Lepton mixing and neutrino oscillations

The present article is a review of phenomena connected with neutrino oscillations. Mixing of two neutrinos (Majorana as well as Dirac) with masses m₁ and m₂ is considered in detail. It is shown that the hypothesis of lepton mixing is not in contradiction with the existing data if |m₁²?m₂²| ? 1 (eV)². Possible experiments designed to reveal neutrino oscillations at reactor, meson factory and high energy accelerator facilities are considered. In such experiments oscillation might be found if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 0.01}\text{(eV)}{}^2$. The possibilities of searching for oscillations by experiments on cosmic ray neutrinos and especially on solar neutrinos are discussed in detail. The last experiments have an incredible high sensitivity from the point of view of testing the lepton mixing hypothesis (oscillation effects might be observable if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 10}{}^{\mathrm{?12}}\text{(eV)}{}^2$). The “solar neutrino puzzle” is also discussed from the point of view of lepton mixing. Neutrino oscillations are considered then in the case where in nature there exist N ? 2 neutrino types.In conclusion the case of heavy lepton mixing is considered. It is shown that in a concrete scheme with right-handed currents, the probabilities of such processes as μ → eγ, μ → 3e etc. can be close to existing experimental upper limits, provided the heavy lepton masses are of an order of a few GeV, whereas the probabilities of the above processes are entirely negligible if only neutrinos are mixed.     

Self-adjointness of the minimal Schrödinger operator with potential belonging to L1, loc

Let $\text{0 ?q(x) ∈L}{}_{\mathrm{1,loc}}\text{(}\text{R}{}^{\mathrm{m}}\text{)}$,m? 1.Consider the operatorT₀ = ?Δ+q with domain consisting of all bounded measurable functions $\text{u(x), x ∈}\text{R}{}^{\mathrm{m}}$, having bounded support, for which the distribution ?Δu+qu belongs to $\text{L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The main result of the paper is essential self-adjointness of $\text{T}{}_0\text{in L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The proof is independent of a method due to Kato who recently established the self-adjointness of a maximal Schrödinger operator corresponding to such potential.     

Parity violation in atoms in SO(3) gauge models

We have evaluated the parity-violation contribution in atoms in the framework of SO(3) gauge theory. Various hadronic models have been used: first, for simplicity, the unrealistic five-quark one, next, others involving three ordinary SU(3) triplets for which all unwanted strangeness-changing processes are suppressed, up to order $\text{Gα}\text{or}\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$. In the free quark approximation, we obtain quite similar parity-violation effects which are proportional to $\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$ (ΔM² is the difference of squared masses of leptons (M_X0² ? M_ν² = M_X0²), or of quarks (ΔM_q²)). Namely, in large atoms (Z ? 1) the electronic contribution which is proportional to

gives the largest effect ($\text{σ}{}_{\mathrm{?}}\text{,}\text{p}{}_{\mathrm{?}}\text{and}\text{m}{}_{\mathrm{?}}$are the spin, momentum operators and mass of the lepton). Parity-violating effects in SO(3) gauge models are ?10^?4 smaller than those evaluated in the Weinberg theory with a neutral parity-violating current and will remain undetectable in the near future.     

Reorientational motion of the OH− ion in cubic sodium hydroxide

The rotational motion of the OH^? ion was studied in cubic NaOH at 575 K with quasielastic incoherent neutron scattering. The data are compared to two simple models yielding values for the radius of rotation R, the translational mean square displacement 〈u²〉_H, the rotational jump rate τ^?1 and the rotational diffusion coefficient D_R. The following parameter values are obtained: (a) rotational jump model: $\text{R = 0.95}\text{A}\text{?}$, $\text{〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.052}\text{A}\text{?}{}^2\text{, τ}{}^{\mathrm{?1}}\text{= 2}\text{meV}$, (b) rotational diffusion model: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

Fermion-fermion condensates and CP violation

We discuss some theoretical difficulties of the standard Kobayashi-Maskawa scheme for CP violation and present an alternative scenario where CP violation arises through non-vanishing phases in fermion-fermion condensates. We illustrate our ideas in the context of a left-right symmetric model with a hierarchy of mass scales (M_WR?M_WL). We show that the mass scale hierarchy leads naturally to a negligible θ-parameter at tree level, , with this result being preserved in higher order. The resulting theory of CP violation in the kaon sector is of the superweak type and the electric dipole moment of the neutron is essentially determined by θ. There is no direct connection in the model between the phases responsible for the univers's baryon asymmetry and those responsible for CP violation in the kaon system — a result we claim is a general feature of gauge theory models of unified interactions.     

