Neutrino physics at the turn of the millennium

I discuss the implications of the latest data on solar and atmospheric neutrinos which strongly indicate the need for physics beyond the Standard Model. I review the theoretical options for reconciling these data in terms of three-neutrino oscillations. Even though not implied by the data, bimaximal models of neutrino mixing emerge as an attractive possibility. Supersymmetry with broken R-parity provides a predictive way to incorporate it, opening the possibility of testing neutrino anomalies at high-energy collider experiments such as the LHC or at the upcoming long-baseline or neutrino factory experiments. Reconciling, in addition, the hint provided by the LSND experiment requires a fourth, light sterile, neutrino. The simplest theoretical scenarios are the most symmetric ones, in which two of the four neutrinos are maximally mixed and lie at the LSND scale, while the others are at the solar mass scale. The lightness of the sterile neutrino, the nearly maximal atmospheric neutrino mixing, and the generation of Δm _⊙ ² &; Δm _atm ² all follow naturally from the assumed lepton-number symmetry and its breaking. These two basic schemes can be distinguished at neutral-current-sensitive solar &; atmospheric neutrino experiments such as the Sudbury Neutrino Observatory. However, underground experiments have not yet proven neutrino masses, since there is a variety of alternative mechanisms. For example, flavor changing interactions can play an important role in the explanation of solar and of contained atmospheric data and could be tested through effects such as μ → e+γ, μ-e conversion in nuclei, unaccompanied by neutrino-less double beta decay. Conversely, the room is still open for heavy unstable neutrinos. A short-lived ν_μ might play a role in the explanation of the atmospheric data. Finally, in the presence of a sterile neutrino v_s, a long-lived ν_τ in the MeV range could delay the time at which the matter and radiation contributions to the energy density of the Universe become equal, reducing the density fluctuations on the smaller scales and rescuing the standard cold-dark-matter scenario for structure formation. In this case, the light v_e ν_μ, and v_s would account for the solar and atmospheric data.     

The mixing angles in matter for three generations of neutrinos and the MSW mechanism

Mikheyev and Smirnov have recently shown that oscillations between two species of neutrinos may be amplified in matter. We give analytic expressions for the energy eigenvalues, all the mixing angles and the CP-violating phase in matter for three generations of neutrinos using the Fritzsch parametrization for the flavor mixing matrix. For clearly separated neutrino masses Δm ₃₁ ² ?Δm ₂₁ ² we find two MSW resonance effects—one forv _e ?v _µ and one forv _e ?v _τ conversions —which can each be approximated by a separate two neutrino treatment as has been recently shown by Kuo and Pantaleone. Nearly degenerate neutrino masses Δm ₃₁ ² ～Δm ₂₁ ² on the other hand lead to only one resonance region withs _{1 2} ^{m 2} no longer necessarily approaching 1 for very high densities.     

Neutrino masses and mixings based on a special set of quark mass matrices (II)

In the framework of a 6×6 neutrino mass matrix with the standard seesaw mechanism, simple empirical forms are used for the leptonic Dirac mass submatrices which exhibit hierarchical chiral symmetry-breaking structure with just six parameters, as suggested by our previous work with quark mass matrices. Through a Monte Carlo analysis of Euler angle rotations applied to diagonal forms for the right-handed Majorana mass submatrix, we generate scatter plots in the δm ₂₃ ² vs sin²2θ ₂₃ and δm ₁₃ ² vs sin²2θ ₁₃ oscillation planes for a fixed point in the nonadiabatic MSW band. Only a small, statistically insignificant, segment of the 23 mixing plane exists corresponding to depletions of both the solarv _e and atmosphericv _μ fluxes; however, for such solutions the righthanded Majorana submatrix exhibits a hierarchical chiral symmetry-breaking form remarkably similar to that for the Dirac submatrices.     

Predicting leptonic CP violation in the light of the Daya Bay result on θ 13

In the light of the recent Daya Bay result $\theta_{13}^{\mathrm{DB}}=8.8^{\circ}\pm0.8^{\circ}$ , we reconsider the model presented in Meloni et?al. (J. Phys.?G 38:015003, 2011), showing that, when all neutrino oscillation parameters are taken at their best fit values of Schwetz et?al. (New J. Phys. 10:113011,?2008) and where $\theta_{13}=\theta_{13}^{\mathrm{DB}}$ , the predicted values of the CP phase are ????±??/4.     

