Consequences of a gut sector in minimal N = 1 supergravity models with radiative SU(2) × U(1) breaking

It is shown that incorporation of a GUT sector in N = 1 supergravity models with radiative SU(2) × U(1) breaking can drastically modify the corresponding low energy phenomenology. The ratio of Higgs VEVs $\text{ω ≡}\text{〈}\text{H}\text{〉}\text{〈}\text{H}\text{〉}$ might be much larger than 1, even for small top quark masses (m_t = O(40 GeV)). Scenarios of this type necessarily imply large squark and slepton masses $\text{m}{}_{\mathrm{<mtext>q</mtext><mtext>,\; </mtext><mtext>?</mtext>}}\text{? 150}\text{GeV}$, whereas light gluinos can easily be accomodated. Furthermore the upper bound on the mass of the light neutral Higgs becomes as large as M_Z and its coupling to down-type quarks and leptons might exceed the standard GWS-value by more than a factor of 5.     

Single crystal magnetization studies of DySb

High resolution magnetization measurements in single crystal-spherical DySb samples have been performed versus T in fields to 23.6 kOe. Measurements with H along principal crystallographic and 〈11$\text{2}$〉 directions are interpreted in terms of the intermediate metamagnetic phase having the HoP structure. Magnetization components parallel and perpendicular to the applied field for field rotations in (110) and (111) crystallographic planes have been measured and are interpreted in terms of a simple model with a single critical field. For H ∥ 〈110〉, M and H are collinear. The (M - H - T) phase diagram has been determined for H ∥ 〈110〉. The metamagnetic transition is 1st order below a critical point P_c = (8.5 K, 14.7 kOe) becoming 2nd order above. Field induced order for T >T_N is observed in agreement with the results of Brun et al. The absence of hysteresis in M_∥(θ) for H in (110) and (111) planes is interpreted as evidence for the tunneling model in DySb.     

Chiral symmetry breaking in lattice electrodynamics

Chiral symmetry breaking is studied in lattice quantum electrodynamics in the quenched approximation by computer simulation methods. Simulations at zero temperature show that $\text{〈}\text{Ψ}\text{Ψ〉}$ is non-zero for all couplings e² greater than a critical value e_c². The sensitivity of $\text{〈}\text{Ψ}\text{Ψ〉}$ to short-distance features of the lattice action is studied by simulating variant gauge actions. Simulations on asymmetric lattices do not reveal significant temperature dependence in the symmetry breaking dynamics. Subtle effects and limitations of quenched calculations are discussed.     

Calculation of baryon masses in quantum chromodynamics

The polarization operator of quark currents with baryon quantum numbers is considered in quantum chromodynamics. The non-zero mean vacuum values of the field operator products are taken into account. The sum rules are obtained assuming that in the virtuality region ～1 GeV, among the mean vacuum values violating the chiral invariance, the most important is $\text{〈0|}\text{ψ}\text{ψ|0〉}$. Saturating these sum rules by the lowest baryonic states one is able to calculate the masses of the isobar Δ and nucleon N, M_Δ = 1.4 GeV, M_N = 1 GeV, up to 15% through the known value $\text{〈0|}\text{ψ}\text{ψ|0〉}$. The mass splitting in the baryonic decuplet $\text{M}{}_{\mathrm{\Sigma 1}}\text{?M}{}_{\mathrm{\Delta }}\text{= 125}\text{MeV}$ is calculated in first order in the current strange quark mass m_s = 150 MeV. Certain results for other baryonic resonances have also been obtained.     

A new proof of the invariance principle in scattering theory

For free and interacting Hamiltonians, H₀ and H = H₀ + V(r) acting in L²(R³, dx) with V(r) a radial potential satisfying certain technical conditions, and for ? a real function on R with ?′ > 0 except on a discrete set, we prove that the Moller wave operators

exist and are independent of ?. The scattering operator

$\text{S = (Ω}{}^{\mathrm{+}}\text{)1Ω}{}^{\mathrm{?}}$

is shown to be unitary. Our proof utilizes time independent methods (eigenfunction expansions) and is effective in cases not previously analyzed, e.g. $\text{V(r) =}\text{sin}\text{r}\text{r}$ and many others.     

Magnetoresistance and open orbits domain in cobalt

A detailed study of the transverse magnetoresistance of cobalt monocrystals is presented. Among other features the angular variations of the magneto-resistance for J 6 〈10$\text{1}$0〉 shows a maximum with a volcano-like structure. This is interpreted as produced by open orbits around 〈0001〉 direction. The 5° angular domain of these open orbits is found to be in excellent agreement with the 5.5° angular width of the Γ neck in the spin ↑ Fermi surface previously obtained from de Haas-van Alphen experiments.     

