PoS - Proceedings of Science
Volume 284 - QCD Evolution 2016 (QCDEV2016) - Tuesday, May 31, 2016 - Afternoon1
Towards the three loop evolution equation for GPDs
A. Manashov
Full text: pdf
Pre-published on: February 10, 2017
Published on: March 28, 2017
QCD in $d=4-2\epsilon$ dimensions and large number of flavors possesses a nontrivial infrared stable critical point.
At the critical point the theory is invariant under the conformal transformations. It implies that the evolution kernel of
leading-twist light-ray operators commutes with the generators of conformal transformations. Taking into account that the evolution
kernels in the \rm{MS}-scheme are not sensitive to the space-time dimensions one concludes that
QCD evolution equations in \rm{MS}-schemes have a hidden
symmetry. Namely, the evolution kernel commutes with the generators of the conformal algebra. The explicit form of the generators differs
from their canonical (classical) form and can be derived by studying conformal Ward identities.
Invariance with respect to the conformal transformations imposes nontrivial constraints on
the form of evolution kernels and allows one to restore the nonforward evolution kernels for the nonsinglet operators from
the known NNLO anomalous dimensions.
We present here the two loop expressions for the generators of conformal algebra.
DOI: https://doi.org/10.22323/1.284.0019
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