Abstract
We argue that the renormalization factors for non-local quark-antiquark and gluon operators at space-like and time-like separations connected by a Wilson line coincide to all orders in perturbation theory. We calculate the anomalous dimensions and renormalization constants of quark-antiquark and gluon operators to three- and two-loop accuracy, respectively, and also compute vacuum expectation values of these operators to three-loop accuracy.
Highlights
Effective field theoryThe interaction of a particle propagating along a classical path in the background gauge field reduces to the path-ordered phase factor along its trajectory
There has been renewed interest in the study of matrix elements of non-local off-light-cone operators of the type
We address the question whether computational methods familiar from HQET can be applied to the calculation of the renormalization constants (RCs) of the operators in eq (1.1), alias for qPDFs, in high orders
Summary
The interaction of a particle propagating along a classical path in the background gauge field reduces to the path-ordered phase factor along its trajectory. Such an auxiliary classical particle can be simulated by supplementing the QCD Lagrangian. One can write the corresponding expression using the Feynman rules of the effective theory in eq (2.1), T (qhv) (zv) Γ hvq (0). The two expressions in eqs. (2.5) and (2.6) are obviously equal up to an overall factor, which is nothing but the free propagator of the “heavy” field, Sh(0)(zv)
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