A positive energy dynamics and scattering theory for directly interacting relativistic particles

Starting from the tensor product of N irreducible positive energy representations of the Poincaré group describing N free relativistic particles with arbitrary spins and positive masses, we construct an interacting positive energy representation by modifying the total 4-momentum operator. We first make a transformation to a Hilbert space on which the free total 4-momentum operator equals the product of a dimensionless center-of-mass 4-vector ($\text{(|k|}{}^2\text{+ 1)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, k) and a free “reduced Hamiltonian” H_r⁰, which is a positive operator acting only on internal variables, and then replace H_r⁰ by an interacting reduced Hamiltonian H_r = H_r⁰ + V, where V commutes with the Lorentz group and is such that H_r is a positive operator. The resulting product form is shown to imply that the wave operators interwine the free and interacting representations so that the S-operator is Lorentz invariant. From a physical point of view the scheme is related to the framework first introduced by Bakamjian and Thomas, in which the Hamiltonian and boost generators are modified, but the above procedure makes a mathematically rigorous discussion much simpler. In the spin-zero case we introduce a natural generalization of the pair potentials of nonrelativistic N-particle Schrödinger theory to the present relativistic setting, study its scattering theory, and point out some problems that do not have analogs at the nonrelativistic level. In the $\text{spin}\text{-}\text{1}\text{2}$ case we propose, inspired by the Dirac equation, explicit reduced Hamiltonians to describe atomic energy levels and present arguments making plausible that their eigenvalues are in closer agreement with the experimental data than their nonrelativistic counterparts. We also consider extensions to arbitrary spin and, in the $\text{spin}\text{-}\text{1}\text{2}$ case, coupling of a quantized radiation field. In view of eventual applications to “completely integrable” one-dimensional field theories the case of one space dimension is studied as well, both in quantum mechanics and in classical mechanics.     

The mass parameters for the average mean-field potential

Starting from a mean-field hamiltonian with pairing interaction, we use the generator coordinate method (GCM) and a generalized gaussian overlap approximation to derive a multidimensional collective hamiltonian for large-amplitude motion. Numerical calculations are performed for Nilsson and Woods-Saxon potentials with BCS pairing. The BCS wave function is taken as the generator function and the deformation parameters of the single-particle mean field are used as the generator coordinates. We find that the GCM mass parameters on the average are smaller than those of the cranking (+ BCS) model by a factor of $\text{～}\text{2}\text{3}$. In the present approach, the zero-point energy correction to the collective potential is shown to vanish identically.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

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: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

A flow velocity zeugmatographic interlace for NMR imaging in humans

We describe a flow sensitizing zeugmatographic phase-modulation interlace for NMR-imaging which is exactly analogous to Lauterbur's spatial-location-sensitizing magnetic field gradients. The method may be implemented by minor modification of any NMR-imaging scanner without interfering with its conventional operation, and enables up to 6-D imaging of the joint (spatial-flow) density of spins $\text{Δ}\text{(}\text{r}\text{,}\text{v}\text{)}$. In a special simplification, specific-flow-density, $\text{〈v(}\text{r}\text{)〉}$, and flow-current-specific-flow-density, $\text{?}{}_0\text{(}\text{r}\text{)〈}\text{v}\text{〉}$, derive directly from “real” and “imaginary” parts of the image reconstruction.     

Contributions from higher twist effects to the quark fragmentation functions in neutrino data

Quark fragmentation functions are studied with ≈3500 charged current events induced in the bubble chamber Gargamelle by neutrinos of the SPS wide band beam, with 〈E_ν〉 ≈ 25 GeV. The Q² and W² regions covered by this experiment are Q² ≈ 0–40 GeV² and W² ≈ 1–100 GeV², the mean values being 〈Q²〉 = 6.5 GeV², 〈W²〉 = 22GeV². A correlation between the variables $\text{z =}\text{E}{}_{\mathrm{\pi }}\text{E}{}_{\mathrm{<mtext>H</mtext>}}$ and $\text{y =}\text{E}{}_{\mathrm{<mtext>H</mtext>}}\text{E}{}_{\mathrm{v}}$ is found in the data in the region Q² = 1–10 GeV², which can be explained in terms of higher twist effects. These effects reproduce the Q² evolution of the non-singlet moments of the fragmentation function without any need for logarithmic terms.     

Effective lagrangian of mesons and baryons in the strong-coupling expansion of lattice QCD

U(N) and SU(N) lattice QCD are considered. By using a method of the strong-coupling expansion, the effective lagrangian of hadrons is calculated up to the first order in 1/(g²N). For the Susskind lattice fermions, it is shown that chiral symmetry is spontaneously broken and as a result there appears the Nambu-Goldstone boson (pion). The fermion condensation 〈$\text{ψ}\text{ψ}$t>, the masses of hadrons and the pion decay constant are calculated and compared with the results of Monte Carlo (MC) simulations. In the strong-coupling region, our result of the order parameter 〈$\text{ψ}\text{ψ}$〉 coincides very well with that calculated by MC simulations.     

