Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-loop conformal generators for leading-twist operators in QCD   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 $d=4-2\epsilon$
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 $d=4-2\epsilon$ 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.

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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph