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.     

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.     

Small-x behaviour of the polarized photon structure function F_3^\gamma(x,Q^2)

We study the small-x behaviour of the polarized photon structure function F₃^gF_3^{\gamma}, measuring the gluon transversity distribution, in the leading logarithmic approximation of perturbative QCD. There are two contributions, both arising from two-gluon exchange. The leading contribution to small-x is related to the BFKL pomeron and behaves like x^-1-w₂x^{-1-\omega_2}, w₂ = O(a_S)\omega_2 ={\cal O}(\alpha_S). The other contribution includes in particular the ones summed by the DGLAP equation and behaves like x^1-w₀(+)x^{1-\omega_0^{(+)}}, w₀⁽⁺⁾ = O(?{a_S})\omega_0^{(+)} = {\cal O}(\sqrt{\alpha_S}).     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

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     

Probing the color glass condensate in an electron-ion collider

Perturbative quantum chromodynamics (pQCD) predicts that the small-x gluons in a hadron wavefunction should form a color glass condensate (CGC), characterized by a saturation scale Q_s(x,A), which is energy and atomic number dependent. In this paper, we study the predictions of CGC physics for electron-ion collisions at high energies. We consider that the nucleus at high energies acts as an amplifier of the physics of high parton densities and estimate the nuclear structure function F₂^A(x,Q²), as well as the longitudinal and charm contributions, using a generalization for nuclear targets of the Iancu–Itakura–Munier model that describes the ep HERA data quite well. Moreover, we investigate the behavior of the logarithmic slopes of the total and longitudinal structure functions in the kinematical region of the future electron-ion collider eRHIC.     

Charm production and parton distributions

Recent accurate data on F ₂(x,Q) and on F ₂ ^c (x,Q) from HERA at small-x require a more precise treatment of charm production in the global analysis of parton distributions. We improve on existing global QCD analyses by implementing the leptoproduction formalism of Aivazis et al. which represents a natural generalization of the conventional zero mass QCD parton framework to include heavy quark mass effects. We also perform analyses based on the fixed-flavor-number scheme, which is widely used in the literature, and demonstrate their uses and limitations. We discuss the implications of the improved treatment of heavy quark mass effect in practical applications of PQCD and compare our results with recent related works.     

Chiral-odd transversity spin structure function h1(x) of the nucleon in a constituent quark model

We study the chiral-odd transversity spin-dependent quark distribution function h₁(x) of the nucleon in a constituent quark model. The twist-2 structure functions, f₁(x), g₁(x) and h₁(x) are calculated within the diquark spectator approximation. Whereas an inequality f₁(x) > h₁(x) > g₁(x) holds with the interaction between quark and diquark being scalar, the axial-vector effective quark-diquark interaction, which contributes to the d-quark distribution, does not lead to such a simple relation. We find that h₁(x) for the d-quark becomes somewhat smaller than g₁^d(x), when we fix the model parameter to reproduce known other structure functions. We also include corrections due to the non-trivial structure of the constituent quark, which is modeled by the Goldstone boson dressing. This improves agreements of f₁(x) and g₁(x) with experiments, and brings further reduction of h₁^d(x) distribution. Consequences for semi-inclusive experiments are also discussed.     

A measurement of the proton structure function F2(x,Q2)

A measurement of the proton structure function F₂(x, Q²) is reported for momentum transfers squared Q² between 4.5 GeV² and 1600 GeV² and for Bjorken x between 1.8 × 10⁻¹⁴ and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that F₂ increases significantly with decreasing x, confirming our previous measurement made with one tenth of the data available in this analysis. The Q² dependence is approximately logarithmic over the full kinematic range covered. The subsample of deep inelastic events with a large pseudo-rapidity gap in the hadronic energy flow close to the proton remnant is used to measure the “diffractive” contribution to F₂.     

