the predicted contributions of m_4 to the effective neutrino masses in beta-decay and neutrinoless double-beta-decay are, respectively, between about 0.06 and 0.49 and between about 0.003 and 0.07 eV at 2 sigma. We also consider the possibility of reconciling the tension between the neutrino MiniBooNE and Gallium data and the antineutrino reactor and Tritium data with different mixings in the neutrino and antineutrino sectors. We find a 2.6 sigma indication of a mixing angle asymmetry.Comment: 14 pages; final version published in Phys.Rev.D82:053005,201

Lepton Numbers in the framework of Neutrino Mixing

In this short review we discuss the notion of lepton numbers. The strong evidence in favor of neutrino oscillations obtained recently in the Super-Kamiokande atmospheric neutrino experiment and in solar neutrino experiments imply that the law of conservation of family lepton numbers L_e, L_mu and L_tau is strongly violated. We consider the states of flavor neutrinos nu_e, nu_mu and nu_tau and we discuss the evolution of these states in space and time in the case of non-conservation of family lepton numbers due to the mixing of light neutrinos. We discuss and compare different flavor neutrino discovery experiments. We stress that experiments on the search for nu_mu->nu_tau and nu_e->nu_tau oscillations demonstrated that the flavor neutrino nu_tau is a new type of neutrino, different from nu_e and nu_mu. In the case of neutrino mixing, the lepton number (only one) is connected with the nature of massive neutrinos. Such conserved lepton number exist if massive neutrinos are Dirac particles. We review possibilities to check in future experiments whether the conserved lepton number exists.Comment: 20 page

Local demands on sterile neutrinos

In a model independent manner, we explore the local implications of a single neutrino oscillation measurement which cannot be reconciled within a three-neutrino theory. We examine this inconsistency for a single region of baseline to neutrino energy $L/E$. Assuming that sterile neutrinos account for the anomaly, we find that the {\it local} demands of this datum can require the addition to the theory of one to three sterile neutrinos. We examine the constraints which can be used to determine when more than one neutrino would be required. The results apply only to a given region of $L/E$. The question of the adequacy of the sterile neutrinos to satisfy a global analysis is not addressed here. Finally, using the results of a 3+2 analysis, we indicate values for unknown mixing matrix elements which would require two sterile neutrinos due to local demands only.Comment: 11 pages, 1 figure, discussion adde

Search for Oscillation of the Electron-Capture Decay Probability of 142^{142}Pm

We have searched for time modulation of the electron capture decay probability of $^{142}$Pm in an attempt to confirm a recent claim from a group at the Gesellschaft f\"{u}r Schwerionenforschung (GSI). We produced $^{142}$Pm via the $^{124}$Sn($^{23}$Na, 5n)$^{142}$Pm reaction at the Berkeley 88-Inch Cyclotron with a bombardment time short compared to the reported modulation period. Isotope selection by the Berkeley Gas-filled Separator is followed by implantation and a long period of monitoring the $^{142}$Nd K$_{\alpha}$ x-rays from the daughter. The decay time spectrum of the x-rays is well-described by a simple exponential and the measured half-life of 40.68(53) seconds is consistent with the accepted value. We observed no oscillatory modulation at the proposed frequency at a level 31 times smaller than that reported by Litvinov {\it et al.} (Phys. Lett. B 664 (2008) 162; arXiv:0801.2079 [nucl-ex]). A literature search for previous experiments that might have been sensitive to the reported modulation uncovered another example in $^{142}$Eu electron-capture decay. A reanalysis of the published data shows no oscillatory behavior.Comment: 12 pages (double-spaced), 6 figure

