Vladimir M. Braun

We develop a new technique and calculate conformal (Gegenbauer) moments of the two-loop coefficient functions in deeply virtual Compton scattering. These results are necessary for the extraction of the generalized parton distributions from the experimental data to the next-to-next-to leading order accuracy within the Mellin-Barnes approach.

We use conformal symmetry to calculate the next to next to leading order (NNLO) anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin N ≤ 8 from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the γ γ * → η and γ γ * → η ′ form factors at large momentum transfers to the NNLO accuracy in perturbative QCD.

We present updated results for the wave function normalization constants and the first moments of the light-cone distribution amplitudes for the lowest-lying baryon octet. The analysis is carried out on a large number of n f = 2 + 1 lattice gauge ensembles, including ensembles at physical pion (and kaon) masses. These are spread across five different lattice spacings, enabling a controlled continuum limit. The main differences with respect to our earlier work [G. S. Bali (RQCD Collaboration), Light-cone distribution amplitudes of octet baryons from lattice QCD, .] are the use of two-loop conversion factors to an MS ¯ -like scheme and of an updated set of low-energy constants in the parametrization of the quark mass dependence. As a byproduct, for the first time, the anomalous dimensions for local leading-twist three-quark operators with one derivative are obtained.

We calculate ( − t / Q ) k and ( m / Q ) k power corrections with k ≤ 4 , where m is the target mass and t is the momentum transfer, to several key observables in deeply virtual Compton scattering (DVCS). We find that the power expansion is well convergent up to | t | / Q 2 ≲ 1 / 4 for most of the observables, but is naturally organized in terms of 1 / ( Q 2 + t ) rather than the nominal hard scale 1 / Q 2 . We also argue that target mass corrections remain under control and do not endanger quantum chromodynamics (QCD) factorization for coherent DVCS on nuclei. These results remove an important source of uncertainties due to the frame dependence and violation of electromagnetic Ward identities in the QCD predictions for the DVCS amplitudes in the leading-twist approximation.

A bstract: We present explicit expressions for the tree-level “kinematic” twist-three contributions to the nucleon matrix elements of gauge-invariant nonlocal quark-antiquark operators which can be used in lattice calculations of generalized parton distributions (GPDs). These contributions in particular restore the translation invariance of the results up to higher twist four. The calculated twist-three corrections are logarithmically enhanced as compared to the leading twist, and are discontinuous at the kinematic points x = ± ξ .

The higher twist corrections refer to a certain class of contributions to hard processes in strong interactions that are suppressed by a power of the hard scale. This is a very broad field of research which is becoming more and more important as the accuracy of the available experimental data increases. I give an overview of some relevant basic theory concepts and technical developments, and briefly discuss a few phenomenological applications.