A study ofv e −v μ universality and search for neutrino oscillations

In the SKAT neutrino bubble chamber experiment at the Serpukhov accelerator we observe 83 events with electrons and no further lepton in the final state. Comparing the ratio of electron to muon charged current events at energies 3<E _v <30 GeV with that expected fromv _e -beam background assuming lepton universality we find \(R = (N_{e^ - } /N_{\mu ^ - } )_{\exp } /(N_{e^ - } /N_{\mu ^ - } )_{calc} = 0.98 \pm 0.15\) . Furthermore we compare experimental observations and theoretical expectations for some differential distributions of the electron-neutrino charged current reaction. No significant deviation from lepton universality is found. Looking in the charged current reaction for oscillations of muon to electron type neutrinos we find no effect down to the 90% confidence limits Δm ² =1.3 eV² at sin²2θ=1 and sin²2θ=2.5·10^?3 at Δm ²=60 eV².     

中微子非标准相互作用对大亚湾实验的影响

大亚湾中微子实验的目标是测量中微子混合矩阵中的最小混合角θ13.如果考虑中微子的非标准相互作用(NSIs),中微子的振荡概率公式要做相应的改写,其效应将和θ13纠缠在一起,从而降低了实验对θ13的敏感度(sensitivity).讨论了在NSIs存在的情况下大亚湾实验对θ13的敏感度,发现这个实验不可能同时测量出NSIs和θ13的值.由于当θ13=0时反应堆产生的反中微子将没有振荡现象(NSIs的效应也将消失),如果大亚湾实验测量到了中微子振荡效应,那将表明θ13≠0;但是,由于非零的θ13的效应和NSIs的效应有可能抵消而导致中微子没有振荡.如果大亚湾实验没有测量到中微子振荡,不能排除非零的θ13.     

The\overline {MS} and on-shell renormalization schemes in the analysis of neutrino scattering experiments

The relationship between the \(\overline {MS} \) and on-shell renormalization schemes is discussed and the correction, for finite top quark mass, to the formula connecting sin² θ _W =1?M _W ² /M _Z ² and sin² \(\widehat\theta _W (M_W )\) is given. A table is presented to allow easy conversion. The relative sensitivity, to the top quark and Higgs masses, of the two definitions, when extracted from semi-leptonic neutrino scattering experiments is considered.     

New results from the T2K neutrino oscillation experiment

The T2K experiment searches for the appearance of electron neutrinos in a muon neutrino beam. The rate of this process is sensitive to the neutrino mixing parameter θ ₁₃. Recent measurements that $\theta_{13} \ne 0$ imply that ν _μ → ν _e oscillations should be observable. Using all data through May 15, 2012 the T2K experiment has detected 10 candidate ν _e events, with an expected background for θ ₁₃?=?0 of 2.73±0.37 events. This 3.2σ excess of ν _e events is the strongest indication to date for appearance of electron neutrinos in a neutrino oscillation experiment, and for normal mass hierarchy and δ _CP ?=?0 yields $0.059 < \sin^2 2\theta_{13} < 0.164$ at the 68 % C.L.     

A simple modification of the maximal mixing scenario for three light neutrinos

We suggest a simple modification of the maximal mixing scenario (withS ₃ permutation symmetry) for three light neutrinos. Our neutrino mass matrix has smaller permutation symmetryS ₂(ν _μ ?ν _e ), and is consistent with all neutrino experiments except the³⁷Cl experiment. The resulting mass eigenvalues for three neutrinos arem ₁≈(2.55?1.27)×10^?3eV,m _2,3≈(0.71?1.43)eV for Δm _LSND ² =0.5?2.0eV². Then these light neutrinos can account for ～(2.4?4.8)% (6.2?12.4%) of the dark matter forh=0.8 (0.5). Our model predicts theν _μ →ν _τ oscillation probability in the range sensitive to the future experiments such as CHORUS and NOMAD.     

