Does leading ln x resummation predict the rise of g 1 at small x?

We numerically analyse the evolution of the flavor non-singlet g ₁ structure function taking into account the all-order resummation of α_s ln² × terms which is expected to have much stronger effects than the DGLAP evolution in the small x region. We include a part of the next-to-leading logarithmic corrections coming from the resummed “coefficient function” which are not considered in the calculation of Blümlein and Vogt to respect the factorization scheme independence. It is pointed out that the resummed coefficient function gives unexpectedly large suppression factor over the experimentally accessible range of x and Q ². This fact implies that the next-to-leading logarithmic contributions are very important for the g ₁ structure function.     

Momentum space of constant curvature and the “rainbow” approximation in quantum field theory

The behavior of the mass operator is studied in “rainbow” graph approximation in the momentum space of constant curvature with the group of motions SO(4,1). The infrared divergences occuring there are eliminated by a multiplicative renormalization. When x?4ι ^?2 (whereι is the “fundamental length”), the resulting asymptotic (x ? m² _c) expressions for the mass operator Σ_R (x) and its imaginary part are analytic in the coupling constant at zero, while in the domain x?4ι ^?2 a logarithmic branching occurs, and the function grows linearly. The assumption that there are “superheavy particles” in nature (with m _c ² ?hι ^?2) in the asymptotic domain x?4ι _?2 leads to a violation of the positive definiteness for the imaginary part of the mass operator.     

Flavor singlet contribution to the structure functiong 1 at small-x

The singlet contribution to theg ₁(x, Q ²) structure function is calculated in the double-logarithmic approximation of perturbative QCD in the regionx?1. Double logarithmic contributions of the type (α _s ln²(1/x)) ^k which are not included in the GLAP evolution equations are shown to give a power-like rise at small-x which is much stronger than the extrapolation of the GLAP expressions. The dominant contribution is due to the gluons which, in contrast to the unpolarized case, mix with the fermions also in the regionx?1. The two main reasons why the small-x behavior of the double logarithmic approximation is so much stronger than the usual GLAP evolution are: the larger kinematical region of integration (in particular, no ordering in transverse momentum) and the contributions from non-ladder diagrams.     

Small x behaviour of the chirally-odd parton distribution h 1(x,Q 2)

The small x behaviour of the structure function h ₁ (x, Q ²) is studied within the leading logarithmic approximation of perturbative QCD. There are two contributions relevant at small x. The leading one behaves like (1/x)⁰ i.e. it is just a constant in this limit. The second contribution, suppressed by one power of x, includes the terms summed by the GLAP equation. Thus for h ₁ (x, Q ²) the GLAP asymptotics and Regge asymptotics are completely different, making h ₁(x, Q ²) quite an interesting quantity for the study of small x physics.     

On the light-by-light contribution to the sixth-order muon anomaly

We have evaluated analytically the coefficient of log m_μ/m_e for the six photon-photon scattering diagrams contributing to the muon g ? 2 in sixth order. The result is remarkably simple, 2π²/3, in complete agreement with the latest numerical evaluation. This completes the analytic calculation of all logarithmic terms in sixth order.     

QCD analysis of twist-4 contributions to the g i structure functions

We analyze the twist-4 contributions to Bjorken and Ellis-Jaffe sum rules for spin-dependent structure function g ₁(x, Q ²). We investigate the anomalous dimensions of the twist-4 operators which determine the logarithmic correction to the 1/Q ² behavior of the twist-4 contribution by evaluating off-shell Green’s functions in both flavor non-singlet and singlet case. It is shown that the operators which are proportional to the equation of motion play an important role to extract the anomalous dimensions of physical operators. The calculations to solve the operator mixing of higher-twist operators are given in detail     

Spectral resonances which become eigenvalues

The stationary Schrödinger equation is ? _x ² φ + λV(x)φ=zφ for φ∈?²(R ⁺,dx). If the potential is bounded below, singular only atx=0, negative on some compact interval and behaves likeV(x)～1/x ^μ asx→∞ with 2≧μ>0, then the system admits shape resonances which continuously become eigenvalues as λ increases. Here λ>0 and for μ=2 a sufficiently large λ is required. Exponential bounds are obtained on Im(z) as λ approaches a threshold. The group velocity near threshold is also estimated.     

