Two-loop conformal generators for leading-twist operators in QCD

A bstract QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for the...

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Veröffentlicht in:The journal of high energy physics 2016-03, Vol.2016 (3), p.1-41, Article 142
Hauptverfasser: Braun, V.M., Manashov, A.N., Moch, S., Strohmaier, M.
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container_issue 3
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container_title The journal of high energy physics
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creator Braun, V.M.
Manashov, A.N.
Moch, S.
Strohmaier, M.
description A bstract QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer d = 4 − 2ϵ space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in d = 4 − 2ϵ effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD β -function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.
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subjects Broken symmetry
Classical and Quantum Gravitation
Commutation
Elementary Particles
Evolution
Generators
High energy physics
Mathematical analysis
Operators (mathematics)
Physics
Physics and Astronomy
Quantum chromodynamics
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Symmetry
title Two-loop conformal generators for leading-twist operators in QCD
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