Baryon Asymmetry of the Universe without Boltzmann or Kadanoff-Baym

We present a formalism that allows the computation of the baryon asymmetry of the universe from first principles of statistical physics and quantum field theory that is applicable to certain types of beyond the Standard Model physics (such as the neutrino Minimal Standard Model -- $\nu$MSM) and does not require the solution of Boltzmann or Kadanoff-Baym equations. The formalism works if a thermal bath of Standard Model particles is very weakly coupled to a new sector (sterile neutrinos in the $\nu$MSM case) that is out-of-equilibrium. The key point that allows a computation without kinetic equations is that the number of sterile neutrinos produced during the relevant cosmological period remains small. In such a case, it is possible to expand the formal solution of the von Neumann equation perturbatively and obtain a master formula for the lepton asymmetry expressed in terms of non-equilibrium Wightman functions. The master formula neatly separates CP-violating contributions from finite temperature correlation functions and satisfies all three Sakharov conditions. These correlation functions can then be evaluated perturbatively; the validity of the perturbative expansion depends on the parameters of the model considered. Here we choose a toy model (containing only two active and two sterile neutrinos) to illustrate the use of the formalism, but it could be applied to other models.Comment: 26 pages, 10 figure

Influence of second-order corrections to the energy-dependence of neutrino flavor conversion formulae

We discuss the {\em intermediate} wave-packet formalism for analytically quantifying the energy dependence of the two-flavor conversion formula that is usually considered for analyzing neutrino oscillations and adjusting the focusing horn, target position and/or detector location of some flavor conversion experiments. Following a sequence of analytical approximations where we consider the second-order corrections in a power series expansion of the energy, we point out a {\em residual} time-dependent phase which, in addition to some well known wave-packet effects, can subtly modify the oscillation parameters and limits. In the present precision era of neutrino oscillation experiments where higher precision measurements are required, we quantify some small corrections in neutrino flavor conversion formulae which lead to a modified energy-dependence for $\nu_{\mu}\leftrightarrow\nu_{e}$ oscillations.Comment: 13 pages, 3 figure

Towards a unique formula for neutrino oscillations in vacuum

We show that all correct results obtained by applying quantum field theory to neutrino oscillations can be understood in terms of a single oscillation formula. In particular, the model proposed by Grimus and Stockinger is shown to be a subcase of the model proposed by Giunti, Kim and Lee, while the new oscillation formulas proposed by Ioannisian and Pilaftsis and by Shtanov are disproved. We derive an oscillation formula without making any relativistic assumption and taking into account the dispersion, so that the result is valid for both neutrinos and mesons. This unification gives a stronger phenomenological basis to the neutrino oscillation formula. We also prove that the coherence length can be increased without bound by more accurate energy measurements. Finally, we insist on the wave packet interpretation of the quantum field treatments of oscillations.Comment: 30 pages, 1 figure; the proof that plane wave oscillations do no exist is extended to stationary models; the influence of dispersion is explained in more detail

What can the SNO Neutral Current Rate teach us about the Solar Neutrino Anomaly

We investigate how the anticipated neutral current rate from $SNO$ will sharpen our understanding of the solar neutrino anomaly. Quantitative analyses are performed with representative values of this rate in the expected range of $0.8 - 1.2$. This would provide a $5 - 10 \sigma$ signal for $\nu_e$ transition into a state containing an active neutrino component. Assuming this state to be purely active one can estimate both the $^8B$ neutrino flux and the $\nu_e$ survival probability to a much higher precision than currently possible. Finally the measured value of the $NC$ rate will have profound implications for the mass and mixing parameters of the solar neutrino oscillation solution.Comment: Brief discussion on the first NC result from SNO added; final version to be published in the MPL

Remarks on flavor-neutrino propagators and oscillation formulae

We examine the general structure of the formulae of neutrino oscillations proposed by Blasone and Vitiello(BV). Reconstructing their formulae with the retarded propagators of the flavor neutrino fields for the case of many flavors, we can get easily the formulae which satisfy the suitable boundary conditions and are independent of arbitrary mass parameters $\{\mu_{\rho}\}$, as is obtained by BV for the case of two flavors. In this two flavor case, our formulae reduce to those obtained by BV under $T$-invariance condition. Furthermore, the reconstructed probabilities are shown to coincide with those derived with recourse to the mass Hilbert space ${\cal H}_{m}$ which is unitarily inequivalent to the flavor Hilbert space ${\cal H}_{f}$. Such a situation is not found in the corresponding construction a la BV. Then the new factors in the BV's formulae, which modify the usual oscill ation formulae, are not the trace of the flavor Hilbert space construction, but come from Bogolyubov transformation among the operators of spin-1/2 ne utrino with different masses.Comment: revtex, 16 page