The longitudinal structure function F L(x, Q 2) and the gluon distribution G(x, Q 2) at low x

We obtain a relation between the longitudinal structure function F _L(x, Q ²), F ₂(x, Q ²) and G(x, Q ²) at small x, using the formalism recently reported by one of the authors [2]. We also obtain a relation between F _L(x, Q ²), F ₂(x, Q ²) and its slope (dF ₂(x, Q ²))/(dlnQ ²). This provides us with the determination of the longitudinal structure function F _L(x, Q ²) from F ₂(x, Q ²) data and hence extract the gluon distribution G(x, Q ²).     

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.     

Model for the nucleon structure function F2(x,Q2)

A particular j-plane singularity, leading to long-range effects in hadron scattering, is attributed to hard constituent quark interactions. A definite prediction for the nucleon structure function, including scaling violations consistent with QCD. is obtained, which is confronted with the available data.     

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.     

F 2/x G(x,Q 2) ratio at small x and the role of the contribution from infrared region

We consider the light quark electroproduction cross section.     

The gluonic contribution tog 1 P (x,Q 2) in the parton model

We present a careful analysis of the polarized photon-gluon fusion process. Discussing various regularization schemes it is demonstrated that one can safely extract a hard gluonic contribution to the proton's spin dependent structure functiong ₁ ^P . The value of the first moment of the gluonic Wilson coefficient is shown to be in agreement with the anomaly result. Furthermore, we examine the question whether the gluonic contribution alone can account for existing experimental data forg ₁ ^P (x,Q ²) (x≧0.01, <Q ²>?Q ₀ ² =10 GeV²) and find a positive answer.     

Analytic Derivation of the Longitudinal Proton Structure Function FL(x,Q2) and the Reduced Cross Section σr(x,Q2) at the Leading Order and the Next-to-leading Order Approximations

International Journal of Theoretical Physics - We present a set of formulas to extract the longitudinal proton structure function FL(x, Q2) and the reduced cross section σr(x, Q2) by using...     

On the possibility of measuringF L (x,Q 2) at HERA using radiative events

It is shown that a significant measurement of the longitudinal structure functionF _L (x, Q ²) can be performed at HERA, forQ ²=2 GeV² andQ ²=5 GeV² and forx around 10^?4, using radiative events with hard photon emission collinear to the incident lepton beam, under the present running conditions and with an integrated luminosity of 10 pb^?1. The influence of experimental conditions is discussed.     

Jacobi polynomials and non-singlet structure function F2(x,Q2)up to N3LO

In this paper we present the non-singlet QCD analysis to determine valence quark distribution up to four loop.We obtain the fractional difference between the 4-loop and the 1-,2-and 3-loop presentations of xuv(x,Q2)and xdv(x,Q2).     

Measurement of the proton spin structure function g1(x,Q2) for Q2 from 0.15 to 1.6 GeV2 with CLAS

Double-polarization asymmetries for inclusive ep scattering were measured at Jefferson Lab using 2.6 and 4.3 GeV longitudinally polarized electrons incident on a longitudinally polarized NH3 target in the CLAS detector. The polarized structure function g(1)(x,Q2) was extracted throughout the nucleon resonance region and into the deep inelastic regime, for Q(2)=0.15-1.64 GeV2. The contributions to the first moment Gamma(1)(Q2)= integral g(1)(x,Q2) dx were determined up to Q(2)=1.2 GeV2. Using a parametrization for g(1) in the unmeasured low x regions, the complete first moment was estimated over this Q2 region. A rapid change in Gamma(1) is observed for Q2<1 GeV2, with a sign change near Q(2)=0.3 GeV2, indicating dominant contributions from the resonance region. At Q(2)=1.2 GeV2 our data are below the perturbative QCD evolved scaling value.     

A new numerical method for obtaining gluon distribution functions G(x,Q 2)=xg(x,Q 2), from the proton structure function F_{2}^{\gamma p}(x,Q^{2})

An exact expression for the leading-order (LO) gluon distribution function G(x,Q ²)=xg(x,Q ²) from the DGLAP evolution equation for the proton structure function $F_{2}^{\gamma p}(x,Q^{2})$ for deep inelastic γ ^* p scattering has recently been obtained (Block et al., Phys. Rev. D 79:014031, 2009) for massless quarks, using Laplace transformation techniques. Here, we develop a fast and accurate numerical inverse Laplace transformation algorithm, required to invert the Laplace transforms needed to evaluate G(x,Q ²), and compare it to the exact solution. We obtain accuracies of less than 1 part in 1000 over the entire x and Q ² spectrum. Since no analytic Laplace inversion is possible for next-to-leading order (NLO) and higher orders, this numerical algorithm will enable one to obtain accurate NLO (and NNLO) gluon distributions, using only experimental measurements of $F_{2}^{\gamma p}(x,Q^{2})$ .     

Spin structure function g 1 (x, Q) and the DHGHY integral I(Q) at low Q: predictions from the GVMD model

Theoretical predictions for the polarized nucleon structure function g ₁ (x, Q ² ) at low Q² are obtained in the framework of the generalized vector meson dominance model. Contributions from both light and heavy vector mesons are evaluated. In the photoproduction limit the first moment of g₁ is related to the static properties of the nucleon via the Drell-Hearn-Gerasimov-Hosoda-Yamamoto sum rule. This property is employed to fix the magnitude of the light vector meson contribution to g₁, using the recent measurements in the region of baryonic resonances. The results are compared to the data on g ₁ (x, Q ² ). Finally, the DHGHY moment function I(Q ² ) is calculated, and our theoretical predictions are confronted with the recent preliminary data obtained at the Jefferson Laboratory. Received: 9 July 2002 / Published online: 7 October 2002 RID="a" ID="a" e-mail: badelek@fuw.edu.pl RID="b" ID="b" e-mail: jan.kwiecinski@ifj.edu.pl RID="c" ID="c" e-mail: ziaja@tsl.uu.se     

Optical Properties of the (CuInSe2) x ·(2ZnSe)1−x and (CuInTe2) x (·2ZnTe)1−x Solid Solutions

Crystals of the compounds CuInSe₂, CuInTe₂, ZnSe, and ZnTe, and the solid solutions (CuInSe₂) _x ·(2ZnSe)_1–x and (CuInTe₂) _x ·(2ZnTe)_1–x were grown by the Bridgman and chemical transport reactions methods. Their transmission and reflection spectra in the region of the main absorption line edge were studied. The forbidden band gap of the indicated materials was determined and its concentration dependences were built for the solid solutions. It is established that the forbidden band gap changes linearly with the x composition and is satisfactorily described by the square-law dependence.