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D. Müller

Publications and source records attributed to D. Müller.

At least 73 records · Page 4Linked to original sources
arXiv2000

Twist-three effects in two-photon processes

We give a general treatment of twist-three effects in two-photon reactions. We address the issue of the gauge invariance of the Compton amplitude in generalized Bjorken kinematics and relations of twist-three `transverse' skewed parton distributions to twist-two ones and interaction dependent three-particle correlation functions. Finally, we discuss leading order evolution of twist-three functions and their impact on the deeply virtual Compton scattering.

hep-ph↗
arXiv2000

Extraction of skewed parton distributions

Skewed parton distributions contain new non-perturbative information about hadronic states. Thus, their extraction from experimental data is an important goal. Properties and models for skewed parton distributions as well as their extraction, based on perturbative leading-order results, are shortly reviewed.

hep-ph↗
arXiv2000

NLO Exclusive Evolution Kernels

We outline a formalism used for a construction of two-loop flavor singlet exclusive evolution kernels in the MS bar scheme. The approach is based on the known pattern of conformal symmetry breaking in MS bar as well as constraints arising from the superconformal algebra of the N = 1 super Yang-Mills theory.

hep-ph↗
arXiv2000

Off-forward gluonometry

We explore the deeply virtual Compton scattering process at NLO with the emphasis on the measurement of the tensor gluon skewed distributions. We recalculate the one-loop coefficient function and give two-loop results for anomalous dimensions and exclusive evolution kernels required for studying the logarithmic scaling violation. We evaluate weighted cross sections which give direct access to these functions on experiment.

hep-ph↗
arXiv1999

Evolution kernels of skewed parton distributions: method and two-loop results

We present a formalism and explicit results for two-loop flavor singlet evolution kernels of skewed parton distributions in the minimal subtraction scheme. This approach avoids explicit multiloop calculations in QCD and is based on the known pattern of conformal symmetry breaking in this scheme as well as constraints arising from the graded algebra of the $\cN = 1$ super Yang-Mills theory. The conformal symmetry breaking part of the kernels is deduced from commutator relations between scale and special conformal anomalies while the symmetric piece is recovered from the next-to-leading order splitting functions and $\cN = 1$ supersymmetry relations.

hep-ph↗
arXiv1999

Radiative corrections to deeply virtual Compton scattering

We discuss possibilities of measurement of deeply virtual Compton scattering amplitudes via different asymmetries in order to access the underlying skewed parton distributions. Perturbative one-loop coefficient functions and two-loop evolution kernels, calculated recently by a tentative use of residual conformal symmetry of QCD, are used for a model dependent numerical estimation of scattering amplitudes.

hep-ph↗
arXiv1999

Deeply virtual Compton scattering in next-to-leading order

We study the amplitude of deeply virtual Compton scattering in next-to-leading order of perturbation theory including the two-loop evolution effects for different sets of skewed parton distributions (SPDs). It turns out that in the minimal subtraction scheme the relative radiative corrections are of order 20-50%. We analyze the dependence of our predictions on the choice of SPD, that will allow to discriminate between possible models of SPDs from future high precision experimental data, and discuss shortly theoretical uncertainties induced by the radiative corrections.

hep-ph↗
arXiv1999

Reconstruction of non-forward evolution kernels

We develop a framework for the reconstruction of the non-forward kernels which govern the evolution of twist-two distribution amplitudes and off-forward parton distributions beyond leading order. It is based on the knowledge of the special conformal symmetry breaking part induced by the one-loop anomaly and conformal terms generated by forward next-to-leading order splitting functions, and thus avoids an explicit two-loop calculation. We demonstrate the formalism by applying it to the chiral odd and flavour singlet parity odd sectors.

hep-ph↗
arXiv1999

Exclusive evolution kernels in two-loop order: parity even sector

We complete the construction of the non-forward evolution kernels in next-to-leading order responsible for the scale dependence of e.g. parity even singlet distribution amplitudes. Our formalism is designed to avoid any explicit two-loop calculations employing instead conformal and supersymmetric constraints as well as known splitting functions.

hep-ph↗
arXiv1999

$\cN = 1$ supersymmetric constraints for evolution kernels

We provide a complete set of supersymmetric constraints for the anomalous dimensions of the conformal twist-two operators to all orders of perturbation theory. Employing them we derive new relations between the exclusive evolution kernels and apply them in QCD in order to get definite predictions at leading order and beyond.