Superconductivity and ferromagnetism in the orthorhombic system (TbxLu1−x)RuB2

The pseudoternary orthorhombic system Tb_xLu_1?xRuB₂) (0 ? x ? 0.1 andx = 1.0) has been investigated by static magnetization, ac susceptibility and resistivity measurements down to 1.5 K. Superconductivity occurs for 0 ? x ? 0.1, while ferromagnetic order occurs for x = 1.0. For each sample studied, the Tb ion maintains a configurationally stable trivalent state. The initial linear depression of the superconducting transition temperature yields a coupling constant value N(0)Γ² between conduction electrons and magnetic Tb³⁺ moments of 3.5 x 10^-4 ev-atom-states/spin-direction.     

The asymptotic behaviour of form factors

Similar to the method of S.A. Anikin and O.I. Zavialov a modified renormalization procedure is applied to the already renormalized current operator. This allows the derivation of an identity for the coefficient functions of this operator and the proof of new renormalization group equations. These equations are applied to the theory and the electromagnetic form factor of quarks in QCD. In the last case the one-loop approximation gives the leading behaviour exp(?clnlnQ²lnQ²) for large euclidean values of the momentum transfer Q² = ?q² at the external electromagnetic vertex. If the leading logarithmic terms (g²ln²Q²)ⁿ are extracted from this result, then the behaviour exp(?g²c′ln²Q²) is obtained. Whereas the first result is modified by contributions from two-loop calculations, the result concerning the leading logarithmic terms does not change.     

Possible anionic clusters and mixed valence effects in transition metal chalcogenides and oxides

The formation of anionic clusters similar to O₂^2?, S₂^2?, Se₂^2? but with higher internuclear distances can be responsible for the more specific forms of interaction required to explain the properties of UO₂₊x, and many transition metal chalcogenides such as Fe_1?xS, Ni_1?x,S etc. Resonant structures can lead to clusters of this type even in stoichiometric chalcogenides with NiAs-type structure due to the $\text{d}\text{p}$ mixing, and low energy differences between metal d- and chalcogen p-bands. The mixed valence effects involved are discussed qualitatively.     

Evidence for a valence transition in UxY1-xSb

Electrical, optical and lattice-constant measurements on single crystalline U_xY_1-xSb (x=0, 0.01, 0.03, 0.08, 0.15, 0.20, 0.30, 0.70 and 1) reveal a nonmagnetic U 5f² singlet groundstate for x ? 0.15, a lowering of the f³→f²d¹ transition energy with decreasing x for x > 0.15 and a marked anomaly of the lattice parameter for x ? 0.15. These results as well as the anomalous concentration dependence of the U moment can be described by a valence transition of U at a concentration of about 15% U (x = 0.15).     

Pecularities of EPR spectra of the Gd impurity in the Sn-Rich Pb1−x Sn x Te(Gd) solid solutions

An electron paramagnetic resonance (EPR) experimental study of crystalline and powder p-Pb_1?x?y Sn _y Gd _y Te samples for various matrix compositionx and Gd contenty has been carried out. The study reveals that grinding the crystals into powder as well as their low-temperature annealing turns Gd impurity ions from the EPR-silent Gd²⁺ state to the EPR-active Gd³⁺ state, whereas high-temperature annealing in vacuum quenches EPR signals from Gd³⁺ ions. The experimental results are interpreted in terms of a model assuming that the trivalent charge state of the Gd impurity ions in lead and tin tellurides is a component part of the “substituting Gd impurity-Te vacancy” complex.     

Higher-twist effects in deep-inelastic scattering

Non-scaling, non-factorizing 1/Q² contributions to cross sections are derived for semi-inclusive deep-inelastic scattering, ?N → ?′πX. These higher twist terms are dominant at large z = p_π · p_N/Q · p_N. They provide unusual (1 ? y) terms in the cross section. as well as asymmetries in the azimuthal angle dependence. Calculations are also presented for the quark to pion fragmentation function D_π(z, Q²).     

Angular distributions and structure functions from two-jet events at the CERN SPS pp collider

The two-jet cross section measured in the UA1 apparatus at the CERN $\text{p}\text{p}$ Collider has been analysed in terms of the centre-of-mass scattering angle θ and the scaled longitudinal parton momenta x₁ and x₂. The angular distribution dσ/d cos σ rises rapidly as cos → 1, independent of x₂ and x₂, as expected in vector gluon theories (QCD). The differential cross section in x₁ and x₂ is consistent with factorization and provides a measurement of the proton structure function $\text{F(x) = G(x) +}\text{4}\text{9}\text{[Q(x) +}\text{Q}\text{(x)]}$ at values of the four-momentum transfer squared, -t? ≈ 2000 GeV². Over the range x = 0.10?0.80 the structure function shows an exponential x dependence and may be parametrized by the form F(x) = 6.2 exp (?9.5x).     

