Deep inelastic structure functions of the photon

Three independent structure functions of a real photon can be measured in photon-photon collisions in e^±e^? storage rings. These are M₁ and M_L (related to the usual structure functions W₁andνW₂, as defined for any target) and a third function M₃, which arises from the strong plane polarisation of the colliding photons. We show, using a dispersion relation in the photon mass, that M₃ and the longitudinal structure function M_L both scale and are independent of the vector-dominant hadronic structure of the real photon. Therefore in a parton model, or in the quark light-cone algebra, they are given by the bare quark box diagrams which also dominate when both photons have large q²; this uniquely predicts the behaviour , $\text{M}{}_3\text{= [(}\text{1}\text{2}\text{π)Σ e}{}_{\mathrm{i}}{}^4\text{](?x}{}^2\text{)}$ for the real photon structure functions in the Bjorken limit (q₂² → ?∞, q₁²=0, x=?q₂²/2q₁·q₂=constant).     

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.     

Evidence for a narrow peak in Ksoπ±π+π- at 2.6 gev in 12 gev/cpp interactions

We report the evidence for a narrow charged peak (5.5 s.d.), which we suggest calling the I, in the 6-prong-V⁰ topology of $\text{p}$p interactions at 12 GeV/c. The mass, widht and the product of cross section σ_I times the branching ratio BR into the final state (K_s^oτ±τ⁺τ^? are found to be: $\text{M}{}_{\mathrm{I}}\text{=2.60 ±}\text{0.01}\text{GeV}\text{/}\text{c}{}^2$, $\text{Γ}{}_{\mathrm{I}}\text{?}\text{0.018}\text{GeV}\text{/}\text{c}{}^2$, σ_I·BR≈20 μbarn     

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%     

Investigation of the central component of SrTiO3 by neutron scattering with eV resolution

We studied the energy width and the width in reciprocal space Δq of the central mode of SrTiO₃ above T_c. At T_c+4° we observed an energy width of about 6×10^?7 eV. If the measured Δq is interpreted by a correlation length $\text{Δq}{}^{\mathrm{?1}}\text{= ξ = ξ}{}_0\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>2</mtext><mtext>3</mtext>}}$ we obtain $\text{ξ}{}_0\text{= 75}\text{A}\text{?}$.     

Dielectric susceptibility and correlation length of one-dimensional CDW with impurties. II. weak disorder

Dependence of static dielectric susceptibility and correlation length of charge density waves (CDW) with weak defects on parameter of incommensurability with lattice is investigated. In almost commensurate phase (h?h_ch_c), $\text{χ ～ (h?h}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{In}{}^{\mathrm{<mtext>-4</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h?h}{}_{\mathrm{c}}$ and R_c ～ (h ? h_c)^{$\text{2}\text{3}$}. In${}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h ? h}{}_{\mathrm{c}}$. Far from commensurability $\text{(h?h}{}_{\mathrm{c}}\text{) χ～ (a+h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, $\text{R}{}_{\mathrm{c}}\text{～ (a + h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, where a is the dimensionless ratio of random potential intensities, corresponding to backward and forward scattering impurities.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Core-level reflectance spectroscopy of germanium by means of synchrotron radiation

Reflectance spectra due to 3d core-levels of Ge have been measured in the photon-energy region from 29 to 38 eV by means of synchrotron radiation. Second-energy-derivative spectra have newly shown pairs of doublet structures with energy separation of the Ge $\text{3d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{?}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core-level splitting. The observed doublet structures are assigned to the transitions from the $\text{3d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and $\text{3d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core-levels to the flat regions of the conduction band around the particular symmetry points of Δ₆^c and L(₃^c(L₆^c, L_4,5^c).     