Search for the K L 0 → π0ν \tilde v decay at the INEP U-70 accelerator: The KLOD project

The rare decay K _L ⁰ → π⁰ν $ \tilde v $ branching ratio measurement is one of the clearest Standard Model test. Calculations based on the SM predict Br(K _L ⁰ → π⁰ν $ \tilde v $ ) ≈ 2.8 × 10^?11, but the most accurate experimental value Br(K _L ⁰ → π⁰ν $ \tilde v $ ) < 6.7 × 10^?8 (90% C.L.). We present design of a new experimental setup KLOD (U-70 accelerator, IHEP, Protvino) for K _L ⁰ → π⁰ν $ \tilde v $ branching ratio measurement. Sensitivity of the KLOD experiment will be enough for registration of 2.4 events K _L ⁰ → π⁰ν $ \tilde v $ for every 10 days of the data taking (according to SM predictions).     

Gauge boson masses and lepton mixing inO(4)⊗U(1) gauge model

The Cabibbo angle is introduced as a mixing angle of the gauge bosonsW ^± andX ^± in anO(4)?U(1) gauge model. Masses of gauge bosons are calculated to beM _W=82 (input), \(M_z = \sqrt 2 M_W s\gamma = 130\) (γ is mixing angle, sin² γ=0.21),M _x=666, andM _Y=660, in units GeV. TheW _μ ^± andZ _μ ⁰ couple to the familiar charged and neutral currents, respectively. The effective neutrino oscillation angle is found to be the Cabibbo angle.     

Neutrino-induced deuteron disintegration in an experiment at the Krasnoyarsk nuclear reactor

The results of studying antineutrino interactions with deuterons (CCD and NCD reactions) and hydrogen (CCP) at the Krasnoyarsk underground reactor with the Deuteron detector are presented. The cross sections for NCD and CCD were measured with a precision of 9%. For CCP, the precision is 3%: σ _expt ^NCD =(3.35±0.31)×10^?44 cm²/fission ²³⁵U, σ _expt ^NCD =(1.08±0.09)×10^?44 cm²/fission ²³⁵U, and σ _expt ^NCD =(6.39±0.19)×10^?43 cm²/fission ²³⁵U. The precision of the experimental results is close to the theoretical one and is in good agreement with other experiments. The limit on the parameters of antineutrino oscillations into the sterile state was obtained: Δm ²≤4.7×10^?2 eV² for sin²(2?)=1.0 (68% C.L.). A comparison of the measured and theoretical cross section gives us the neutron-neutron scattering length of a _nn(S)=?17±6 fm in the approach of zero momentum transfers. The weak neutral current constant is in good agreement with the prediction of the Standard Model: G _A ^NC =G _A ^CC /0.932±0.056.     

Photogeneration of neutrinos and axions under the stimulating effect of a strong magnetic field

Photogeneration of neutrinos and axions at nuclei, $\gamma (Ze) \uparrow \gamma (\nu \bar \nu ),\gamma a$ , and inelastic photon-photon scattering, $\gamma \gamma \uparrow \gamma (\nu \bar \nu ),\gamma a$ , are considered in the 2D covariant theory being developed for calculating matrix elements of Feynman diagrams in a strong magnetic field. Since the matrix elements of four-pole diagrams are linear functions of the magnetic induction B, the contribution of the radiative photogeneration of neutrinos at nuclei to the luminosity of magnetic neutron stars at early stages of their evolution may compete with URCA processes for values of B ～ (10³–10⁴)B ₀ (B ₀ = m ₂ ^e /|e| = 4.41 × 10¹³ G). The upper estimate of the axion mass obtained from the condition of dominance of the neutrino luminosity over the axion luminosity for the proposed values of temperature and magnetic induction is in accord with other independent results.     

Electroweak parameters from a high statistics neutrino nucleon scattering experiment

The final results from the WA 1/2 neutrino experiment in the 1984 CERN 160 GeV narrow band beam are presented. The ratiosR _ν and \(R_{\bar v} \) of neutral to charged current interaction rates of neutrinos and antineutrinos in iron are measured to beR _ν=0.3072±0.0033 and \(R_{\bar v} \) =0.382±0.016. A value of the electroweak parameter sin² θ _w = 1 ?m _W ² /m _Z ² is extracted fromR _ν. The result is sin² θ _w =0.228+0.013(m _c ?1.5)±0.0003 (theor.) wherem _c is the mass of the charmed quark in GeV form _t =60 GeV,M _H =100 GeV, ρ=1. CombiningR _ν and \(R_{\bar v} \) one obtains a value for ρ=0.991+0.023(m _c ?1.5)±0.020(exp.). Alternatively,R _ν and \(R_{\bar v} \) yield a precise value of the ratio of intermediate vector boson massesm _W /m _Z =0.880?0.007(m _c ?1.5)±0.002(exp.)±0.002(theor.). Comparison of these results with those from direct measurements of the vector boson masses are presented. In a model-independent analysis the left- and right-handed neutral current coupling constants,g _L ² andg _R ² , are determined.     

