Twist-two Operators Research Articles

Generalized parton distributions and double distributions forqq¯pions

We consider two simple covariant models for pions (one with scalar and the other with spin-1/2 constituents). Pion generalized parton distributions are derived by integration over the light-cone energy. The model distributions are consistent with all known properties of generalized parton distributions, including positivity. We also construct the corresponding double distributions by appealing to Lorentz invariance. These ostensibly constructed double distributions lead to different generalized parton distributions that need not respect the positivity constraints. This inconsistency arises from the ambiguity inherent in defining double distributions in a one-component formalism (even in the absence of the Polyakov-Weiss term). We demonstrate that the correct model double distributions can be calculated from non-diagonal matrix elements of twist-two operators.

The Radiative rare decays B ? K**? in the light-cone QCD sum rule approach

We predict contributions of higher K-resonances to the radiative rare decays b → sγ, in the framework of the QCD sum rules on the light cone, which combines the traditional QCD sum rule method with the description of final state mesons in terms of the light-cone wave functions of increasing twist. Our calculations are restricted to the leading twist-two operators for K*(892) and to the asymptotic wave function for the other K**-mesons.Using experimental data on the semileptonic τ → K**ντ decays, we extract the corresponding decay constants for vector and axial-vector K**-mesons. Based on our estimate of the transition form factor F1K*(892)(0) = 0.32 ± 0.06 and the K2*(1430) decay constant fK2*(1430) = (160 ± 20) MeV, we find good agreement with experimental results. The two largest fractions of the inclusive b → sγ branching ratio are found to be (10.0 ± 4.0)% for B → K*(892)γ and (5.0 ± 2.0)% for B → K2*(1430)γ decays. We also compare our results with the existing theoretical predictions.

Resummation of target mass corrections in two-photon processes: twist-two sector

We develop a formalism for the resummation of target mass corrections in off-forward two-photon amplitudes given by a chronological product of electromagnetic currents, arising in, e.g., deeply virtual Compton scattering. The method is based on a relation of composite operators with a definite twist to harmonic tensors, which form an irreducible representation of the Lorentz group. We give an application of the framework for the matrix elements of twist-two operators.

Counting form factors of twist-two operators

We present a simple method to count the number of hadronic form factors based on the partial wave formalism and crossing symmetry. In particular, we show that the number of independent nucleon form factors of spin-$n,$ twist-2 operators (the vector current and energy-momentum tensor being special examples) is $n+1.$ These generalized form factors define the generalized (off-forward) parton distributions that have been studied extensively in the recent literature. In proving this result, we also show how the ${J}^{\mathrm{PC}}$ rules for quarkonium states arise in the helicity formalism.

N = 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.

Second-order contributions to the structure functions in deep inelastic scattering (I). Theoretical calculations

In this paper we present a simple analytical expression for the next-to-leading corrections to the contributions to scaling violations of non-singlet, twist-two operators. Using these expression, we solve the point-like inversion problem to this order of perturbation theory in an explicit form. The formulas given are general enough to allow continuation of the procedure to arbitrary orders in perturbation theory. The method is furthermore extended to give also an analytic treatment of target mass corrections. To exemplify the method, a few phenomenological implications are discussed, a full comparison with experiment being left for a following paper.

Jet and lepton-pair production in high-energy lepton-hadron and hadron-hadron scattering

Cross sections for jet and lepton-pair production at large transverse momenta are studied in a class of renormalizable field theories including quantum chromodynamics. To all orders in perturbation theory, appropriate moments are seen to factorize short-distance from long-distance dependence in leptoproduction. Scale breaking is governed by the anomalous dimensions of twist-two operators. These results are extended to hadron-hadron scattering for theories where infrared divergences cancel in the sum over soft particle emissions, even in the limit that all particle masses vanish. This cancellation is explicitly demonstrated for totally massless QED.

High-energy behavior of jet and lepton-pair production

The cross section for jet and lepton-pair production at large transverse momenta has been studied to all orders in QCD perturbation theory. Appropriate moments of these cross sections are seen to factorize short-distance from long-distance dependence, and scale breaking is governed by the anomalous dimensions of twist-two operators.

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ⩽ Q 2 ⩽ 16 GeV 2. Excellent agreement is obtained using g 2(2 GeV) 4π 2 = 0.17 for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of M 0 2 Q 2 . We use data from the resonance region to show M 0 ⋍ 400 MeV , in agreement with theoretical expectations. Our fit to νW 2 in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of R = σ L σ T at large x and Q 2 are systematically higher than our predictions.

Gauge invariance in the operator-product expansion in non-Abelian gauge theory

Non-gauge-invariant operators appear in addition to manifestly gauge-invariant operators in the operator-product expansion in non-Abelian gauge theories. However, with the help of various Ward-Takahashi identities, it is shown that these operators which are not gauge invariant do not mix with the gauge-invariant operators to all orders in perturbation theory. These "null" operators have vanishing matrix elements in the physical subspace. Accordingly, the null operators may be neglected completely in the operator-product expansion, and the anomalous dimensions of gauge-invariant operators can be found by simply examining the mixing between the gauge-invariant operators if the correct separation between the gauge-invariant operators and the null operators is made. Our discussion is restricted to the light-cone-dominant twist-two operators with arbitrary spin.

Asymptotically free gauge theories. II

Deep-inelastic lepton-hadron scattering is analyzed in asymptotically free gauge theories of the strong interactions. The renormalization-group equations for the coefficients of the twist-two operators in the Wilson expansion are reviewed. A careful treatment of the mixing of operators with identical quantum numbers and dimensions is given. The relevant anomalous dimensions of the twist-two operators are calculated to second order in perturbation theory. These are used to calculate the asymptotic ${q}^{2}$ behavior of the moments of the structure functions. It is shown that the approach to the asymptotic limit is logarithmic, that Bjorken scaling is violated by powers of $\mathrm{ln}(\ensuremath{-}{q}^{2})$, and that the naive light-cone or parton-model relations for the moments of the structure functions are true asymptotic theorems. A new sum rule for the first moment of ${F}_{2}$, in terms of the energy-momentum tensor, is derived. An example of a function whose moments have roughly the correct asymptotic ${q}^{2}$ behavior is constructed. The ${q}^{2}$ behavior of the structure functions for a given $x$ is discussed.