On a modified Lindemann-like criterion for 2D melting

By means of a molecular dynamics simulation the existence of a Lindemann-like criterion for 2D melting is proved. The criterion is the constancy of the value $\text{γ}{}_{\mathrm{<mtext>M</mtext>}}{}^{\mathrm{<mtext>c</mtext>}}\text{≡}\text{〈[}\text{u}\text{(}\text{R}\text{+}\text{a}{}_0\text{)?}\text{u}\text{(}\text{R}\text{)]}{}^2\text{〉}\text{a}{}^2$ along the melting curve; this value being practically independent of the nature of a 2D classical crystal (the Lindemann constant is infinite for a 2D crystal in the thermodynamical limit). For 2D dipole and 2D Lennard-Jones crystals γ_M^c = 0.12. For a 2D electron crystal γ_M^c ≈ 0.10. These values are consistent with the results of calculations in the framework of the phonon-mediated melting theory.     

A Mössbauer study of amorphous Fe40Ni40B20

Amorphous Fe₄₀Ni₄₀B₂₀ (VITROVAC 0040) alloy has been investigated using ⁵⁷Fe Mössbauer Spectroscopy. The Curie temperature T_c is found to be well defined and is 695 ± 1 K. The quadrupole splitting just above T_c is 0.64 mm sec^?1. The crystallization temperature is 698 ± 2 K, close to but definitely above T_c. The average hyperfine field H_eff(T) of the glassy state shows a temperature dependence of $\text{H}{}_{\mathrm{<mtext>eff</mtext>}}\text{(0)[1 ? B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{? C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{? …]}$ indicative of the existence of spin wave excitations. The values of $\text{B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ are found to be 0.40 and 0.06, respectively, for T/T_c ? 0.72. At temperatures close to T_c, H_eff(T) varies as (1 ? T/T_c)^β where β is one of the critical exponents and its value is found to be 0.29 ± 0.02.     

Solving φ1,24 field theory with Monte Carlo

We study lattice g₀φ⁴ field theory for all g₀ and fixed renormalized mass M in one and two dimensions using Monte Carlo techniques. We calculate the dimensionless renormalized coupling constant $\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{=}\text{g}{}_{\mathrm{<mtext>R</mtext>}}\text{M}{}^{\mathrm{4?d}}\text{,}\text{where}\text{d}$ is the dimension of space—time, at fixed small values of the lattice spacing a for various g₀ and lattice sizes. Our results are in quantitative agreement with the analyses of high temperature and strong coupling series which rely on extrapolation from large to small lattice spacing.     

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 $\text{?10}{}^7\text{GeV}$.     

Surface cyclotron resonance in Si under uniaxial stress

The cyclotron resonance of inversion-layer electrons on (100)p-type Si is found to depend sensitively on an externally applied compressive stress. At low temperatures (T ? 10 K) we observe a considerable increase of the cyclotron mass m¹_c with stress S along the [001] direction. The effect is most strongly observed at low electron densities n_s. For $\text{S～1.5 × 10}{}^9\text{dyne}\text{cm}{}^2$ and n_s～2 × 10¹¹cm^-2 we obtain $\text{m}{}^1{}_{\mathrm{c}}\text{～0.4 m}{}_0$ instead of the expected 0.2m₀. Along with this change of $\text{m}{}^1{}_{\mathrm{c}}$ a strong narrowing of the resonance is noted. Raising the temperature gives an additional n_s- dependent increase of $\text{m}{}^1{}_{\mathrm{c}}$.     

Structure magnetique en champ applique nul de l'acetate de manganese tetrahydrate Mn(CH3COO)2, 4H2O

The magnetic structure of manganous acetate Mn(CH₃COO)₂, 4H₂O has been solved by neutron diffraction. Manganous acetate crystallizes in the space group $\text{P2}{}_1\text{c}$ with Z = 6. Manganese atoms (in position 2a and 4e) are located in (100) planes. Below T_N = 3.18 K this compound is antiferromagnetic in a zero applied field with the k vector [$\text{1}\text{2}$ 00]. The plane (100) is ferromagnetic. The magnetic group is $\text{P}{}_{\mathrm{2a}}\text{2}{}_1\text{c}$.     