Spontaneous CP violation in a Z4 horizontal symmetry model for flavor mixing

The implications of a Z₄ horizontal symmetry model of flavor mixing for CP violation are studied in the framework of minimal SU(2)_L × SU(2)_R × U(1)_{B – L} gauge theory. We show that CP violation in this model arises purely from right-handed currents. We also note that spontaneous breaking of CP symmetry requires a fine tuning of coupling parameters to the level of , which can be avoided by the inclusion of one additional singlet Higgs field, of the kind recently introduced for other purposes.     

Electromagnetic mass differences of the old and the charmed mesons

We predict for M_?⁺?M_?⁰ the values -3.4 ± 0.8 MeV using the ?-ω mixing and the quark model, respectively. The extracted parameters indicate the necessity of a relativistic treatment of the old mesons. The problem of extrapolating these parameters to the charmed mesons is discussed. Under conservative assumptions, we predict 1.7 ? M_D⁰ ? 2.2 MeV and .     

Hole mass measurement in p-type InP and GaP by submillimetre cyclotron resonance in pulsed magnetic fields

The first observation of cyclotron resonance in p-type InP is reported. The holes were thermally excited at 110 K and the resonance was observed at 337μm wavelength (HCN laser) using a pulsed magnetic field of 0–350 kG. The effective masses of the light and heavy holes in the 〈111〉 direction were found to be $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.12 ± 0.01 m}{}_0$, and in the 〈100〉 direction $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.12 ± 0.01 m}{}_0$, $\text{m}{}^1{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.56 ± 0.02 m}{}_0$. We obtain an estimate of the Dresselhaus parameters A = ?5.04, |B| = 3.12, C² = 6.57. We also report the effective masses for p-type GaP in the 〈111〉 direction as $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.18 ± 0.02 m}{}_0$, $\text{m}{}^1{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.56 ± 0.04 m}{}_0$.     

Some properties of heavy lepton families

The simplest four-quark SU(2) ? U(1) models with an anomally-free heavy lepton sector can have two charged heavy leptons and one or two neutral leprons. Such models also explain the rise in R (the ratio of hadronic to muon pair production in e⁺e^? collisions). We study some consequences of different choices of leptonic numbers for L₁ and L₂. In particular, we derive, the leptonic decay width when several final-stae leptons are massive; the cross section for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_1\text{L}{}_2$ production; the branching ratio for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{L}{}_2\text{L}{}_2\text{→}\text{e}\text{3μ+}\text{missing energy}$.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Cosmological bounds on a left-right symmetric model

The right-handed neutrino cross sections of the processes ν_L + ? → ν_R + ? and ν_R + ? → ν_R + ?, where ? is a relativistic lepton, are calculated in the SU(2)_L × SU(2)_R × U(1) model. According to a cosmological criterion the parameters of the model are bounded. In particular we obtain the bound $\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}_{\mathrm{<mtext>R</mtext>}}\text{? 30 M}{}_{\mathrm{<mtext>W</mtext>}}{}_{\mathrm{<mtext>L</mtext>}}$, assuming the neutrinos are Dirac four-component particles.     

The ′T Hooft-Polyakov monopole near the Prasad-Sommerfield limit

A perturbative classical monopole solution for the SO(3) gauge theory is constructed in the limit of small but non-vanishing Higgs potential. This corresponds to the limit $\text{μ}{}^2\text{2M}{}_{\mathrm{W}}{}^2\text{=}\text{λ}\text{? 1}$, where μ equals the mass of the scalar particle and M_W equals the mass of the intermediate vector particles. The monopole solution and mass are found to involve non-analytic functions of λ: $\text{γ}$ and λ ln λ. The monopole mass M_m is calculated to order $\text{μ}{}^2\text{M}{}_{\mathrm{W}}$ as

$\text{M}{}_{\mathrm{m}}\text{=}\text{4π}\text{e}{}^2\text{M}{}_{\mathrm{w}}\text{1+}\text{1}\text{2}\text{μ}\text{M}{}_{\mathrm{w}}\text{+}\text{1}\text{2}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}\text{ln}\text{μ}\text{M}{}_{\mathrm{w}}\text{+0.7071}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}$

.     

