Analysis of the electroproduction structure functions in the lowQ 2 region,combining the vector meson dominance and the parton model with possible scaling violation

The nucleon structure functionF ₂ is constructed and analysed for low values ofQ ² using the generalised vector meson dominance representation with the largeQ ² spectral function calculated from the analytic continuation of the parton model structure function. Various parametrisations of the parton distributions are considered. Possible effects of the largeQ ² scaling violation on the lowQ ² part of the structure function are investigated. The magnitude of the total contribution given by this asymptotic part can be as high as 50% of the vector meson contribution in the low-Q ², low-χ region. The contribution of the valence quarks alone to the structure function at lowQ ² turns out to be at least as important as the corresponding non-Pomeron Regge-pole-like terms coming from the vector meson part. Increase of the structure function with ν coming from the increase of the quark sea in the limit of small χ implied by QCD turns out to be relatively weak at lowQ ². Predictions of the model are compared with available experimental data. The photoproduction cross section and the nuclear effects in the structure function are also briefly discussed.     

Infrared contribution to the double-logarithmic small-x asymptotics of structure functions

The role playing by the “soft” (κ _T < 1 GeV/c) region in the small-x behaviour ofg ₁(x,Q ²) and the non-singlet structure functionf _{1, NS}(x, Q²) has been studied with the help of the effective QCD Lagrangian which takes into account the lightest degrees of freedom — the constituent quarks and the π-mesons (Goldstone bosons). It has been shown that the quark-quark interaction due to the pion exchange has a negative couplingg for the isovector component (I = 1 in thet-channel) off ₁(x,Q ²) and isosinglet component ofg ₁(x, Q²). Here the pion induced interaction changes mainly the normalization of the quark distribution (it decreasesf _1,NS ^{I = 1} (x,Q ²) two times atx < 3·10^?3) and changes slightly the effective exponents λ (?_1,NS ,g ₁ ～x ^?λ atx → 0). On the other hand due to a positive value of couplingg the value of λ increases by 15% for the isovector part ofg ₁ (x,Q ²) and up to λ ≈ 0.5 (instead of λ ≈ 0.2 without the pion contribution) for the isoscalar non-singlet structure functionf _1,NS ^{I = 0} (x,Q ²).     

Spin structure of hadrons in supersymmetric quantum chromodynamics at short distances

We study the short-distance spin structure of nucleons in supersymmetric QCD. We calculate the Altarelli-Parisi spin transition coefficients ΔP _ba and corresponding anomalous Δ γ _ab ⁿ fora, b=quarks, gluons, gluinos and squarks and present the supersymmetric relations between them. Further analysis is divided into two parts: the parity conserving case and parity violating case, both following from the mass mixing in the squark sector. Solving theQ ²-evolution equations we determine the quark, gluon, gluino and squark spin distribution at variousQ ² above the threshold for production of supersymmetric partners. We also show the analytic solutions for the first moments in the nonsinglet and singlet sector. In particular the spin carried by the valence quarks turn out to vanish asymptotically except of one particular case of squark mixing.     

Scaling violations for the spin-dependent structure function G1

With the formalism of Altarelli and Parisi, we study scaling violations for the spin dependent structure function G₁. We find that the variation of G₁ with Q² is essentially determined by that of the valence quarks helicity distributions, the antiquark densities contributing negligibly.     

The spectral class of the quantum-mechanical harmonic oscillator

The purpose of this paper is to study the so-calledspectral class Q of anharmonic oscillatorsQ=?D ²+q having the same spectrum λ _n =2n (n≧0) as the harmonic oscillatorQ ⁰=?D ²+x ²?1. Thenorming constants \(t_n = \mathop {\lim }\limits_{x \uparrow \infty } \ell g[( - 1)^n {{e_n (x)} \mathord{\left/ {\vphantom {{e_n (x)} {e_n }}} \right. \kern-0em} {e_n }}( - x)]\) of the eigenfunctions ofQ form a complete set of coordinates inQ in terms of which the potential may be expressed asq=x ²?1?2D ² ?g? with $$\theta = \det \left[ {\delta _{ij} + (e^{ti} - 1)\int\limits_x^\infty {e_i^0 e_j^0 :0 \leqq i,j,< \infty } } \right],$$ e _n ⁰ being then ^th eigenfunctionQ ⁰. The spectrum and norming constants are canonically conjugate relative to the bracket [F, G]=∫ΔFDΔGdx,to wit: [λ _i , λj=0, [t _i, 2λ _j ]=1 or 0 according to whetheri=j or not, and [t _i,t _j]=0. This prompts an investigation of the symplectic geometry ofQ. The function ? is related to the theta function of a singular algebraic curve. Numerical results are also presented.     

On theQ 2-extrapolations of AF-corrected Drell-Yan processes

TheQ ²-dependence of the integrated Drell-Yan cross sections with asymptotic freedom (AF) corrections is investigated forQ ²≦ 10⁷ GeV². Existing AF-parametrizations lead to widely differing predictions. Lowest order QCD indicates a strong dependence on thex-behaviour of the input momentum distributions (atQ ²=Q ₀ ² ) which for sea quarks and gluons are guesses. Consequently, AF-corrected Drell-Yan extrapolations toW-energies and beyond involve considerable uncertainties.     