Obtaining Mw = Mz cos θ in technicolor theories

We show that the successful relation M_w = M_z cos θ is preserved in the technicolor formulation of the dynamical Higgs mechanism provided only that the creation operators for Goldstone bosons associated with broken generators belong to the $\text{I}{}_{\mathrm{<mtext>w</mtext>}}\text{=}\text{1}\text{2}$ representation of the weak isospin group. We present a plausibility argument that this is indeed the case. No additional isospin or isospin-like global SU(2) symmetries are then required allowing isospin to be spontaneously broken. This may be of help in producing a large $\text{m}{}_{\mathrm{<mtext>c</mtext>}}\text{m}{}_{\mathrm{<mtext>s</mtext>}}$ splitting. It is also shown how the weak hyperchange interaction can produce substantial vacuum isospin breaking in a theory which is only marginally asymptotically free. This mechanism predicts , providing a natural explanation for small neutrino masses.     

Complexified Pöschl–Teller II potential model

With the help of complexifying a five-parameter exponential-type potential model, we obtain a general complex version of the Pöschl–Teller II potential, , where q_c=q₀e^2iαε, real V₁>0, q₀>0 and $\text{0<λε<}\text{π}\text{2}$. It has been shown that this complex potential is P-pseudo-Hermitian and PT-symmetric, where the parity operator P acts on the position operator as $\text{PxP}{}^{\mathrm{-1}}\text{=}\text{ln}\text{q}{}_0\text{λ}\text{−x}$. The discrete energy eigenvalues are shown to be real when $\text{V}{}_2\text{⩾−}\text{q}{}_0\text{λ}{}^2\text{4}$ while they are complex conjugate pairs if $\text{V}{}_2\text{<−}\text{q}{}_0\text{λ}{}^2\text{4}$.     

Antiproton-proton total elastic cross sections in the T and U regions (0.69−2.43 GeV/c)

Antiproton-proton total elastic cross sections at 21 incident momenta in the range 0.69 to 2.43 GeV/c have been deduced by combining p?p elastic differential cross sections over a c.m. angular range $\text{?0.95 ?}\text{cos}\text{θ}{}^1\text{? 0.93}$ with forward elastic cross sections derived from recent real-part measurements and p?p total cross sections. Two bumps are observed, at $\text{M}{}_1\text{? 2.155}$ and $\text{M}{}_2\text{? 2.345}\text{GeV}\text{/c}{}^2$, having widths of Г₁ ～ 0.135 and $\text{Г}{}_2\text{～ 0.135}\text{GeV}\text{/c}{}^2$. Corresponding structures in other p?p reaction channels are discussed.     

Critical slowing down of fluctuations in squaric acid (H2C4O4) at the phase transition observed by 13C spin-lattice relaxation

Spin lattice relaxation T₁ of naturally abundant ¹³C nuclei in squaric acid was measured close to the antiferroelectric-paraelectric phase transition temperature T_c = 373 K. A rapid increase in $\text{1}\text{T}{}_1$ is observed close to T_c coming from above, which follows the power law $\text{1}\text{T}{}_1\text{～ ε}{}^{\mathrm{?1.4}}$ where $\text{ε =}\text{(T ? T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}$. This behaviour is explained on the basis of the two-dimensional character of the fluctuations.     

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ? Q² ? 16 GeV². Excellent agreement is obtained using $\text{g}{}^2\text{(2}\text{GeV}\text{)}\text{4π}{}^2\text{= 0.17}$ for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of $\text{M}{}_0{}^2\text{Q}{}^2$. We use data from the resonance region to show $\text{M}{}_0\text{? 400}\text{MeV}$, in agreement with theoretical expectations. Our fit to νW₂ in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of $\text{R =}\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{T}}$ at large x and Q² are systematically higher than our predictions.