Two-loop evolution equations for light-ray operators

V.M Braun,A.N Manashov

doi:10.1016/j.physletb.2014.05.037

V.M Braun, A.N Manashov

Open Access

https://doi.org/10.1016/j.physletb.2014.05.037

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Abstract

QCD in non-integer d=4−2ϵ space–time dimensions possesses a nontrivial critical point and enjoys exact scale and conformal invariance. This symmetry imposes nontrivial restrictions on the form of the renormalization group equations for composite operators in physical (integer) dimensions and allows to reconstruct full kernels from their eigenvalues (anomalous dimensions). We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark–antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions and light-cone distribution amplitudes in the most compact form.

Highlights

It has been known for some time [6] that conformal symmetry of the QCD Lagrangian allows one to restore full evolution kernels at given order of perturbation theory from the spectrum of anomalous dimensions at the same order, and the calculation of the special conformal anomaly at one order less
In Ref. [10] we have suggested an alternative technique, the difference being that instead of studying conformal symmetry breaking in the physical theory [7,8,9] we make use of the exact conformal symmetry of a modified theory – QCD in d = 4 − 2ǫ dimensions at critical coupling
Exact conformal symmetry allows one to use algebraic group-theory methods to resolve the constraints on the operator mixing and suggests the optimal representation for the results in terms of light-ray operators

Summary

Introduction

It has been known for some time [6] that conformal symmetry of the QCD Lagrangian allows one to restore full evolution kernels at given order of perturbation theory from the spectrum of anomalous dimensions at the same order, and the calculation of the special conformal anomaly at one order less. Eliminating the ǫ-dependence of the expressions derived in the d-dimensional (conformal) theory for the critical coupling by the expansion ǫ = −b0a∗s + O(a∗s2) allows one to restore the evolution kernels for the theory in integer dimensions for arbitrary coupling a∗s → as; this rewriting is simple and exact to all orders.

Results

Conclusion