On neutrino mixing in matter and CP and T violation effects in neutrino oscillations

Aspects of 3-neutrino mixing and oscillations in vacuum and in matter with constant density are investigated working with a real form of the neutrino Hamiltonian. We find the (approximate) equalities θm23= θ23and δm=δ, θ23(θm23) and δ (δm) being respectively the atmospheric neutrino mixing angle and the Dirac CP violation phase in vacuum (in matter) of the neutrino mixing matrix, which are shown to represent excellent approximations for the conditions of the T2K (T2HK), T2HKK, NOνA and DUNE neutrino oscillation experiments. A new derivation of the known relation sin 2θm23sin δm=sin 2θ23sin δ is presented and it is used to obtain a correlation between the shifts of θ23and δ due to the matter effect. A derivation of the relation between the rephasing invariants which determine the magnitude of CP and T violating effects in 3-flavour neutrino oscillations in vacuum, JCP, and of the T violating effects in matter with constant density, JmT≡ Jm, reported in [1]withouta proof, is presented. It is shown that the function F which appears in this relation, Jm= JCPF , and whose explicit form was given in [1], coincides with the function ˜F in the similar relation Jm= JCP˜F derived in [2], although F and ˜F are expressed in terms of different sets of neutrino mass and mixing parameters and have completely different forms

Three-Neutrino Mixing and Combined Vacuum Oscillations and MSW Transitions of Solar Neutrinos

Assuming three flavour neutrino mixing takes place in vacuum, we investigate the possibility that the solar nu_e take part in MSW transitions in the Sun due to Delta m^2_{31} from 10^{-7} eV^2 to 10^{-4} eV^2, followed by long wave length vacuum oscillations on the way to the Earth, triggered by Delta m^2_{21} (or Delta m^2_{32}) from 10^{-12} eV^2 to 10^{-10} eV^2, Delta m^2_{31} and Delta m^2_{21} (Delta m^2_{32}) being the corresponding neutrino mass squared differences. The solar nu_e survival probability is shown to be described in this case by a simple analytic expression. Depending on whether the vacuum oscillations are due to Delta m^2_{21} or Delta m^2_{32} there are two very different types of interplay between the MSW transitions and the vacuum oscillations of the solar nu_e. Performing an analysis of the most recently published solar neutrino data we have found several qualitatively new solutions of the solar neutrino problem of the hybrid MSW transitions + vacuum oscillations type. The solutions differ in the way the pp, 7Be and 8B neutrino fluxes are affected by the transitions in the Sun and the oscillations in vacuum. The specific features of the new solutions are discussed.Comment: 37 pages Latex, 16 Postscript Figure

Flavoured resonant leptogenesis at sub-TeV scales

We consider sub-TeV scale flavoured resonant leptogenesis within the minimal type-I seesaw scenario with two right-handed singlet neutrinos N1,2forming a pseudo-Dirac pair, concentrating on the case of masses of the pseudo-Dirac pair having values M1,2100 GeV. The case when the CP violating asymme-tries in the individual lepton charges Ll, l=e, μ, τ, and in the total lepton charge Lof the Universe are generated in 1 ↔2 decay processes is investigated. We show that successful leptogenesis is possible for M1,2lying in the interval M1,2=(0.3 −100)GeV. Our results show also, in particular, that for vanishing initial N1,2abundance, flavour effects can play an important role in the generation of the baryon asymme-try, leading to an enhancement of the asymmetry by a factor up to ∼300 with respect to the “unflavoured” leptogenesis scenario

Enhancing the Seasonal Variation Effect in the Case of the Vacuum Oscillation Solution of the Solar Neutrino Problem