Scattering lengths of pionic 3He and 4He

Scattering lengths of pionic ³He and ⁴He and the charge exchange contribution to the 1s width of pionic ³He are calculated within the fixed scatterer approximation of the multiple scattering formalism. Particular attention is focussed on the nuclear physics part and on πN p-wave contributions. For the first time triple scattering and double-spin-flip contributions have been included. We find significant deviations from previous estimates and calculations. Good agreement is achieved with the experimental π^?3He scattering length, whereas in the case of ⁴He a repulsive dispersion contribution is clearly needed. We propose to use the measured 1s level shift of pionic ³He as a constraint to deduce a precise value of the isoscalar πN scattering length. Furthermore, we find that multiple scattering reduces the impulse approximation value for Γ_1s(π^?3He → π^{0 3}H) by more thsn 20 %. This result casts some doubt on impulse approximation calculations of radiative pion capture as well.     

Less singular terms and small x evolution in a soluble model

We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in φ³ theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading order contributions are also studied. We show that the small-x approximation does not deliver the dominant contributions.     

Ionic conductivity of Zr1−xIn2xO2−x

As x in Zr(In)O_2?x is increased from 0.08 to 0.16 (9–19 mole per cent In₂O₃) the activation energy E(x) for ionic conduction increases from 1.05 to 1.51 eV; the concuctivity decreases from 2 × 10^?5 to 3 × 10^?6Ω^?1cm^?1at 400°C, is composition-independent at about 580°C, and increases from 1 × 10^?2 to 4 × 10^?2Ω^?1cm^?1 at 800°C. The pre-exponential term of the Boltzmann-type conductivity equation depends exponentially on E(x), a much stronger dependence on x than theoretically expected with a model for ionic conductivity that includes nearest-neighbor defect interactions. Analysis of reported conductivity data for Zr(M)O_2?x (M = Sc, Y, Ca and rare earth metals) and other doped oxide electrolytes with fluorite-type structure reveals that the same relationship is observed with these materials when x γ0.08. It is shown that ionic conduction in these oxides is consistent with nearest neighbor vacancy-cation defect interaction forx < 0.08 but that an additional complex interaction with composition-dependent free energy ΔG(x) occurs when xγ 0.08.The lattice constant of Zr(In)O_2?x with the cubic fluorite-type structure is independent of composition, 5.114 ± 0.002 Å, in agreement with ionic size considerations.     

Can recently measured moments of F3vN discriminate between field theories of strong interactions?

It is demonstrated that moments of the flavor non-singlet structure function F₃^vN cannot discriminate, contrary to recent claims, between QCD and other nontrivial fixed point theories of strong interactions, even by taking into account the CDHS precision measurements. Only quantities, such as F₂(x, Q²), which receive also flavor singlet contributions (dominant at small x) can provide us with discriminative tests of strong interaction theories using present experiments; it is not sufficient to study just moments (n > 2) of F₂, since these are sensitive mainly to the non-singlet (large-x) contribution.     

F L structure function and heavy quark contributions

In this paper we obtain the heavy-quark contribution to the longitudinal structure functions F _L (x, Q ²). Since F _L structure functions contains rather large heavy flavor contributions in the small x region, we need to use the massive operator matrix elements, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q ²?>?>?m ². The method of QCD analysis, based on the Jacobi polynomials method, is also described. Our results for longitudinal structure function are in good agreement with the available experimental data.     

Separation of the contributions to the magnetization of Tm1 − x Yb x B12 solid solutions in steady and pulsed magnetic fields

The magnetization of substitutional Tm_{1 ? x} Yb _x B₁₂ solid solutions is studied in the composition range 0 < x ≤ 0.81. The measurements are performed at low temperatures (1.9–300 K) in steady (up to 11 T) and pulsed (up to 50 T, pulse duration of 20–100 ms) magnetic fields. An analysis of the experimental data allowed the contributions to the magnetization of the paramagnetic phase of the Tm_{1 ? x} Yb _x B₁₂ compounds to be separated. These contributions include a Pauli component, which corresponds to the response of the heavy-fermion manybody states that appears in the energy gap in the vicinity of the Fermi level (density of states (3?4) × 10²¹ cm^?3 meV^?1), and a contribution with saturation in high magnetic fields attributed to the localized magnetic moments ((0.8–3.7)μ_B per unit cell) of the nanoclusters formed by rare-earth ions with an antiferromagnetic interaction.     