Structure,vibrational study and conductivity of the trihydrated uranyl bis(dihydrogenophosphate): UO2(H2PO4)2·3H2O

The X-ray structure (293 K) of UO₂(H₂PO₄)₂·3H₂O has been refined (R = 0.062): M_r = 518g, space group: P2₁/c (Z = 4); $\text{a = 10.816(1)}\text{A}\text{?}$, $\text{b = 13.896(2)}\text{A}\text{?}$, $\text{c = 7.481(1)}\text{A}\text{?}$, β = 105.65(1)^°, $\text{V = 1082.7(2)}\text{A}\text{?}{}^3$; D_c = 3.17 Mg m^?3. The structure consists of infinite chains along the (101) axis with U atoms bridged by two H₂PO₄ groups. The U atom is surrounded by a pentagonal bipyramid of oxygen atoms, one of them being an equatorial water molecule. The cohesion between the chains is ensured by hydrogen bonds involving the two last water molecules. An assignment of IR and Raman bands with isotopic substitution spectra is proposed. A phase transition at 128 K was made evident by DSC and spectroscopy. The room-temperature phase is characterized by a high disorder of the OH bond orientation while in the low-temperature phase H₂O and POH species appear well oriented. The conductivity seems to occur by proton transfer and protonic-species rotation at the POH-water molecular interface between the chains. ac conductivity has been determined by means of the complex-impedance method ($\text{σ}{}_{\mathrm{<mtext>RT</mtext>}}\text{～ (3?12) × 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$; E ～ 0.20 eV).     

The HH1Σg+ state of hydrogen: Adiabatic calculation of vibronic states in H2, HD,and D2

The nuclear-mass-dependent diagonal corrections to the electronic energies of the $\text{H}\text{H}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state of hydrogen are computed in the range 1.25 ≤ R ≤ 11 a.u. The correction energy goes through a pronounced peak near R = 3 a.u., which is discussed in terms of the character of the electronic wavefunction. The rovibrational structures of H₂, HD, and D₂ in the adiabatically corrected double-minimum potential curves of these isotopes in the $\text{H}\text{H}$ state are presented. Comparison with experimental data indicates the presence of appreciable nonadiabatic perturbations.     

Dipole moment function and vibration-rotation matrix elements of HCl35 and DCl35

The infrared intensity measurements and molecular beam electric resonance dipole moment measurements for HCl and DCl have been reviewed. A method not previously exploited is used to determine infrared matrix elements from the electric resonance dipole moment measurements. A ‘best’ set of matrix element values was selected for HCl and from these the M_i-coefficients of a polynomial dipole moment approximation were determined; M₀ = 1.0935±0.0007 D, $\text{M}{}_1\text{= 0.947±0.023 D/}\text{A}\text{?}$, $\text{M}{}_2\text{= 0.015±0.041 D/}\text{A}\text{?}{}^2$, $\text{M}{}_3\text{= -0.814± 0.116 D/}\text{A}\text{?}{}^3$. Calculations using this dipole moment function for both HCl and DCl are shown to give good agreement with available band strength and vibration-rotation interaction factor measurements. RKR potentials are also calculated for both molecules.     

Nuclear matrix elements from L/K electron capture ratios in 59Ni decay

Using a recent theoretical method, the ratio of nuclear matrix elements $\text{R = (}{}^{\mathrm{v}}\text{F}{}^0{}_{220}\text{?√}\text{3}\text{2}{}^{\mathrm{A}}\text{F}{}^0{}_{221}\text{/}{}^{\mathrm{v}}\text{F}{}^0{}_{211}\text{)}$ was determined to be either 20.50^+0.35_?0.55 or 25.22^+0.28_?0.17 in the second-forbidden nonunique decay of 8 × 10⁴ y ⁵⁹Ni. These values of R were obtained from a value of L₃/K = 0.008 ± 0.002 found by subtracting the theoretical ratio $\text{(L}{}_1\text{+ L}{}_2\text{)}\text{K}$ = 0.113 (based on Q_PEC = 1070 ± 8 keV) from the total ratio L/K = 0.121 ± 0.002, which was measured with a reactor-produced, doubly-mass-separated ⁵⁹Ni source introduced as gaseous nickel-ocene, (C₅H₅)₂, into a wall-less, anticoincidence, multiwire proportional counter. The 854–1008 eV L and the 8.33 keV K peaks were measured simultaneously.     

Experimental limits on the mass and decay lifetime of νμ

The nonobservation of photon-induced e⁺e^? pairs pointing in the neutrino beam direction in large bubble chambers would allow one to set an upper limit on the product m_νμλ^CM for muon-type neutrinos, where m_νμ is the mass and λ^CM is the intrinsic partial decay width in sec^?1 for ν_μ→γ+X. In the theory of Eliezer and Ross where , this implies an upper limit on m_νμ considerably smaller than the present upper limit, and a large lower limit on the lifetime τ_νμ.     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.