Heterotic string dark matter from the graviton multiplet

In the string theory framework for physics beyond the standard model the hidden sector of E₈×E₈ heterotic string theory and the graviton multiplet provide compelling sources for the dark matter in the universe.

In the present investigation I consider the graviton multiplet as one particular dark matter source in heterotic string theory. In particular, it is pointed out that an appreciable fraction of dark matter from the graviton multiplet requires a mass generating phase transition around T_c10⁸ GeV, where the symmetry partners of the graviton would evolve from an ultrahard fluid to pressureless dark matter. This indicates m10 MeV for the massive components of the graviton multiplet, and it is reassuring that the corresponding dilaton lifetime τ10¹⁷ s is compatible with a dark matter interpretation.     

Off-energy-shell continuation of the two-nucleon transition matrix in the presence of tensor forces

For a coupled partial wave with a bound state, the entire T-matrix is determined by the bound-state energy and wave function, the on-shell mixing parameter and a real symmetric matrix function σ(k₂,₂ k₁₁) of the continuous momentum variables k and the discrete eigenchannel labels . The on-shell part of σ is given by the eigenphases, the arbitrariness of the T-matrix is the off-shell continuation of this phase-shift matrix σ(k₂, k₁) into two dimensions. Three possible techniques are suggested to go from to the entire T-matrix. This construction procedure for T avoids the usual complications of a potential fit.     

Quadrupole interactions in pionic and muonic tantalum and rhenium

The hyperfine splitting of pionic and muonic X-rays in natural Re has been studied using the known ratio (accurate to 1.6 parts in 10⁵) of the quadrupole moments of the two naturally occurring ¹⁸⁵Re and ¹⁸⁷Re isotopes. From the hyperfine splitting of the ⁵g → 4f and 4f → 3d pionic X-rays the effective quadrupole hyperfine constants were determined to be ¹⁸⁷A₂^eff(4f) = 1.163 ± 0.010 keV and ¹⁸⁷A₂^eff(3d) = 5.39 ± 0.63 keV, giving strong interaction quadrupole shifts ₂(4f) = 46 ± 10 eV and ₂(3d) = 1.3 ± 0.6 keV. The strong interaction monopole shifts ₀ and widths Γ₀ of the 5g, 4f and 3d levels have also been measured. For the two higher orbits, standard optical-potential calculations fit the measured shifts and widths quite well. The observed deeper-lying 3d state, however, has shifts and widths that differ by a factor of 2 or more from the predictions. From the measured quadrupole hyperfine constants of the 4f level we calculate the spectroscopic quadrupole moments to be ¹⁸⁷Q^μ(gm) = 2.09 ± 0.04 b, ¹⁸⁷Q^π = 2.07 ± 0.02 b, ¹⁸⁵Q^μ = 2.21 ± 0.04 b, and ¹⁸⁵Q^π = 2.1 addition, muonic X-rays from ¹⁸¹Ta were observed; using the same methods for determining the quadrupole moment as above, a value of ¹⁸¹Q^μ = 3.28 ± 0.06 b was obtained, in good agreement with earlier published data.     

Microscopic measurements in La-NQR of the ternary carbide superconductor LaNiC2

¹³⁹La-NQR measurements have been carried out in the ternary carbide superconductor LaNiC₂. The nuclear quadrupole frequency and the asymmetry parameter of ¹³⁹La in LaNiC₂ were estimated to be about 1.9 MHz and 0, respectively. In the normal state, the nuclear spin relaxation rate (1/T₁) in the ¹³⁹La NQR signal was proportional to temperature (T) in zero external field above the superconducting transition temperature (T_c) or in an external field larger than the superconducting critical field, which means the system is in the Fermi-liquid state. In the superconducting state, on the other hand, 1/T₁ decreases no more linearly with T, but decreases rapidly exponentially as exp (−Δ/k_BT) at low T with an appreciable enhancement just below T_c. The value of the superconducting energy gap, 2Δ, was estimated to be 3.34k_BT_c, compared with 3.52k_BT_c of the BCS-value. This result strongly suggests that the superconductivity in LaNiC₂ is of a conventional BCS type.     