Scattering of very light scalar particles,off leptons

Within the scope of a new diquark model for deep inelastic structure functions presented by us recently we use the existing data onF ₁ ^ep (x,Q²) to learn about the admixture of spin-1 diquarks in nucleons. It turns out that they are so rare, heavy and extended compared to spin-0 diquarks that they are presumably accidental and not dynamical. Their number and form factors can be understood qualitatively within this picture. Still, the spin-1 diquarks give interesting structures in data and, together with quarks and spin-0 diquarks, carry enough momentum to account for the full nucleon energy. A gluon component is hence not needed in the nucleon!     

A model for FL and R = FL/FT at low x and low Q2

A model for the longitudinal structure function F_L at low x and low Q² is presented, which includes the kinematical constraint F_L ～ Q⁴ as Q² → 0. It is based on the photon-gluon fusion mechanism suitably extrapolated to the region of low Q². The contribution of quarks having limited transverse momentum is treated phenomenologically assuming that it is described by the soft pomeron exchange mechanism. The ratio R = F_L/(F₂ ? F_L), with the F₂ appropriately extrapolated to the region of low Q², is also discussed.     

Investigations of the electron paramagnetic resonance parameters and defect structures for Ni ions in CdX2 (X=Cl,Br) crystals

The high-order perturbation formulas of electron paramagnetic resonance (EPR) parameters (g factors g_∥,g_⊥ and zero-field splitting D) for 3d⁸ ions in trigonal octahedral clusters are established. These formulas contain the contributions not only from the crystal-field (CF) mechanism, but also from the charge-transfer (CT) mechanism (which is not considered in the widely used CF theory). From these formulas, the EPR parameters and the impurity-induced defect structures for Ni²⁺ ions in CdX₂ (X=Cl, Br) crystals are studied. The calculated EPR parameters are coincident with the experimental values, and the defect structure of Ni²⁺ impurity center obtained from the calculation is different from the corresponding structure in the host crystal. The sign of Q^CT (Q=Δg_∥, Δg_⊥, or D) due to CT mechanism agrees with that of the corresponding Q^CF due to CF mechanism and the relative importance of CT mechanism (characterized by Q^CT/Q^CF) increases with increasing covalence of 3d⁸ clusters and hence with raising atomic number of ligand X. So, in the explanations of the EPR parameters of 3d⁸ (or other 3dⁿ) ions in crystals with the heavy-element ligand ion (e.g., Br⁻), the calculated formulas based on the two-mechanism (CF and CT mechanisms) model are preferable to those based on only the CF mechanism in the CF theory.     

Dynamical determination of parton and gluon distributions in quantum chromodynamics

Using the dynamical assumption that at low resolution-energies hadrons consist of valence quarks only, we calculate uniquely nucleonic as well as pionic parton and gluon distributions within the framework of QCD, and give analytic expressions for their x- and Q²-dependence. Applications to dilepton and W-boson Drell-Yan production in pN and πN reactions are illustrated and possible applications to high-p_T processes are discussed.     

Model for nucleon valence structure functions at allx,allp ⊥ and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon valence structure functions at allx, allp _⊥ and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =3 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ². Excellent agreement is obtained with existing data.     

Multilevel systems and generalizations of the superalgebra

A new approach to constructing the various generalizations of the one-dimensional supersymmetric quantum mechanics is proposed, including the parasupersymmetric quantum mechanics constructed by Rubakov and Spiridonov as the special case. In particular, we derive the generalized superalgebra, which possesses the features both of the familiar superalgebra and of the parasuperalgebra. Namely, the generalized supercharges Q_i ^± and the Hamiltonian H forms the generalized superalgebra, where Q_i ^±2=0 (as for ordinary superalgebra), but the triple products of generalized supercharges obey the relations Q₁ ⁺Q_j ^–Q_j ⁺=Q_i ⁺H (i, j=1, 2) and Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺, Q_i ⁺Q_i ^–Q_j ⁺=(1/4)kQ_i ⁺(i, j=1, 2; ij) (analogous to the parasuperalgebra). Furthermore, the generalized supercharges are conserved, i.e. [H, Q_i ^±]=0.Presented at the International Workshop on Squeezed and Correlated States, Moscow, December 3–7, 1990.     