hep-ph↗
arXiv1999

Scheme dependence of NLO corrections to exclusive processes

We apply the so-called conformal subtraction scheme to predict perturbatively exclusive processes beyond leading order. Taking into account evolution effects, we study the scheme dependence for the photon-to-pion transition form factor and the electromagnetic pion form factor at next-to-leading order for different pion distribution amplitudes. Relying on the conformally covariant operator product expansion and using the known higher order results for polarized deep inelastic scattering, we are able to predict perturbative corrections to the hard-scattering amplitude of the photon-to-pion transition form factor beyond next-to-leading order in the conformal scheme restricted to the conformal limit of the theory.

hep-ph↗
arXiv1998

Restricted conformal invariance in QCD and its predictive power for virtual two-photon processes

The conformal algebra provides powerful constraints, which guarantee that renormalized conformally covariant operators exist in the hypothetical conformal limit of the theory, where the $β$-function vanishes. Thus, in this limit also the conformally covariant operator product expansion on the light cone holds true. This operator product expansion has predictive power for two-photon processes in the generalized Bjorken region. Only the Wilson coefficients and the anomalous dimensions that are known from deep inelastic scattering are required for the prediction of all other two-photon processes in terms of the process-dependent off-diagonal expectation values of conformal operators. It is checked that the next-to-leading order calculations for the flavour non-singlet meson transition form factors are consistent with the corrections to the corresponding Wilson coefficients in deep inelasitic scattering.

hep-ph↗
arXiv1998

Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD

The widely used nonperturbative wave functions and distribution functions of QCD are determined as matrix elements of light-ray operators. These operators appear as large momentum limit of nonlocal hadron operators or as summed up local operators in light-cone expansions. Nonforward one-particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. These distribution functions depend besides other variables on two scaling variables. They are applied for the description of exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes are derived on the basis of the renormalization group equation of the considered operators. This includes that also the evolution kernels follow from the anomalous dimensions of these operators. Relations between different evolution kernels (especially the Altarelli-Parisi and the Brodsky-Lepage) kernels are derived and explicitly checked for the existing two-loop calculations of QCD. Technical basis of these results are support and analytically properties of the anomalous dimensions of light-ray operators obtained with the help of the $α$-representation of Green's functions.

hep-ph↗
arXiv1997

Non-local generalization of the axial anomaly and $x$-dependence of the anomalous gluon contribution

The generalization of the axial anomaly is considered. It is shown that bilocal axial quark operators on the light cone possess, beside the point-like anomaly, also a light-like anomaly. The consequences for the definition of anomaly-free quark distribution functions and the effect of both gluon coefficient function and splitting kernels in polarized deep inelastic scattering are discussed.

hep-ph↗
arXiv1997

Calculation of higher-twist evolution kernels for polarized deep inelastic scattering

Based on the non-local light-ray operator technique, we develop an algorithm for the computational calculation of evolution kernels for higher-twist operators in leading order of the perturbation theory. We compute the evolution kernel for the twist-3 operators in the flavour singlet channel. Our result confirms the local anomalous dimensions computed by Bukhvostov, Kuraev, and Lipatov as well as the non-local evolution kernels of Balitzky and Braun.

hep-ph↗
arXiv1996

The evolution of the nonsinglet twist-3 parton distribution function

The twist three contributions to the $Q^2$-evolution of the spin-dependent structure function $g_2(x_{Bj},Q^2)$ are considered in the non-local operator product approach. Defining appropriate twist three distribution function we derive their evolution equation for the nonsinglet case in leading order approximation. In the limit $x_{Bj} \rightarrow 1$ as well as in the large $N_c$ limit we confirm the result that the evolution of the nonsinglet part of $g_2$ is governed by a Gribov-Lipatov-Altarelli-Parisi equation.

hep-ph↗
arXiv1996

Evolution Kernels of Twist-3 Light-Ray Operators in Polarized Deep Inelastic Scattering

The twist three contributions to the $Q^2$-evolution of the spin-dependent structure function $g_2(x)$ are considered in the non-local operator product approach. Starting from the perturbative expansion of the T-product of two electromagnetic currents, we introduce the nonlocal light-cone expansion proved by Anikin and Zavialov and determine the physical relevant set of light-ray operators of twist three. Using the equations of motion we show the equivalence of these operators to the Shuryak-Vainshtein operators plus the mass operator, and we determine their evolution kernels using the light-cone gauge with the Leibbrandt-Mandelstam prescription. The result of Balitsky and Braun for the twist three evolution kernel (nonsinglet case) is confirmed.

hep-ph↗