Higher-order effects in asymptotically free gauge theories

Three loop renormalization of 3-quark operators in QCD

“…At three loops two new structures emerge, C 6 and C 642 , which involve the evanescent Γ µ 1 ...µ 6 (6) matrix. However, similar to (6.8) one can deduce that in d-dimensions…”

“…At low energies the internal structure of the baryons and in particular protons, can be probed by measuring the structure functions and their moments. For the latter the field theoretic quantities of relevance are 3-quark operators involving covariant derivatives, [1,2,3,4,5,6]. Knowledge of the proton structure can assist with understanding the strong interaction in the infrared regime and hence how quarks condense or hadronize to form the nucleon states we see in nature.…”

Dynamical parton distributions of the nucleon

“…1.4). Together with the well-known one-loop splitting functions [191,192], and the two-loop ones [37,190,193,194], the expressions for the 3-loop splitting functions [195,196] are necessary for the evolution of parton densities up to NNLO. For these latter quantities we use the x-space parametrizations presented also in [195,196], and transform them to n-space using, e.g., [197].…”

The Mellin moments of deep inelastic structure functions at two loops

“…It provides unique information about the structure of the hadrons and tests one of the most important predictions of perturbative QCD, the scale evolution of the structure functions [1,2,3]. At the same time, the ever increasing accuracy of deep inelastic scattering (DIS) experiments demands more accurate theoretical predictions and despite all achievements [4,5,6,7], no complete next-to-nextto-leading order (NNLO) analysis for DIS reactions is available.…”

“…[9] to calculate more fixed Mellin moments, is not feasible. One such possibility that actually dates back to the origins of QCD [1,3], is to calculate the Mellin moments of the structure functions analytically as a general function of N . This approach, further pioneered by Kazakov and Kotikov [4] to obtain the structure function F L at 2-loops, turns out to be flexible and very promising in view of the ultimate goal, the anomalous dimensions at 3-loops.…”