Basis transformation properties of anomalous dimensions for hard exclusive processes

Abstract

When considering the renormalization of composite operators for the description of hard exclusive scattering processes, two types of operator basis called the derivative basis and the Gegenbauer basis are often used in the literature. In this work we set up the explicit similarity transformations between these two bases, both for quark and gluon operators. This way, one can use the properties of both bases to their advantage in the computation of the operator anomalous dimensions, which describe the scale dependence of non-perturbative non-forward parton distributions. We provide several applications of our framework. As an application of the gluon transformation formula, we compute the one-loop non-forward purely gluonic anomalous dimension matrix. For the rest of the applications we focus on the transformation formula of the quark operator. We derive the Gegenbauer anomalous dimensions, in the limit of a large number of quark flavors $n_f$, to all orders in the strong coupling ${\alpha }_s$, extending the computation previously performed in the derivative basis. Next a numeric calculation of the two-loop anomalous dimensions in the derivative basis beyond the leading-color limit is presented. Finally, we discuss a novel way of validating existing computations of the conformal anomaly based on the leading-color anomalous dimensions in the derivative basis.

arXiv comment39 pages, LaTeX, 2 figures, journal version, fixed a typo in Eq.(7.5) [conclusions remain unchanged]

References in corpus (36)

• Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-Off
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD
• Generalized Parton Distributions
• Deeply Virtual Compton Scattering
• Scaling Limit of Deeply Virtual Compton Scattering
• FORM version 4.0
• The Spin Structure of the Nucleon
• Transverse Polarisation of Quarks in Hadrons
• Harmonic sums, Mellin transforms and Integrals
• The angular momentum controversy: What's it all about and does it matter?
• The theory and phenomenology of polarized deep inelastic scattering
• Asymmetric Gluon Distributions and Hard Diffractive Electroproduction
• Harmonic Sums and Mellin Transforms up to two-loop Order
• The Uses of Conformal Symmetry in QCD
• Broken conformal invariance and spectrum of anomalous dimensions in QCD
• A Critical Appraisal and Evaluation of Modern PDFs
• Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
• Scale dependence of twist-three contributions to single spin asymmetries
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• The Virtual Compton Amplitude in the Generalized Bjorken Region: Twist--2 Contributions
• A lattice determination of moments of unpolarised nucleon structure functions using improved Wilson fermions
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Single spin asymmetries in inclusive high energy hadron-hadron collision processes
• Three loop anomalous dimension of the second moment of the transversity operator in the MSbar and RI' schemes
• Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD
• Two-loop conformal generators for leading-twist operators in QCD
• On the Anomalous Dimension of the Transversity Distribution $h_1(x,Q^2)$
• Two-loop evolution equations for light-ray operators
• Two loop renormalization of the n = 2 Wilson operator in the RI'/SMOM scheme
• Amplitudes for the n = 3 moment of the Wilson operator at two loops in the RI/'SMOM scheme
• Moments $n=2$ and $n=3$ of the Wilson twist-two operators at three loops in the RI${}^{\prime }$/SMOM scheme
• Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering
• Higher Twists
• NNLO anomalous dimension matrix for twist-two flavor-singlet operators

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• Constraints for twist-two alien operators in QCD