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W. L. van Neerven

Publications and source records attributed to W. L. van Neerven.

At least 55 records · Page 3Linked to original sources
arXiv1999

Deep inelastic lepton-hadron scattering as a test of perturbative QCD

Exploration of the small $x$ kinematic region by the HERA experiments led to a revival of some models which existed before the advent of Quantum Chromo Dynamics (QCD) as the theory of the strong interactions. Predictions of these models for the deep inelastic structure functions are compared with those given by QCD. Future experiments will concentrate on the large $x$-region and we will discuss some issues which are important for the test of QCD. In particular we emphasize the next-to-next-to-leading (NNLO) order analysis of the structure functions and the determination of the strong coupling constant $α_s$. We also make some critical remarks about the relevance of so called large corrections in the small and large $x$-region.

hep-ph↗
arXiv1999

Relations among Higher Order QCD corrections

We study the scheme transformation of next to leading order QCD corrections to various processes. An interesting relation by Drell, Levy and Yan (DLY) among space like and time like processes is studied carefully in the next to leading order level. We construct factorisation scheme invariants and show that they are DLY-invariant.

hep-ph↗
arXiv1998

Relations among QCD corrections beyond leading order

The status of various relations among higher order QCD corrections is discussed. In particular, Drell-Levy-Yan relation and Supersymmetric relation are studied at the two-loop level. We have also investigated the validity of such relations for physical observables.

hep-ph↗
arXiv1998

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 ϕ^3 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.

hep-ph↗
arXiv1998

Heavy flavour contributions to the deep inelastic sum rules

We have calculated the first and second order corrections to several deep inelastic sum rules which are due to heavy flavour contributions. A comparison is made with the existing perturbation series which has been computed up to third order for massless quarks only. In general it turns out that the effects of heavy quarks are very small except when $Q \sim m$ or $Q \gg m$. Here $Q$ and $m$ denote the virtual mass of the vector boson and the mass of the heavy quark, respectively. For $Q \gg m$ the radiative corrections reveal large logarithms of the type $\ln Q^2/m^2$ which have to be absorbed in the running coupling constant so that the number of light flavours $n_f$ is enhanced by one unit. However this has to happen at much larger values of Q i.e. $Q \sim 6.5~ m$ than one usually assumes for the flavour thresholds which appear in the running coupling constant. An alternative description for the heavy flavour dependence of the running coupling constant in the context of the MOM-scheme is discussed.

hep-ph↗
arXiv1998

Second order QCD corrections to the forward-backward asymmetry in e^+e^- - collisions

The sentence, 11th line below Eq. (30), starting with "Further in [14] one has included all interference terms ...." is wrong and has been corrected. Second line below Eq. (40) m_bar(m)=m is replaced by m_bar(μ_0)=μ_0 with μ_0=4.10 GeV, μ_0=1.30 GeV and μ_0=166.1 GeV for bottom, charm and top respectively. The numbers in the second and third column of table 3 are a little bit changed. In the acknowledgement the funding agency is mentioned and one reference i.e. [20] is added.

hep-ph↗
arXiv1998

Heavy flavour mass corrections to the longitudinal and transverse cross sections in e^+e^- - collisions

The sentence, 7th line below Eq. (28), starting with "Further we exclude all interference terms ...." is wrong and has been corrected. Eq. (33) : f_k^{l,(i)} -> h_k^{l,(i)} i=0,1 Second line below Eq. (33) m_bar(m)=m is replaced by m_bar(μ_0)=μ_0 with μ_0=4.10 GeV and μ_0=166.1 GeV for bottom and top respectively. The numbers in the third column of tables 1 and 2 are a little bit changed.

hep-ph↗
arXiv1998

The Unpolarized Gluon Anomalous Dimension at Small x

We discuss the quantitative consequences of the resummation of the small-x contributions to the anomalous dimensions beyond next-to-leading order in alpha_s and up to next order in ln(1/x) (NLx) in a framework based on the renormalization group equations. We find large and negative effects leading to negative values for the {\sf total} splitting function P_{gg}(x,alpha_s) already for x \lsim 0.01 at Q^2 \simeq 20 GeV^2. Terms less singular than those under consideration turn out to be quantitatively as important and need to be included. We derive the effects of the conformal part of the NLx contributions to the anomalous dimensions and discuss the exponent omega describing the s^omega behavior of inclusive cross sections.

hep-ph↗
arXiv1998

Relations among polarized and unpolarized splitting functions beyond leading order