An SO(10) model with 54 + 126 + 10 higgs

We find an absolute minimum of an SO(10) symmetric potential with SU(3) × U(1) invariance. By fixing the higher scales M_R(〈126〉) ? M_x(〈54〉), the model is consistent with the experimental knowledge about matter stability and the value of sin²θ_w. We determine the spectrum of scalar particles and show that their tree-diagram contributions to nucleon decay amplitudes are proportional to 1/M_x².     

Deep-inelastic scattering in κ factorization and the anatomy of the differential gluon structure function of the proton

The differential gluon structure function of the proton, ?(x, Q ²), introduced by Fadin, Kuraev, and Lipatov in 1975 is extensively used in small-x QCD. We report here the first determination of ?(x, Q ²) from experimental data on the small-x proton structure function F _2p (x, Q ²). We give convenient parametrizations for ?(x, Q ²) based partly on the available DGLAP evolution fits (GRV, CTEQ, and MRS) to parton distribution functions and on realistic extrapolations into the soft region. We discuss the impact of soft gluons on various observables. The x dependence of the so-determined ?(x, Q ²) varies strongly with Q ² and does not exhibit simple Regge properties. Nonetheless, the hard-to-soft diffusion is found to give rise to a viable approximation of the proton structure function F _2p (x, Q ²) by the soft and hard Regge components with intercepts Δ_soft=0 and Δ_hard ～ 0.4.     

Intrinsic coercive field in cubic intermetallic compounds. II: TbxGd1−xAl2 and ErAl2

The thermal dependence of the coercive field in the pseudobinary cubic Laves phase compounds Tb_xGd_1−xAl₂(0 ⩽ x ⩽1.0) and ErAl₂ has been measured from 3.7 K up to de Cirie temperatures. The coercive field has two contributions: one from the intrinsic pinning of narrow domain walls in the Peierls crystal potential wells; this contribution is preponderant at low temperatures, decaying exponentially with the domain walls width. The other, which for x ⩾ 0.4 is dominant, comes out from the pinning of domain walls by defects (Kersten mechanism). The domain walls seem very narrow in those materials, between 2 and 5 interlayer atomic spacings.     

Exchange and hyperfine fields acting on dilute Eu In SmCo5, Sm2(Co1-xFex)17 and Sm2CoxMy( rm M = Fe, Cu, Zn, Zr)

Mössbauer source experiments of dilute ¹⁵³Eu and ⁵⁷Fe in SmCo₅ and ¹⁵³Eu in Sm₂(Co_1-xFe_x)₁₇ and Sm₂ Co_x M_y at 4.1 K were performed. After the ${}^{153}\text{Sm}\text{→β?}{}^{153}$ decay the Eu ion is trivalent and exhibits extremely large hyperfine interactions due to strong exchange fields. Since the exchange interactions are comparable to the Eu³⁺ spin-orbit coupling, we calculated the expectation values of the Eu³⁺ spin, magnetic hyperfine field and electric field gradient as a function of exchange field and second order crystalline field, by diagonalization of the full Hamiltonian of spin orbit, exchange and crystalline field. For SmCo₅ and Sm₂(Co_1-xFe_x)₁₇ the exchange and crystalline fields are known and thus allow us to analyze our experimental results and obtain the polarized conduction electron contributions to the magnetic hyperfine field. The contribution due to magnetic neighbour polarization of conduction electrons is found to be linear in exchange field. The experimental results together with the theoretical analysis yield the Eu electric field gradient 4f Sternheimer shielding factor R_Q to be 0.26±04. It is shown that Mössbauer studies of two probes (¹⁵⁵Gd and Eu³⁺) in magnetic systems yield directly the second order crystalline field, the exchange field and the various contributions to the hyperfine field acting on the Eu nucleus. From the experimentally measured magnetic hyperfine fields alone, approximate values for the exchange fields in the mixed systems Sm₂Co_xM_y were determined.