We study in detail the threshold energy dependence of the seasonal variation effect in the energy integrated solar neutrino signal of the Super-Kamiokande detector in the case of the $\nu_{e}\leftrightarrow \nu_{\mu,\tau}$ vacuum oscillation (VO) solution of the solar neutrino problem. We show, in particular, that for the values of $\Delta m^2$ and $\sin^22\theta$ from the VO solution region, the predicted time and threshold e^- energy ($T_{e,Th}$) dependence of the event rate factorize to a high degree of accuracy. As a consequence, the VO generated seasonal variation asymmetry is given by the product of an time-independent function of $T_{e,Th}$ and the standard geometrical asymmetry. For any given $\Delta m^2$ and $\sin^22\theta$ from the VO solution region there exists at least one value of $T_{e,Th}$ from the interval (5 - 11) MeV, for which the seasonal variation effect in the solar neutrino sample of events, formed by recoil electrons with kinetic energy $T_{e} \geq T_{e,Th}$, is either maximal or very close to the maximal; it can vary dramatically with $T_{e,Th}$. Measuring the seasonal effect in each one of a large number of samples corresponding to different values of $T_{e,Th}$ from the indicated interval, say, to $T_{e,Th} = 5; 6; 7;...; 11 MeV$, provides a very effective test of the VO solution. Predictions for the magnitude of the seasonal effect in such samples are given for a large set of representative values of $\Delta m^2$ and $\sin^22\theta$ from the VO solution region.Comment: 18 pages latex; the text includes 3 postscript figures and 3 table

Describing Analytically the Matter-Enhanced Two-Neutrino Transitions in a Medium

A general exact analytic expression for the probability of matter-enhanced two-neutrino transitions in a medium (MSW, RSFP, generated by neutrino FCNC interactions, etc.) is derived. The probability is expressed in terms of three real functions of the parameters of the transitions: the ``jump'' probability and two phases (angles). The results obtained can be utilized, in particular, in the studies of the matter-enhanced transitions/conversions of solar and supernova neutrinos. An interesting similarity between the Schroedinger equation for the radial part of the non-relativistic wave function of the hydrogen atom and the equation governing the MSW transitions of solar neutrinos in the exponentially varying matter density in the Sun is also briefly discussed.Comment: 14 pages, latex; published in Phys. Lett. B406 (1997) 35

Diffractive-Like (or Parametric-Resonance-Like?) Enhancement of the Earth (Day-Night) Effect for Solar Neutrinos Crossing the Earth Core

It is shown that the strong enhancement of the Earth (day-night) effect for solar neutrinos crossing the Earth core in the case of the small mixing angle MSW electron neutrino to muon (tau) neutrino transition solution of the solar neutrino problem is due to a new resonance effect in the solar neutrino transitions in the Earth and not just to the MSW effect in the core. The effect is in many respects similar to the electron paramagnetic resonance. The conditions for existence of this new resonance effect are discussed. They include specific constraints on the neutrino oscillation lengths in the Earth mantle and in the Earth core, thus the resonance is a ``neutrino oscillation length resonance''. The effect exhibits strong dependence on the neutrino energy. Analytic expression for the probability accounting for the solar neutrino transitions in the Earth, which provides a high precision description of the transitions, including the new resonance effect, is derived. The implications of our results for the searches of the day-night asymmetry in the solar neutrino experiments are briefly discussed. The new resonance effect is operative also in the muon neutrino to electron neutrino (electron neutrino to muon neutrino) transitions of atmospheric neutrinos crossing the Earth core.Comment: 20 pages, 2 Postscript figures, LATEX; version published in Phys. Lett. B434 (1998) 321; includes also the corrections published as Erratum in Phys. Lett. B444 (1998) 58

New Enhancement Mechanism of the Transitions in the Earth of the Solar and Atmospheric Neutrinos Crossing the Earth Core