Magnetic ordering in U4Cu4P7 single crystal

The magnetic ordering in the tetragonal ternary compound U₄Cu₄P₇ has been studied by neutron diffraction. It orders below T_N = 146 K with an antiferromagnetic structure of wave vector k = (001). The magnetic ordering corresponds to a stacking of ferromagnetic (001) uranium planes according to the sequences m₁, m₁, m₂, -m₂, -m₁, -m₁, -m₂, m₂ where m₁ and m₂ represent the magnetic moment, directed along the tetragonal axis of the two uranium sites U(1) (0,0,± z₁) and U(2) (0,0, ± z₂) respectively. The magnetic moments on these two sites have different temperature dependencies as well as well as they reach the different values of 1.1 and 2.2.μ_B for the U(1) and U(2) sites, respectively.     

The angular intensity correlation functions C(1) and C(10) for the scattering of light from randomly rough dielectric and metal surfaces

We study the statistical properties of the scattering matrix S(q|k) for the problem of the scattering of light of frequency ω from a randomly rough one-dimensional surface, defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) constitutes a zero-mean, stationary, Gaussian random process. This is done by studying the effects of S(q|k) on the angular intensity correlation function C(q,k|q',k')=〈I(q|k)I(q'|k')〉-〈I(q|k)〉〈I(q'|k')〉, where the intensity I(q|k) is defined in terms of S(q|k) by I(q|k)=L^-1₁(ω/c)|S(q|k)|², with L₁ the length of the x₁ axis covered by the random surface. We focus our attention on the C⁽¹⁾ and C⁽¹⁰⁾ correlation functions, which are the contributions to C(q,k|q',k') proportional to δ(q-k-q'+k') and δ(q-k+q'-k'), respectively. The existence of both of these correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface and in the presence of weak surface roughness. We show that the deviation of the statistics of the scattering matrix from complex circular Gaussian statistics and the C⁽¹⁰⁾ correlation function are determined by exactly the same statistical moment of S(q|k). As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case the C⁽¹⁰⁾ correlation function should therefore vanish. This result is confirmed by numerical simulation calculations.     

Neutrino masses, mixing and hierarchy

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for Δ_sol and Δ_atm, and for the mixing angles determined from neutrino oscillation experiments, including that from KamLAND. Since the hierarchy assumption is a statement about mass ratios, it lets us obtain all three neutrino masses. We obtain a mass matrix, M_ν and a mixing matrix, U, where both M_ν and U are given in terms of powers of Λ, the analog of the Cabibbo angle λ in the Wolfenstein representation, and two parameters, ρ and κ, each of order one. The expansion parameter, Λ, is defined by

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, and ρ expresses our ignorance of the lightest neutrino mass m₁, (m₁=ρΛ⁴m₃), while κ scales s₁₃ to the experimental upper limit, s₁₃=κΛ²≈0.16κ. These matrices are similar in structure to those for the quark and lepton families, but with Λ about 1.6 times larger than the λ for the quarks and charged leptons. The upper limit for the effective neutrino mass in double β-decay experiments is 4×10⁻³ eV if s₁₃=0 and 6×10⁻³ eV if s₁₃ is maximal. The model, which is fairly unique, given the hierarchy assumption and the data, is compared to supersymmetric extension and texture zero models of mass generation.     

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ, f₀ and a₀ resonances. The ππ → ππ, phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the π⁰η and mass distributions in the T = 1 channel. Furthermore, the total and partial strong decay widths of the f₀ and a₀ resonances are properly reproduced. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the meson-meson interaction below GeV.     

Interactions between a tetraanionic porphyrin and the methylviologen dication in methanol studied by fluorescence quenching reaction

Fluorescence decay curves for 5,10,15,20-tetrakis(4-sulfonatophenyl)-21H,23H-porphine tetraanion (TPPS⁴⁻) have been measured in the absence and presence of the methylviologen dication (MV²⁺) with various ionic strengths in methanol. In the presence of MV²⁺ the fluorescence decays can be expressed by a double exponential function, I(t = I₁exp(−t/τ₁) + I₂exp(−t/τ₂). The contribution by the faster decay component to the total fluorescence signal increases with increasing MV²⁺ concentration. The faster decay process is attributed to fluorescence from the excited state of a solvent-separated ion pair (SSIP) formed between TPPS⁴⁻ and MV²⁺, and the slower process is attributed to fluorescence from free TPPS⁴⁻ ions in the solution. Rate constants for the quenching of fluorescence from free TPPS⁴⁻ by MV²⁺ (k_q) and formation constants for the SSIP (K_SSIP) were calculated and both are found to decrease with increasing ionic strength. The decrease in k_q and K_SSIP values can be interpreted in terms of the shielding of electrostatic attraction between the ions.     

