Two-loop operator matrix elements calculated up to finite terms for polarized deep inelastic lepton-hadron scattering

We present the two-loop corrected operator matrix elements contributing to the scale evolution of the longitudinal spin structure function $g_1(x,Q^2)$ calculated up to finite terms which survive in the limit $\epsilon = N - 4 \to 0$. These terms are needed to renormalize the local operators up to third order in the strong coupling constant $\alpha_s$. Further the expressions for the two-loop corrected operator matrix elements can be inserted into one loop graphs to obtain a part of the third order contributions to these matrix elements. This work is a first step in obtaining the third order anomalous dimensions so that a complete next-to-next-to-leading order (NNLO) analysis of the above mentioned structure function can be carried out. In our calculation particular attention is paid to the renormalization constant which is needed to restore the Ward-identities violated by the HVBM prescription for the $\gamma_5$-matrix in $N$-dimensional regularization.Comment: 25 pages, Phys. Rev. Tex, no figure

Two-loop operator matrix elements calculated up to finite terms

We present the two-loop corrected operator matrix elements calculated in N-dimensional regularization up to the finite terms which survive in the limit been previously extracted from the pole terms and determine the scale evolution of the deep inelastic structure functions measured in unpolarized lepton hadron scattering. The finite $\epsilon$-independent terms in the two-loop expressions are needed to renormalize the local operators up to third order in the strong coupling constant $\alpha_s$. Further the unrenormalized expressions for the two-loop corrected operator matrix elements can be inserted into specific one loop graphs to obtain a part of the third order contributions to these matrix elements. This work is a first step in obtaining the anomalous dimensions up to third order so that a complete next-to-next-to-leading order (NNLO) analysis can be carried out for deep inelastic electroproduction

Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory

Starting from fixed-order perturbation theory (FOPT) we derive expressions for the heavy-flavour components of the deep-inelastic structure functions FL and F2 in the variable-flavour number scheme (VFNS). These expressions are valid in all orders of perturbation theory. This derivation establishes a relation between the parton densities parametrized at N and N light flavours. The consequences for the existing parametrizations of the parton densities are discussed. Further we show that in charm electroproduction the exact and asymptotic expressions for the heavy-quark coefficient functions yield identical results for F2 when Q^2>20 (GeV/c)^2. We also study the differences between the FOPT and the VFNS descriptions for F2. It turns out that the charm structure function in the VFNS is larger than the one obtained in FOPT over the whole Q^2-range. Furthermore inspection of the perturbation series reveals that the higher order corrections in the VFNS are smaller than those present in FOPT for Q^2>10 (GeV/c)^2. Therefore the VFNS gives a better prediction for the charm structure function at large Q^2-values than FOPT.Comment: 48 pages, Latex and 13 figures, Postscrip

Deep-inelastic production of heavy quarks

Deep-inelastic production of heavy quarks at HERA, especially charm, is an excellent signal to measure the gluon distribution in the proton at small $x$ values. By measuring various differential distributions of the heavy quarks this reaction permits additional more incisive QCD analyses due to the many scales present. Furthermore, the relatively small mass of the charm quark, compared to the typical momentum transfer $Q$, allows one to study whether and when to treat this quark as a parton. This reaction therefore sheds light on some of the most fundamental aspects of perturbative QCD. We discuss the above issues and review the feasibility of their experimental investigation in the light of a large integrated luminosity.Comment: 10 pages, uses epsfig.sty, five ps figures included. To appear in the proceedings of the workshop Future Physics at HERA, eds. G. Ingelman, A. De Roeck and R. Klanner, DESY, Hamburg, 199

Comparison between the various descriptions for charm electroproduction and the HERA-data

We examine the charm component F_{2,c}(x,Q^2,m^2) of the proton structure function F_2(x,Q^2) in three different schemes and compare the results with the data in the x and Q^2 region explored by the HERA experiments. Studied are (1) the three flavour number scheme (TFNS) where the production mechanisms are given by the photon-gluon fusion process and the higher order reactions with three light-flavour parton densities as input (2) the four flavour number scheme (FFNS) where F_{2,c} is expressed in four light flavour densities including one for the charm quark and (3) a variable-flavour number scheme (VFNS) which interpolates between the latter two. Both the VFNS and the TFNS give good descriptions of the experimental data. However one cannot use the FFNS for the description of the data at small Q^2

Determination of the asymptotic behaviour of the heavy flavour coefficient functions in deep inelastic scattering

Using renormalization group techniques we have derived analytic formulae for the next-to-leading order heavy-quark coefficient functions in deep inelastic lepton hadron scattering. These formulae are only valid in the kinematic regime Q^2 >> m^2, where Q^2 and m^2 stand for the masses squared of the virtual photon and heavy quark respectively. Some of the applications of these asymptotic formulae will be discussed.Comment: Latex with two PostScript figures and style file. Presentation at the Rheinsberg Meeting on Higher Order QCD and QE

Deep-inelastic production of heavy quarks

Deep-inelastic production of heavy quarks at HERA, especially charm, is an excellent signal to measure the gluon distribution in the proton at small $x$ values. By measuring various differential distributions of the heavy quarks this reaction permits additional more incisive QCD analyses due to the many scales present. Furthermore, the relatively small mass of the charm quark, compared to the typical momentum transfer $Q$, allows one to study whether and when to treat this quark as a parton. This reaction therefore sheds light on some of the most fundamental aspects of perturbative QCD. We discuss the above issues and review the feasibility of their experimental investigation in the light of a large integrated luminosity

The light-cone gauge and the calculation of the two-loop splitting functions

We present calculations of next-to-leading order QCD splitting functions, employing the light-cone gauge method of Curci, Furmanski, and Petronzio (CFP). In contrast to the `principal-value' prescription used in the original CFP paper for dealing with the poles of the light-cone gauge gluon propagator, we adopt the Mandelstam-Leibbrandt prescription which is known to have a solid field-theoretical foundation. We find that indeed the calculation using this prescription is conceptionally clear and avoids the somewhat dubious manipulations of the spurious poles required when the principal-value method is applied. We reproduce the well-known results for the flavour non-singlet splitting function and the N_C^2 part of the gluon-to-gluon singlet splitting function, which are the most complicated ones, and which provide an exhaustive test of the ML prescription. We also discuss in some detail the x=1 endpoint contributions to the splitting functions.Comment: 41 Pages, LaTeX, 8 figures and tables as eps file