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).     

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.     

The next-to-leading order (NLO) gluon distribution from DGLAP equation and the logarithmic derivatives of the proton structure functionF 2(x, Q 2) at lowx

At lowx, an analytic solution of the DGLAP equation for gluon in the next-to-leading order (NLO) is obtained by applying the method of characteristics. Its compatibility with double leading logarithmic approximation (DLLA) asymptotics is discussed and comparison with the exact ones like GRV98NLO is made. The solution is then utilized to calculate the derivatives∂F ₂ (x,Q ²)/∂ lnQ ² and ∂ lnF ₂(x,Q ²)/∂ ln (1/x) and compared with the recent HERA data. Our solution is found to reproduce most of the essential features of the data on the derivatives.     

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.     

Higher order QCD corrections to the photoproduction of a direct photon at HERA

The contribution of resolved photons to the photoproduction cross section of direct photons is reexamined. Higher order,O(α ² α _s), QCD corrections to this contribution are calculated and turn out to be important at HERA energies. The observation of direct photons in the medium-p _⊥ range (p _⊥～5 GeV/c) should provide the opportunity to measure the gluon content of the photon.     

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).     

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}).     

Two-loop QCD corrections to the coefficient functions of the deep inelastic structure functionsF 2 andF L

We present the analytic two-loop perturbative QCD corrections in the leading twist approximation to the coefficient functions of the operator product expansion for the second to tenth moments of the nonsinglet and singlet deep inelastic structure functionsF ₂ andF _L .     

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 $F_{2}^{\gamma p}(x,Q^{2})$ .     

Perturbative QCD analysis of the nucleon's Pauli form factor F2(Q2)

We perform a perturbative QCD analysis of the nucleon's Pauli form factor F2(Q2) in the asymptotically large Q2 limit. We find that the leading contribution to F2(Q2) has a 1/Q6 power behavior, consistent with the well-known result in the literature. Its coefficient depends on the leading- and subleading-twist light-cone wave functions of the nucleon, the latter describing the quarks with one unit of orbital angular momentum. We also derive at the logarithmic accuracy the asymptotic scaling F2(Q2)/F(1)(Q2) approximately (log2Q2/Lambda2)/Q2 which describes recent Jefferson Lab data well.     

Solutions of independent DGLAP evolution equations for the gluon distribution and singlet structure functions in the next-to-leading order at low x

We present a set of independent formulas to extract the gluon distribution and the singlet structure function from its derivatives with respect to lnQ ² in the next-to-leading order of perturbation theory at low x based on a hard Pomeron exchange. In this approach, both singlet quarks and gluons have the same high-energy behavior at small x. This approach requires the QCD input parameterizations for independent DGLAP evolutions, which we calculated numerically and compared with the MRST, GRV, and DL models. The Pomeron has a hard nature. Its evolution gives a good fit to the experimental data. The values obtained are in the range 10⁻⁴ ≤ x ≤ 10⁻² at Q ² = 20 GeV². The text was submitted by the author in English.     

QCD corrections to the parton-model sum rules for structure functions of deep inelastic scattering

The results of two-loop calculations of the O(α_s²) corrections to the first nonsinglet moments of the deep inelastic scattering structure functions for polarized and unpolarized targets are presented.