27Al NMR study in ZrNiAl

We have studied the microscopic properties of the hexagonal ZrNiAl, a model compound for a wide family of intermetallic compounds crystallizing in this type of structure, by using ²⁷Al NMR spectroscopy. We have investigated the lineshape of static and MAS NMR spectra as a function of magnetic field strength (4.7–9.4 T) and temperature (5–300 K). Our data indicate that the ²⁷Al NMR spectra result from a combined effect of quadrupole and anisotropic shift interactions. The ²⁷Al nuclei are in an environment characterized by the quadrupole coupling constant e²qQ/h of 3.3 MHz, asymmetry parameter η_Q of 0.42, isotropic shift δ_iso of 393 ppm, shift anisotropy δ_anis = δ_zz − (δ_xx + δ_yy)/2 of 150 ppm, and asymmetry factor η_S of 0.5. They are found to be temperature independent. The spin–lattice relaxation rate measured at 7.05 T is proportional to the temperature with T₁T = 135 s K. The mechanisms responsible for observed values of δ_iso, δ_anis, T₁T, and the enhanced Korringa constant are discussed.     

环二硅氨烷的29Si和13C NMR研究

本文报道了十种环二硅氨烷衍生物(R₁=Me、ф;R₂=Me、ф1 R₃=Me;X=Me、ф、OH、OSiMe₃、H和cl)及与此有关的九种聚合物m+n(m=2,3,4,7,10)的²⁹Si和¹³C化学位移,讨论了取代基X、R₁、R₂及硅氧链节数m对化学位移的影响。通过考察化学位移随R₁、R₂的变化,推断环二硅氨烷中N与其周围的三个Si之间存在(p→d)π相互作用。     

In-band M1 and E2 transition rates and collective structures in Ba

Subpicosecond mean lifetimes of eight excited states in ¹²⁸Ba populated via the ⁹⁶Zr(³⁶S,4n) reaction were measured by the Doppler-shift attenuation (DSA) technique using a line-shape analysis. The differential decay-curve method (DDCM) was applied for the lifetime determination. The B(E2) values in the yrast band indicate that the first band-crossing is with a proton S-band. The configuration πh_11/2d_5/2 of the negative-parity semi-decoupled bands is confirmed by the measured B(E2, I → I − 2) and B(M1, I → I − 1) transition strengths. The higher-lying “dipole” band in ¹²⁸Ba can be described as a high-K four-quasiparticle band built on the prolate configuration (πh_11/2d_5/2) (νh_11/2g_7/2).     

Cl nuclear quadrupole resonance studies of molecular motions of ClO3 and water diffusion in Ca(ClO3)2·2H2O

A ³⁵Cl nuclear quadrupole resonance (³⁵Cl-NQR) investigation of polycrystalline Ca(ClO₃)₂·2H₂O is described. The ³⁵Cl-NQR frequencies (ν_Q) for two resonance lines (ν_Q1 and ν_Q2), the spin lattice relaxation time (T_1Q) for ν_Q2 only and the line width δν_Q2 were measured in the temperature range 292–345 K, except for the frequency measured up to 455 K. The observed decrease in the resonance frequencies with increasing temperature permitted the determination of the frequencies of librations of the ClO₃⁻ ion about two axes perpendicular to the three-fold axis of the ion mainly responsible for this effect. The temperature dependence of the relaxation time T_1Q proved the occurrence of water diffusion and hindered rotation of ClO₃⁻ ions. The activation energies of these two molecular motions were determined, and their effect on the electric field gradient at the site of a chlorine nucleus was discussed. Temperature measurements of the line width δν_Q2 confirmed the conclusions drawn from the analysis of T_1Q(T).     

Spectral intensities in the ν1 band of NH3

Intensities have been measured for individual transitions in the Q and R branches of the ν₁ band of NH₃ using a difference-frequency laser spectrometer. The data yield an integrated band strength of S⁰_v=219.36±1.03 cm^-2/MPa at 297 K, corresponding to a transition moment of μ_v = 8.535(20) × 10^-32 C·m, and a Herman-Wallis correction factor, (1 + _jm)², where _j = 0.0209(20). The intensities of a few lines for K 7 were noticeably perturbed by a perpendicular Coriolis interaction with 2ν₄ (E, L = 2), so were excluded from the fit. A small sample of ν₃ band lines occurring in the ν₁ band scans also yields a rough estimate of the ν₃ band intensity with evident irregular perturbations.     