The Q<Superscript>2</Superscript> dependence of polarized and unpolarized proton structure functions in the relativistic quark exchange framework

In this article we intend to discuss the evolution of polarized and unpolarized structure functions in the (x,Q²) plane. We analyze the proton data on the spin dependence asymmetry A₁(x,Q²), by making the dynamical assumption that at low resolution energies, the hadrons consist only of valence quarks and the scaling violation of F₂(x,Q²) at low x comes only from the gluons density. While the sea quark and the gluon distributions are calculated using the inverse Mellin technique and the various moments of the valence quarks, the valence quark distribution itself is obtained from the relativistic quark-exchange model. A comparison is made with the corresponding available experimental data. Finally in agreement with the data, it is demonstrated that there is no significant Q²-dependence of asymmetry A₁(x,Q²) for x ranging 0.014 ≤ x ≤ 0.25. Received: 11 September 1999 / Revised version: 8 December 1999     

改进的双重Q2重标度模型

提出了改进的双重Q²重标度模型,在保持核动量守恒的条件下,用唯象的方法找到了一套重标度参数公式,建立了重标度参数ξ_v,ξ_s及ξ_g与原子核平均结合能之间的联系.利用该模型所得到的束缚核子内部分子分布函数,对核DIS过程,核Drell-Yan过程和J/Ψ光生过程均给出满意的解释 关键词： 2重标度模型')" href="#">双重Q²重标度模型 核效应 结合能     

Mössbauer studies and nuclear quadrupole moments of186, 188, 189, 190 Os

Mössbauer transmission experiments with the 137, 155, 69 and 187 keV gamma rays of^{186, 188, 189, 190}Os, respectively, yielded the electric quadrupole splitting of these gamma resonance lines in OsO₂ and OsP₂. From the results the following ratios of quadrupole moments were derived:Q ₂ ⁺(¹⁸⁶Os, 137 keV):Q ₂ ⁺(¹⁸⁸Os, 155keV):Q ₂ ⁺(¹⁹⁰Os, 187 keV):Q _3/2 ^?(¹⁸⁹Os, g.s.)=(+1.100±0.020): 1.0:(+0.863±0.051): (?0.586±0.011) andQ _5/2 ^?(¹⁸⁹Os, 69 keV)/Q _3/2 ^?(¹⁸⁹Os, g.s.)=?0.735 ±0.012. The ratios for^{180, 188, 190}Os are, within their limits of error, in agreement with the expectation of the rotational model, indicating that the pairing-plusquadrupole model calculations of Kumar and Baranger predict too rapid a transition form rotational to vibrational nuclei. Applying this argument to¹⁸⁶Os in particular and using the measured ratios, one obtains a set of values for the quadrupole moments themselves, namelyQ ₂ ⁺ (¹⁸⁶Os)=?(1.50 ± 0.10)b,Q ₂ ⁺(¹⁸⁸Os)=?(1.36± 0.09) b,Q ₂ ⁺ (¹⁹⁰Os)=?(1.18 ± 0.08) b,Q _3/2 ^?(¹⁸⁹Os)=+ (0.80 ± 0.06) b, andQ _5/2 ^? (¹⁸⁹Os)=? (0.59 ± 0.05) b. For the electric field gradient at Os nuclei in Re metal a value ofV _zz=?(3.3 ± 0.6) · 10¹⁷ V/cm² was found. A measurement with a magnetically split source yielded δ=+ 0.685 ± 0.025 for theE2/M1 mixing parameter of the 69 keV transition of¹⁸⁹Os,g _5/2 ^?/g _3/2 ^?=0.895 ± 0.006 for the ratio of theg-factors of the 69 keV state and the groundstate, andH _i=?(1135 ± 20) kOe for the hyperfine field at Os nuclei in an iron matrix.     

Resolving the EPR Spectra in the Cytochrome bc 1 Complex from Saccharomyces cerevisiae

Quinone molecules are ubiquitous in living organisms. They are found either within the lipid phase of the biological membrane (quinone pool) or are bound in specific binding sites within membrane-bound protein complexes. The biological function of such bound quinones is determined by their ability to be reduced and/or oxidized in two successive one-electron steps. As a result, quinones are involved as one- or two-electron donors or acceptors in a large number of biological electron-transfer steps occurring during respiratory or photosynthetic processes. The intermediate formed by a one-electron reduction step is a semiquinone, which is paramagnetic and can be studied by electron paramagnetic resonance (EPR) spectroscopy. Detailed studies of such states can provide important structural information on these intermediates in such electron-transfer processes. In this study, we focus on the redox-active ubiquinone-6 of the yeast cytochrome bc ₁ complex (QCR, ubiquinol: cytochrome c oxidoreductase) from Saccharomyces cerevisiae at the so-called Q_i site. Although the location of the Q_i binding pocket is quite well known, details about its exact binding are less clear. Currently, three different X-ray crystallographic studies suggest three different binding geometries for Q_i. Recent studies in the bacterial system (Rhodobacter sphaeroides) have suggested a direct coordination to histidine as proposed in the chicken heart crystal structure model. Using the yeast system we apply EPR and especially relaxation filtered hyperfine (REFINE) spectroscopy to study the Q_i binding site. ¹⁴N-electron spin-echo envelope modulation spectroscopy together with an inversion-recovery filter (REFINE) is applied to resolve the question of whether ¹⁴N modulations arise from interactions to Q _i ^·? or to the Rieske iron–sulphur center. These results are discussed with regard to the location and potential function of Q_i in the enzyme.     

Quark mass effects in deeply inelastic scattering

We argue that the difference between the structure functions corresponding to deep inelastic scattering with and without heavy quarks in the current fragmentation region scales at high Q² and fixed (low) x _Bj.