Eigenfunction expansions of operators admitting separation of an infinite number of variables

Let A_k be a self-adjoint operator in a Hilbert space H_k (k = 1, 2, …) and let $\text{L}$ be an operator of the form $\text{L}\text{= A}{}_{\mathrm{r}}\text{? 1 ? 1 ? … + 1 ? A}{}_2\text{? 1 ? 1 ? … + …}$ acting in the infinite tensor product $\text{?}\text{k=1}\text{∞}\text{H}{}_{\mathrm{k}}$. We construct the spectral theory of these operators. In particular, the expansion is generalized eigenvectors of this operator is constructed using the eigenvectors of the operators A_k.     

Correlation between band structure and hydride formation in dilute palladium alloys

Data on the free energy change ΔG, following solution of hydrogen in dilute Pd-alloys Pd_1?xM_x have been reviewed for different concentrations of M (M = Au, Ag, Pt, Ir, Rh, V, Cu, Ni, Pb, Sn and Ti) in both the α and β phases. The dependence of ΔG values upon the nature of the substituents (transition metals) is consistently explained within the framework of a metal-hydrogen bonding mechanism in the hydrides. For the β-hydride the ΔG values can be calculated on the basis of the equation ΔG = ΔG_pd + a(T)(〈?^M_LB〉 ? 〈?^Pd_LB〉)x, where $\text{ΔG}{}_{\mathrm{<mtext>Pd</mtext>}}\text{= ? 0.0489}\text{eV}\text{H}$ atom and is the free energy change of solution of hydrogen in pure Pd, a(T) = 0.194 at T = 298 K, 〈?^m_LB〉 and 〈?^pd_LB〉 are the average energies of the lowest band of the pure constituents ($\text{〈?}{}^{\mathrm{<mtext>Pd</mtext>}}{}_{\mathrm{<mtext>LB</mtext>}}\text{〉 = ?9.15}\text{eV}\text{atom}$). The stability of the palladium-hydrogen bond in dilute Pd-alloys depends on the value of 〈?^M_LB〉; for substituents having lower 〈?^M_LB〉 values than Pd the bond will strengthen, while for those having higher 〈?^M_LB〉 values it will weaken. This behaviour agrees well with the general trend of the stability of the stoichiometric hydrides predicted by Gelatt, Ehrenreich and Weiss using band structure results.     

Fission-fragment energy correlation measurements for (nth, f) of 232U and 233U

Fission-fragment mass and kinetic energy distributions and their correlations have been measured for ²³²U and ²³³U. The results on these uranium isotopes and ²³⁵U are compared. The mass peak/valley ratio of 785 ± 68 for ²³²U is the highest of the three isotopes. The 〈E_K〉(μ_H) distributions show significant differences. The dip ΔE_K at symmetry is $\text{16.2 ± 1.0}\text{MeV}\text{(}{}^{232}\text{U}\text{)}$, $\text{17.0 ± 1.0}\text{MeV}\text{(}{}^{233}\text{U}\text{)}\text{and}\text{20.6 ± 1.1}\text{MeV}\text{(}{}^{235}\text{U}\text{)}$. In the yields for high-kinetic-energy-selected events, the mass 134 dominates for ²³³U and ²³⁵U, but for ²³²U it is μ_H≈144, which dominates. This complete reversal of profiles can be understood in terms of fragment shells.     

The Glimm-Jaffe-Spencer expansion for the classical boundary conditions and coexistence of phases in the λφ24 Euclidean (quantum) field theory

The λφ₂⁴ Euclidean (quantum) field theory is studied in the multiphase region, and the following results are proven: (1) The “low temperature” expansion converges for Dirichlet (D), free (F), Neumann (N), and periodic (P), boundary conditions, and the even-point Schwinger functions for these boundary conditions have a mass gap; (2) $\text{〈}\text{o}\text{〉}{}^{\mathrm{b}}\text{=}\text{1}\text{2}\text{〈o〉}{}^{\mathrm{+}}\text{+}\text{1}\text{2}\text{〈o〉}{}^{\mathrm{?}}$, where b = D, F, N, P, and 〈o〉^± are the pure states of Glimm, Jaffe, and Spencer; (3) 〈o〉^±ξ = 〈o〉^± for all ξ > 0, where ξ is the buondary field; (4) alternative characterizations of the pure states 〈·〉^± are given.     

An experimental determination of the critical exponents at the metal-insulator transition

This work deals with a determination of the magnitude of the critical exponents and their ratio from an analysis of the temperature dependence of the conductivity and magnetoresistivity of doped Ge 〈 As 〉 with an impurity concentration making it an insulator near the metal-insulator transition. The values found are $\text{?? = 0.60 ± 0.04}$, ξ = 1.38 ± 0.07, $\text{ξ}\text{??}\text{= 2.3 ± 0.2}$; neither the critical exponents nor their ratio depend on compensation within 0 < k < 60%.     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.