It is shown that the $\nu_2 \to \nu_{e}$ and $\nu_{\mu} \to \nu_{e}$ ($\nu_e \to \nu_{\mu (\tau)}$) transitions respectively of the solar and atmospheric neutrinos in the Earth in the case of $\nu_e - \nu_{\mu (\tau)}$ mixing in vacuum, are strongly enhanced by a new type of resonance when the neutrinos cross the Earth core. The resonance is operative at small mixing angles but differs from the MSW one. It is in many respects similar to the electron paramagnetic resonance taking place in a specific configuration of two magnetic fields. The conditions for existence of the new resonance include, in particular, specific constraints on the neutrino oscillation lengths in the Earth mantle and in the Earth core, thus the resonance is a ``neutrino oscillation length resonance''. It leads also to enhancement of the $\nu_2 \to \nu_e$ and $\nu_e \to \nu_s$ transitions in the case of $\nu_e - \nu_s$ mixing and of the $\bar{\nu}_{\mu} \to \bar{\nu}_{s}$ (or $\nu_{\mu} \to \nu_{s}$) transitions at small mixing angles. The presence of the neutrino oscillation length resonance in the transitions of solar and atmospheric neutrinos traversing the Earth core has important implications for current and future solar and atmospheric neutrino experiments, and more specifically, for the interpretation of the results of the Super-Kamiokande experiment.Comment: 6 pages, two eps-files, one espcrc2.sty file; the text includes 2 figures. Talk given at the ``Neutrino'98'' International Conference on Neutrino Physics and Astrophysics, June 3 - 9, 1998, Takayama, Japan (to be published in the Proceedings of the Conference

Constraints from Neutrino Oscillation Experiments on the Effective Majorana Mass in Neutrinoless Double β\beta-Decay

We determine the possible values of the effective Majorana neutrino mass $|< m > |= |\sum_j U_{ej}^2 m_j|$ in the different phenomenologically viable three and four-neutrino scenarios. The quantities $U_{\alpha j}$ ($\alpha = e,\mu,\tau,...$) denote the elements of the neutrino mixing matrix and the Majorana neutrino masses $m_j$ ($j=1,2,3,...$) are ordered as $m_1 < m_2 < ...$ Assuming $m_1 \ll m_3$ in the three-neutrino case and $m_1 \ll m_4$ in the four-neutrino case, we discuss, in particular, how constraints on $| |$ depend on the mixing angle relevant in solar neutrino oscillations and on the three mass-squared differences obtained from the analyses of the solar, atmospheric and LSND data. If neutrinoless double $\beta$-decay proceeds via the mechanism involving $||$, conclusions about neutrinoless double $\beta$-decay can be drawn. If one of the two viable four-neutrino schemes (Scheme A) is realized in nature, $||$ can be as large as 1 eV and neutrinoless double $\beta$-decay could possibly be discovered in the near future. In this case a Majorana CP phase of the mixing matrix $U$ could be determined. In the other four-neutrino scheme (Scheme B) there is an upper bound on $||$ of the order of $10^{-2}$ eV. In the case of three-neutrino mixing the same is true if the neutrino mass spectrum is hierarchical, however, if there exist two quasi-degenerate neutrinos and the first neutrino has a much smaller mass, values of $||$ as large as $\sim 0.1$ eV are possible.Comment: 15 pages, REVTEX, 2 figures, final version to be published in Phys. Lett.

Non-adiabatic level crossing in (non-) resonant neutrino oscillations

We study neutrino oscillations and the level-crossing probability P_{LZ}=\exp(-\gamma_n\F_n\pi/2) in power-law like potential profiles $A(r)\propto r^n$. After showing that the resonance point coincides only for a linear profile with the point of maximal violation of adiabaticity, we point out that the ``adiabaticity'' parameter $\gamma_n$ can be calculated at an arbitrary point if the correction function \F_n is rescaled appropriately. We present a new representation for the level-crossing probability, P_{LZ}=\exp(-\kappa_n\G_n), which allows a simple numerical evaluation of $P_{LZ}$ in both the resonant and non-resonant cases and where \G_n contains the full dependence of $P_{LZ}$ on the mixing angle $\theta$. As an application we consider the case $n=-3$ important for oscillations of supernova neutrinos.Comment: 4 pages, revtex, 3 eps figure

The sign of the day-night asymmetry for solar neutrinos

A qualitative understanding of the day-night asymmetry for solar neutrinos is provided. The greater night flux in nu_e is seen to be a consequence of the fact that the matter effect in the sun and that in the earth have the same sign. It is shown in the adiabatic approximation for the sun that for all values of the mixing angle theta_V between 0 and pi/2, the night flux of neutrinos is greater than the day flux. Only for small values of theta_V where the adiabatic approximation badly fails does the sign of the day-night asymmetry reverse.Comment: 3 pages, 3 figures, typos corrected and references adde