Braun, V. M. and Manashov, A. N. and Moch, S. and Strohmaier, M. (2016) Two-loop conformal generators for leading-twist operators in QCD. JOURNAL OF HIGH ENERGY PHYSICS (3): 142. ISSN 1029-8479,
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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 - 2 is an element of 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 - 2 is an element of 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 beta-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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EVOLUTION-EQUATIONS; GAUGE-THEORIES; SYMMETRY; Perturbative QCD; Renormalization Group; Conformal and W Symmetry |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Braun > Group Vladimir Braun |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Apr 2019 11:22 |
| Last Modified: | 03 Apr 2019 11:22 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3235 |
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