Generalized Bjorken Region Research Articles

Target mass and finite momentum transfer corrections to unpolarized and polarized diffractive scattering

A quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering is given. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized Bjorken region. Target mass and finite t corrections of the diffractive hadronic tensor are derived at the level of the twist-2 contributions both for the unpolarized and the polarized case. They modify the expressions contributing in the limit t, M 2 → 0 for larger values of β or/and t in the region of low Q 2 . The different diffractive structure functions are expressed through integrals over the relative momentum of non-perturbative t-dependent 2-particle distribution functions. In the limit t, M 2 → 0 these distribution functions are the diffractive parton distribution. Relations between the different diffractive structure functions are derived.

Leading twist amplitudes for exclusive neutrino interactions in the deeply virtual limit

Neutrino scattering on nucleons in the regime of deeply virtual kinematics is studied both in the charged and the neutral electroweak sectors using a formalism developed by Blumlein, Robaschik, Geyer and Collaborators for the analysis of the Virtual Compton amplitude in the generalized Bjorken region. We discuss the structure of the leading twist amplitudes of the process.

Virtual Compton scattering in the generalized Bjorken region and positivity bounds on generalized parton distributions

The positivity bounds on generalized parton distributions are derived from the positivity properties of the absorptive part of the amplitude of the virtual Compton scattering in the generalized Bjorken region.

Probing generalized parton distributions with electroproduction of lepton pairs off the nucleon

We evaluate the differential cross section for the electroproduction of lepton pairs off a polarized nucleon target in the generalized Bjorken region to leading power accuracy in hard momentum. We discuss the importance of this process for phenomenology of generalized parton distributions. A special attention is given to the sensitivity of physical observables, i.e., diverse asymmetries, to their dependence on scaling variables that allows to map directly the functional two-dimensional surface of generalized parton distributions.

Polarized deep inelastic diffractiveepscattering: Operator approach

Polarized inclusive deep-inelastic diffractive scattering is dealt with in a quantum field theoretic approach. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized Bjorken region applying the generalized optical theorem. The diffractive structure functions $g_1^{D(3)}$ and $g_2^{D(3)}$ are calculated in the twist-2 approximation and are expressed by diffractive parton distributions, which are derived from pseudo-scalar two-variable operator expectation values. In this approximation the structure functions $g_2^{D(3)}$ is obtained from $g_1^{D(3)}$ by a Wandzura-Wilczek relation similar as for deep inelastic scattering. The evolution equations are given. We also comment on the higher twist contributions in the light-cone expansion.

Scaling violations of diffractive structure functions: operator approach

A quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering is given. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized Bjorken region. Evolution equations of the diffractive hadronic matrix elements are derived at the level of the twist-2 contributions and are compared to those of inclusive deep-inelastic forward scattering (DIS). The diffractive parton densities are obtained as projections of two-variable parton distributions. We also comment on the higher twist contributions in the light-cone expansion.

Deeply virtual Compton scattering amplitude at the tree level: Transversality, twist-3, and factorization

We study the virtual Compton amplitude in the generalized Bjorken region (q^2 -> Infinity, t small) in QCD by means of a light-cone expansion of the product of e.m. currents in string operators in coordinate space. Electromagnetic gauge invariance (transversality) is maintained by including in addition to the twist-2 operators 'kinematical' twist-3 operators which appear as total derivatives of twist-2 operators. The non-forward matrix elements of the elementary twist-2 operators are parametrized in terms of two-variable spectral functions (double distributions), from which twist-2 and 3 skewed distributions are obtained through reduction formulas. Our approach is equivalent to a Wandzura-Wilczek type approximation for the twist-3 skewed distributions. The resulting Compton amplitude is manifestly transverse up to terms of order t/q^2. We find that in this approximation the tensor amplitude for longitudinal polarization of the virtual photon is finite, while the one for transverse polarization contains a divergence already at tree level. However, this divergence has zero projection on the polarization vector of the final photon, so that the physical helicity amplitudes are finite.

Quantum field theoretic treatment of the non-forward compton amplitude in the generalized bjorken region

A quantum field theoretic treatment of the leading light-cone part of the virtual Compton amplitude is presented. The twist-decomposition of the operators is performed by a group-theoretic procedure respecting the Lorentz group O(3,1). The twist-2 contributions to the Compton amplitude are calculated and it is shown that the electromagnetic current is conserved for these terms. Relations between the amplitude functions associated to the symmetric and asymmetric part of the Compton amplitude are derived. These relations generalize the Calln-Gross and Wandzura-Wilczek relations of forward scattering for the non-forward Compton amplitude.

On the structure of the virtual Compton amplitude in the generalized Bjorken region: integral relations

Abstract A systematic study is performed of the structure of the twist-2 contributions to the virtual Compton amplitude in deep-inelastic non-forward scattering for general spin states in the non-local light cone expansion. The gauge invariance is proven in this approach for the twist-2 contributions for non-forward scattering. Relations are derived between the contributing non-forward amplitudes.

The virtual Compton amplitude in the generalized Bjorken region: Twist-2 contributions

A systematic derivation is presented of the twist-2 anomalous dimensions of the general quark and gluon light-ray operators in the generalized Bjorken region in leading order both for unpolarized and polarized scattering. Various representations of the anomalous dimensions are derived both in the non-local and the local light cone expansion and their properties are discussed in detail. Evolution equations for these operators are derived using different representations. General two- and single-variable evolution equations are presented for the expectation values of these operators for non-forward scattering. The Compton amplitude is calculated in terms of these distribution amplitudes. In the limit of forward scattering a new derivation of the integral relations between the twist-2 contributions to the structure functions is given. Special limiting cases which are derived from the general relations are discussed, as the forward case, near-forward scattering, and vacuum-meson transition. Solutions of the two-variable evolution equations for non-forward scattering are presented.

Representation of the virtual Compton amplitude for polarized scattering in the generalized Bjorken region

The Compton amplitude is calculated in terms of expectation values of light-ray quark operators. As a technical tool we apply the nonlocal light-cone expansion. Thereby we express the expectation value of the vector light-ray operator with the help of the expectation value of the corresponding scalar operator of twist 2. This allows important simplifications. In the limit of forward scattering the integral relations between the twist-2 contributions of the structure functions are implied directly.

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 $\beta$-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.