The role of various symmetries in the evaluation of splitting functions and coefficient functions is discussed. The scale invariance in hard processes is known to be a guiding tool to understand the dynamics. We discuss the constraints on splitting functions coming from various symmetries such as scale, conformal and supersymmetry. We also discuss the Drell-Levy-Yan relation among splitting and coefficient functions in various schemes. The relations coming from conformal symmetry are also presented.

hep-ph↗
arXiv1998

On the Gluon Regge Trajectory in $O(α_s^2)$

We recalculate the gluon Regge trajectory in next-to-leading order to clarify a discrepancy between two results in the literature on the constant part. We confirm the result obtained by Fadin et al.~\cite{FFK}. The effects on the anomalous dimension and on the $s^ω$ behavior of inclusive cross sections are also discussed.

hep-ph↗
arXiv1998

Higher order QCD Corrections to Fragmentation Functions in e^+~e^- Annihilation

We analyze the second order QCD corrections to the fragmentation functions F_^H_k(x,Q^2) (k=T,L,A) which are measured in e^+~e^- annihilation From these fragmentation functions one can derive the integrated transverse (sigma_T), longitudinal (sigma_L) and asymmetric (sigma_A) cross sections. The sum sigma_{tot}=sigma_T+sigma_L corrected up to order alpha_s^2 agrees with the well known result in the literature. It turns out that the order alpha_s^2 corrections to the transverse and asymmetric quantities are small in contrast to our findings for F_L^H(x,Q^2) and sigma_L where they turn out to be large. Therefore in the latter case one gets a better agreement between the theoretical predictions and the data obtained from he LEP experiments.

hep-ph↗
arXiv1998

Resummation of Large Logarithms in the Charm Structure Function

We show how one can resum the large logarithms which occur in the charm component of the structure function F_{k,c}(x,Q^2,m_c^2) (k=2,L) taken at three light flavours, in the limit Q^2 \gg m_c^2. This resummation leads to an expression of the above quantity for four light flavours including the charm quark density. The latter is related to the parton densities in the three light flavour number scheme.

hep-ph↗
arXiv1998

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 $ε= N - 4 \to 0$. These terms are needed to renormalize the local operators up to third order in the strong coupling constant $α_s$. 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 $γ_5$-matrix in $N$-dimensional regularization.

hep-ph↗
arXiv1998

Second order QCD contributions to polarized spacelike and timelike processes

We will give an outline of the computation of the QCD corrections to the spin structure function g_1(x,Q^2) and the spin fragmentation function g_1^H(x,Q^2) which are measured in deep inelastic electron-proton scattering and in electron-positron annihilation respectively. In particular we show how to deal with the gamma_5-matrix and the Levi-Civita tensor, appearing in the amplitudes of the parton subprocesses, when the method of N-dimensional regularization is used.

hep-ph↗
arXiv1998

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 $ε= N - 4 \to 0 $. The anomalous dimensions of the local operators have 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 $ε$-independent terms in the two-loop expressions are needed to renormalize the local operators up to third order in the strong coupling constant $α_s$. 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.

hep-ph↗
arXiv1997

Heavy flavour contributions to the spin structure function g_1(x,Q^2) and the Bjorken sum rule

We discuss the order alpha_s^2 corrections to the longitudinal spin structure function g_1(x,Q^2,m^2) which are due to heavy flavour contributions. Here Q denotes the virtuality of the photon and m stands for the heavy flavour mass. Since the exact heavy quark coefficient functions are not known yet we have used the asymptotic forms which are strictly speaking only valid in the region Q^2 >> m^2. However an analysis of the exact and asymptotic expressions for F_2^{NLO}(x,Q^2,m^2) and g_1^{LO}(x,Q^2,m^2) reveals that the asymptotic forms can be also used at smaller Q^2. It appears that for the region 0.01 < x < 0.1 the NLO charm quark component can become twice as large as in LO. However it is still much smaller than g_1(x,Q^2) due to light parton contributions. This is in contrast to the observations made for F_2(x,Q^2) at small x. Also the charm quark contribution to the Bjorken sum rule turns out to be very small.

hep-ph↗
arXiv1997

Charm Production in Deep Inelastic Lepton-Hadron Scattering

A review is given of the QCD corrections to charm quark production in deep inelastic electron-proton scattering. An outline of the computation of the virtual photon-parton subprocesses, from which one obtains the heavy quark coefficient functions, is given. The dominant production mechanisms are discussed. Further we show that the asymptotic heavy quark coefficient functions, computed in the limit Q^2 >> m^2, can be derived using the operator product expansion technique. Further we present the various schemes proposed in the literature to describe the charm component of the structure function and compare them with the most recent data from the experiments carried out at HERA.

hep-ph↗