An analysis of a quantum chromodynamic structure function

We obtain an approximate solution of Altarelli-Parisi equations yielding a sample of quantum chromodynamic structure function. The SLAC-MIT data are analysed with it. Possible effects of intrinsic charm and higher twist are also included. Agreement is found to be good forx⩾0.25.     

Comments on structure functions at low-x

We present further analysis of the structure functions at low-x using the approximate solutions of Altarelli-Parisi equations recently reported by us. We also compare our results with non-perturbative and non-linear evolutions.     

Comment on a solution of Altarelli Parisi equations

We show that the assumptions of factorizability of the structure functionF(x, t) inx andt and the equality oft evolution of the singlet and gluon distributions are not necessary to obtain the approximate solutions of Altarelli-Parisi equations derived by us recently.     

Analysis of structure function equations up to the seventh order

We examine balances of structure function equations up to the seventh order N = 7 for longitudinal, mixed and transverse components. Similarly, we examine the traces of the structure function equations, which are of interest because they contain invariant scaling parameters. The trace equations are found to be qualitatively similar to the individual component's equations. In the even-order equations, the source terms proportional to the correlation between velocity increments and the pseudo-dissipation tensor are significant, while for odd N, source terms proportional to the correlation of velocity increments and pressure gradients are dominant. Regarding the component equations, one finds under the inertial range assumptions as many equations as unknown structure functions for even N, i.e. can solve for them as function of the source terms. On the other hand, there are more structure functions than equations for odd N under the inertial range assumptions. Similarly, there are not enough linearly independent equations in the viscous range r → 0 for orders N > 3.     

Lepton-hadron processes beyond leading order in quantum chromodynamics

We present a summary of QCD formulae describing the effects of scaling violation in leptonhadron processes, with the inclusion of recently derived higher order corrections. Deep inelastic leptoproduction, one-hadron inclusive distributions in leptoproduction and ine ⁺ e ^? annihilation and Drell-Yan processes are discussed in detail. Higher order corrections to parton densities, fragmentation functions and to lepton-parton cross-sections in the above processes are presented in a common factorization scheme, so that a comparative analysis of various processes as well as an independent analysis of each of them is possible. A discussion of the various scheme dependences at next-to-leading level is also included.     

Perturbative and non-perturbative evolutions of structure functions at low-x

Approximate solutions of Altarelli-Parisi equations are obtained in low-x limit and have tested them in EMC low-x and low-Q ² data. The results are compared with the phenomenological non-perturbative evolutions. Data conform to perturbative as well as non-perturbative evolutions but do not conform to the predictions of non-linear evolution.     

Remarks on beyond leading order

In recent years a two-scale expansion was established to study reactions of the type NN→NNπ within chiral perturbation theory. Then the diagrams of some subclasses that are invariant under the choice of the pion field no longer appear at the same chiral order. In this Letter we show that the proposed expansion still leads to well defined results. We also discuss the appropriate choice of the heavy baryon propagator.     

Regge behaviour of structure function and gluon distribution at low-x in leading order

We present a method to find the gluon distribution from the proton structure function data at low-x assuming the Regge behaviour of the gluon distribution function at this limit. We use the leading order (LO) Altarelli–Parisi (AP) evolution equation in our analysis and compare our result with those of other authors. We also discuss the limitations of the Taylor expansion method in extracting the gluon distribution from the structure function used by those authors. Received: 2 January 2000 / Revised version: 23 February 2000 / Published online: 6 July 2000     

An analysis of non-singlet structure function in next-to-next-to-leading order at small-x

A more general form of non-singlet structure function in Next-to-Next-to-leading order (NNLO) by solving Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP) equation at small-x is obtained. Results are compared with Fermi Lab Experiment E665 data.     

Degenerate limit thermodynamics beyond leading order for models of dense matter

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects, but for finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Results from our analytical formulas are compared with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid. Effects of many-body correlations that deserve further investigation are highlighted.     

Evolution of parton densities beyond leading order: The non-singlet case

We develop a technique, based explicitly on the factorization properties of mass singularities, which allows one to calculate the evolution of parton densities beyond leading order. We present the results for the evolution of hadronic structure functions as well as for parton fragmentation functions into hadrons. Within our scheme the predictions for a particular process are obtained by convoluting a universal parton density with a “short-distance” cross section specific to the process. As an application, we calculate the QCD predictions for the Q² dependence of deep inelastic lepton-hadron scattering and of one-particle iclusive e⁺ e^? annihilation cross sections. Our results for electroproduction agree with those obtained with the operator product expansion technique. Physical quantities in scattering are related to the corresponding ones in annihilation by analytic continuation, whereas the Gribov-Lipatov relation is strongly violated.     

The gluon distributions in the smallx region beyond the leading order

The gluon distributions in a proton are calculated in the region of smallx (10^?4?x?10^?2) and largeQ ² taking into account the corrections which correspond to the sum of the leading powers of log 1/x beyond the leading logQ ² approximation. It is shown that they become significant for very small values ofx only provided however that the non-leading terms in the limit of smallx are also consistently included. The leading log 1/x approximation gives the gluon distributions which can differ by a factor of 2 from their leading logQ ² counterpart.