Systematic impact of spent nuclear fuel on θ13 sensitivity at reactor neutrino experiment

Reactor neutrino oscillation experiments, such as Daya Bay, Double Chooz and RENO are designed to determine the neutrino mixing angle θ13 with a sensitivity of 0.01--0.03 in sin2 2θ13 at 90% confidence level, an improvement over the current limit by more than one order of magnitude. The control of systematic uncertainties is critical to achieving the sin2 2θ13 sensitivity goal of these experiments. Antineutrinos emitted from spent nuclear fuel (SNF) would distort the soft part of energy spectrum and may introduce a non-negligible systematic uncertainty. In this article, a detailed calculation of SNF neutrinos is performed taking account of the operation of a typical reactor and the event rate in the detector is obtained. A further estimation shows that the event rate contribution of SNF neutrinos is less than 0.2% relative to the reactor neutrino signals. A global χ2 analysis shows that this uncertainty will degrade the θ13 sensitivity at a negligible level.     

Analysis of experiments on the measurement of the pion electromagnetic formfactor

We analyse the experiments [1–3] on the measurement of the pion electromagnetic formfactor in the time-like and space-like region using an expression with correct analytical properties and with the asymptotics predicted by QCD. The best fit values for the physical quantities (1) electromagnetic radius of the pion:r _π ² =0.466±0.002 fm², (2) the mass and width of the ρ (770) and the ρ′ (1600) meson:m _ρ=768±1 MeV,Г _ρ=138±1 MeV,m _ρ′=1546±26 MeV,Г _ρ'=620±60 MeV; (3) the residuesg _ρ m _ρ ² =0.676±0.003,g _ρ′ m _ρ′ ² =?(0.644±0.009); (4) the ππ-scattering lengtha ₁ ¹ =(0.1±0.01)m _π ^?3 .     

Low energy π-π resonances in the Veneziano model

We attempt to impose elastic unitarity on the forward π-π scattering using the Veneziano Amplitude together with a crossing symmetric subtraction term as an input. TheN/D method is used and thep, ? mesons are interpreted as CDD poles. The self consistency requirement led to the evalutation of the low energy parameters and theS andP-wave phase shifts. The values of the scattering lengths obtained area ₀ ⁰ =0.084m _π ^?1 ,a ₂ ⁰ =?0.024m _π ^?1 ,a ₁ ¹ =0.047m _π ^?3 .     

Hölder’s inequality for matrices

We prove that for arbitraryn×n matricesA ₁,A ₂,…,A _m and for positive real numbersp ₁,p ₂,…,p _m withp ₁ ^?1 +p ₂ ^?1 +…+p _m ^/?1 =1, the inequality 1 $$|Tr(A_1 A_2 ...A_m )^2 |< \mathop {II}\limits_{k = 1}^m [Tr(A_k^\dag A_k )^{p_k } ]P_k^{ - 1} $$ holds.     

Neutrino production of charmed particles in a hybrid experiment E-564

Cryogenically sensitive nuclear emulsion was placed inside the 15-foot bubble chamber of FNAL and exposed to a wide-band energy (up to 200 GeV) neutrino beam. 194 charged-current neutrino interactions and 13 decays of charmed particles were registered. Using the nuclear emulsion as a vertex detector with the good spectrometric properties of the 15-foot bubble chamber has allowed the decays of charmed particles to be effectively analysed. Attentions is focussed on the new physical results. Λ _c ⁺ baryon andD _s ⁺ meson decay channels, production of charmed ∑ _c baryons and Λ _c ⁺ via ∑ _c . For the first time an event interpreted as production of the excited (c \(\overline s\) )-state with mass ～2790 MeV/c² has been registered.