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A. V. Belitsky

Publications and source records attributed to A. V. Belitsky.

At least 127 records · Page 7Linked to original sources
arXiv1999

Integrability and WKB solution of twist-three evolution equations

We identify an integrable one-dimensional inhomogeneous three-site open spin chain which arises in the problem of diagonalization of twist-three quark-gluon evolution equations in QCD in the chiral-odd sector. Making use of the existence of a non-trivial `hidden' integral of motion the problem of diagonalization of the evolution kernels is reduced to the study of a second order finite-difference equation which is solved in WKB approximation for large conformal spins of the three-particle system. The energies (alias anomalous dimensions) of eigenstates with different scale dependence are found in limiting cases and compared with numerical calculations.

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

Fine structure of spectrum of twist-three operators in QCD

We unravel the structure of the spectrum of the anomalous dimensions of the quark-gluon twist-3 operators which are responsible for the multiparton correlations in hadrons and enter as a leading contribution to several physical cross sections. The method of analysis is bases on the recent finding of a non-trivial integral of motion for the corresponding Hamiltonian problem in multicolour limit which results into exact integrability of the three-particle system. Quasiclassical expansion is used for solving the problem. We address the chiral-odd sector as a case of study.

hep-ph↗
arXiv1998

Implications of N=1 supersymmetry for QCD conformal operators

We prove a set of identities for the anomalous dimensions of the quark and gluon conformal operators in the flavour singlet channel in QCD. These relations arise from the graded commutator algebra of the N=1 superconformal group. We evaluate the rotation matrices for the quantities under study from the conventional dimensional regularization to the supersymmetry preserving regularization scheme. Using them we verify the equalities in two-loop approximation employing the results for the NLO anomalous dimensions of the conformal operators in the minimal subtraction scheme derived earlier.

hep-ph↗
arXiv1998

Two-loop renormalization of Wilson loop for Drell-Yan production

We study the renormalization of the Wilson loop with a path corresponding to the Drell-Yan lepton pair production in two-loop approximation of perturbation theory. We establish the renormalization group equation in next-to-leading order and find a process specific anomalous dimension Gamma_DY in the corresponding approximation.

hep-ph↗
arXiv1998

Two-loop effects in the evolution of non-forward distributions

We study the effects of next-to-leading order corrections on the evolution of the twist-two non-forward parton distribution functions in the flavour non-singlet sector. It is found that the deviation from leading order evolution is small for all values of the parton momentum fraction variable for moderately large values of the scale parameter.

hep-ph↗
arXiv1998

Broken conformal invariance and spectrum of anomalous dimensions in QCD

Employing the operator algebra of the conformal group and the conformal Ward identities, we derive the constraints for the anomalies of dilatation and special conformal transformations of the local twist-2 operators in Quantum Chromodynamics. We calculate these anomalies in the leading order of perturbation theory in the minimal subtraction scheme. From the conformal consistency relation we derive then the off-diagonal part of the anomalous dimension matrix of the conformally covariant operators in the two-loop approximation of the coupling constant in terms of these quantities. We deduce corresponding off-diagonal parts of the Efremov-Radyushkin-Brodsky-Lepage kernels responsible for the evolution of the exclusive distribution amplitudes and non-forward parton distributions in the next-to-leading order in the flavour singlet channel for the chiral-even parity-odd and -even sectors as well as for the chiral-odd one. We also give the analytical solution of the corresponding evolution equations exploiting the conformal partial wave expansion.

hep-ph↗
arXiv1998

Next-to-leading order evolution of twist-two conformal operators: The abelian case

We present the method, based on the use of the broken conformal Ward identities, for the calculation of the anomalous dimensions of conformal operators beyond the leading order of perturbation theory. By means of this technique we find the complete set of two-loop corrections to the off-diagonal elements of the anomalous dimension matrix (the diagonal ones are known from deep inelastic scattering calculations) of the parity odd and even singlet local operators in the Abelian gauge theory. We reconstruct corresponding exclusive two-loop evolution kernels and give the reduction formulae for the restoration of the diagonal part of the ER-BL kernels from the DGLAP splitting functions.

hep-ph↗
arXiv1998

Higher orders and IR renormalon phenomenology in DVCS

We present results for higher order perturbative corrections to Compton scattering in the generalized Bjorken kinematics. The approach we have used is based on the combination of two techniques: conformal operator product expansion on the one side, and resummation of the fermion vacuum insertions with consequent restoration of the full QCD beta-function via the naive nonabelianization assumption, on the other. These are terms which are lost in the former approach. Due to the presence of the infrared renormalon poles in the Borel transform of the resummed amplitude the latter suffers from ambiguities which reflect the asymptotic character of perturbation series. The residues of these IR renormalon poles give an estimate for the size of power corrections in deeply virtual Compton scattering.

hep-ph↗
arXiv1997

Predictions from conformal algebra for the deeply virtual Compton scattering

Basing on the constraint equalities which arise from the algebra of the collinear conformal group and the conformal operator product expansion, we predict the solutions of the leading order evolution equations for the non-forward distributions, including transversity, in terms of the conformal moments; next-to-leading order flavour singlet coefficient functions for the polarized and unpolarized deeply virtual Compton scattering; as well as the contribution from renormalon chains to the eigenfunctions of the exclusive non-singlet evolution kernel.

hep-ph↗
arXiv1997

On the leading logarithmic evolution of the off-forward distributions

We have found the analytical solution of the LO-evolution equation for off-forward distributions which arise in the processes of deeply virtual Compton scattering or exclusive production of mesons. We present the predictions for their evolution with an input distribution taken from recent bag model calculations.

hep-ph↗
arXiv1997

Scale dependence of the chiral-odd twist-3 distributions $h_L(x)$ and $e(x)$

We evaluate the complete leading-order evolution kernels for the chiral-odd twist-3 distributions $e(x)$ and $\widetilde h_L(x)$ of the nucleon. We establish the connection between the evolution equations in light-cone position and light-cone fraction representations, which makes a correspondence between the non-local string operator product expansion and the QCD-inspired parton model. The compact expression obtained for the local anomalous dimension matrix coincides with previous calculations. In the multicolour QCD as well as in the large-$x$ limit the twist-3 distributions obey simple DGLAP equations. Combining these two limits, we propose improved DGLAP equations and compare them numerically with the solutions of the exact evolution equations.

hep-ph↗
arXiv1996

Valence parton dencity in the pion from QCD sum rules

We calculate the leading twist valence quark distribution in the pion in the franework of QCD sum rules with nonlocal condensates. Particular attention has been paid to the correct account of the bilocal power corrections.

hep-ph↗