Magnetic properties and domain structure of polycrystalline DyFe3

Magnetization σ vs. temperature T was measured from 80 to 700 K in polycrystalline DyFe₃ in a magnetic field H = 10 kOe. From σ = f(T), the Curie temperature was determined. Also, σ was measured vs. H from 0 to 70 kOe at 4.2 K. Magnetization at saturation σ₀ at 4.2 K and the magnetic moment of DyFe₃ were also determined. First observations of domain structure in DyFe₃ are reported. The mean domain with is determined in its dependence on the grain size . The magnetocrystalline anisotropy constant of polycrystalline DyFe₃ is determined as K₁ = -1.2×10⁷ erg/cm³.     

Two separate Li ionic motions observed by Li and B NMR in xLi2S + (1 − x)B2S3 glassy fast ionic conductors

Studies of ion dynamics in the highly conductive glassy fast ionic conductor (FIC) xLi₂S + (1 − x)B₂S₃ (x = 0.65 and 0.70) were made with NMR nuclear spin lattice relaxation (NSLR) R₁(ω, T) of both mobile ⁷Li and immobile ¹¹B ions, and ⁷Li NMR line narrowing δν(T). The possible dependence of ion dynamics on the short range order structures (SRO) and the distribution of activation energies (DAE) in this highly conductive FIC was investigated. Two Gaussian DAE were employed to fit ⁷Li NSLR data, where each Gaussian DAE was correlated to a separate ¹¹B NSLR in a BS₃ and in a BS₄ group. The long range diffusion of Li ions among BS₃ groups and a seemingly localized ionic hopping motion around BS₄ group is suggested as a microscopic model for the ion dynamics in thioborate glasses, namely a ‘two channel relaxation’.     

Measurement of transition quadrupole moments of high-spin states in the N=74 isotones Pr, Ce and La

The Doppler-Shift Attenuation Method has been used to extract transition quadrupole moments of high-spin bands in the N=74 isotones ¹³³Pr, ¹³²Ce and ¹³¹La, produced in the ³⁷Cl + ¹⁰⁰Mo reaction. The results appear to be configuration dependent and, for ¹³³Pr and ¹³²Ce, the involvement of Ω=1/2 νh_9/2 and νf_7/2 intruder orbitals appears to enhance the collectivity at high spin (I>25 ).     

Mössbauer investigations on Np3S5

The 59.5 keV Mössbauer resonance of ²³⁷Np has been measured in Np₃S₅ at 77 and 4.2 K. At 77 K, two different quadrupolar splittings are observed. The first one (δ₁ = −5(1) mm sec⁻¹/NpAl₂) is assigned to the Np⁴⁺ ions and the second one (δ₂ = 28(1) mm sec⁻¹/NpAl₂) is assigned to the Np³⁺ ions. At 4.2 K the spectrum gives a ratio of areas S(Np³⁺)/S(Np⁴⁺) of 2.0. These results clearly confirm the crystallographic data of this mixed-valence material.     

Low-energy expansion of meson form factors

We calculate the corrections to various low-energy theorems concerning the behaviour of the pseudoscalar meson form factors near t=0. In particular we discuss (i) the Ademollo-Gatto theorem, (ii) Sirlin's relation between the K_l3 form factor ƒ₊^Kπ(t) and the electromagnetic form factors, (iii) the Callan-Treiman relation, and (iv) the Dashen-Weinstein relation, which connects the slope λ₀ of ƒ₀^Kπ(t) with the ratio F_K/F_π. Furthermore, we point out a remarkable isospin breaking effect which is clearly visible in the experimental rates of the decays K⁺→π⁰e⁺ν, K⁰→π⁻e⁺ν.     

Mean power transmission for one-dimensional random wave propagation using a cumulant expansion

In this paper the problem of the mean power transmission for one-dimensional wave propagation in a random medium is studied. We use a cumulant technique valid for small k₀L_c where measures the size of the fluctuations, L_c is the correlation length of the random wave number, and k₀ is the undisturbed wave number. We obtain an integral expression for the mean transmitted power. It shows exponential decay for large width, and linear decay for small width. The relevant scale to measure the width of the slab is ²k²₀∫^∞₀C(x)cos(2k₀x)dx where C(x) is the autocorrelation of the random wave number.