Electromagnetic corrections to neutrino processes in the leading logarithmic approximation,the value of sin θ and the W and Z masses

The parameters of the Weinberg-Salam model can be defined by amplitudes at a momentum scale M = O(M_W, M_Z). We derive the leading logarithmic e.m. correction to the relations giving the neutrino amplitudes at a momentum scale μ ? M in terms of sin²θ(M), α(M), M_W and M_Z. For leptonic processes, the Fermi constant is not corrected, but a running, universal, sin²θ(μ) > sin²θ(M) should be used. The Fermi constant for semileptonic processes is renormalized by a factor $\text{?(μ) > 1}$, for charged currents, and is not renormalized, for neutral current processes. The latter are described by the same sin²θ(μ) as the leptonic ones. We estimate that sin²θ(M) is about 0.013 smaller than the value of sin²θ obtained from semileptonic data with no correction, thereby improving the agreement with grand unified theories. The prediction for W (Z) masses and widths in terms of the low energy parameters are discussed. Using previous calculations at order α, we obtain predictions for the masses which are accurate up to and including terms of order (αlnM²)².     

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP^N, and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ?², and the field equations reduce to an algebraic equation for ?, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C_N/?⁴. Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D_N and E_N. General formulas are given for the gauge coupling g² in terms of C_N and D_N, and the ratio ?²/8πG in terms of C_N and E_N. Numerical values for C_N, D_N, and E_N are obtained for scalar and spinor fields on spheres of odd dimensionality N. It is found that the potential, g² and ?²/8πG can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O(N + 1) gauge couplings and 8φG/?² are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.     

Qualitative theory of three-dimensional rotator model

The 3-dimensional planar rotator (PR) model with short-range interaction is studied in the “harmonic” approximation where spin wave and vortex loop (VL) system decouple. The phase transition (PT) occuring in the PR-model is studied via the correlation and stability properties of the VL-system for which a tentative phase diagram is set up. Under the assumption that the PT of the PR-model is continuous an ansatz for the “dielectric” function ?_q of the VL-system is made which leads at criticality simultaneously to scaling of the VL-system and of the PR-model. Physical arguments are given to justify the dimensional properties of ?_q which led to this result. The critical exponents for the VL-system in usual notation are η_L=1, and γ_L=v_L=0. The latter represent logarithmic singularities, i.e., ?₀～–ln|τ|^z_γ, and κ～–1/ln|τ|^z_v. The critical expon ents of the PR-model can be expressed in terms of those of the VL-system. The low and high-temperature correlation functions are given. It is shown that only in the presence of an anisotropy field, e.g., a magnetic field, the low temperature correlation function decays exponentially. The relation between the PR-model, and the melting of crystals is briefly discussed.     

On the magnetic properties of Pt1−xAgx

The observed rapid continuous isothermal change from enhanced paramagnetism to weak diamagnetism with increasing silver mole fraction x of the Pt_1?xAg_x alloy system is interpreted by means of a semiphenomenological magnetic alloy susceptibility function X(x). The x-dependent Knight shift K(x) of both ¹⁰⁹Ag and ¹⁹⁵Pt nuclei in Pt_1?xAg_x is closely related to the alloy susceptibility and therefore can be used in a combined K(x)?X(x)-analysis.     

Universal estimate of the gap for the Kac operator in the convex case

The aim of this paper is to prove that ifV is a strictly convex potential with quadratic behavior at ∞, then the quotient μ₂/μ₁ between the largest eigenvalue and the second eigenvalue of the Kac operator defined on L²(? ^m ) by exp ?V(x)/2 · exp Δ_x · exp ?V(x)/2 where Δ_x is the Laplacian on ? ^m satisfies the condition: $${{\mu _2 } \mathord{\left/ {\vphantom {{\mu _2 } {\mu _1 {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} \mathord{\left/ {\vphantom {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} {2,}}} \right. \kern-\nulldelimiterspace} {2,}}}}} \right. \kern-\nulldelimiterspace} {\mu _1 {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} \mathord{\left/ {\vphantom {{ \leqslant \exp - \cosh ^{ - 1} (\sigma + 1)} {2,}}} \right. \kern-\nulldelimiterspace} {2,}}}}$$ where σ is such that HessV(x)≥σ>0.