129 research outputs found
Conformal constraints for anomalous dimensions of leading twist operators
Leading-twist operators have a remarkable property that their divergence
vanishes in a free theory. Recently it was suggested that this property can be
used for an alternative technique to calculate anomalous dimensions of
leading-twist operators and allows one to gain one order in perturbation theory
so that, i.e., two-loop anomalous dimensions can be calculated from one-loop
Feynman diagrams, etc. In this work we study feasibility of this program on a
toy-model example of the theory in six dimensions. Our conclusion
is that this approach is valid, although it does not seem to present
considerable technical simplifications as compared to the standard technique.
It does provide one, however, with a very nontrivial check of the calculation
as the structure of the contributions is very different.Comment: 14 pages, 6 figure
Two-loop evolution equations for light-ray operators
QCD in non-integer d=4-2 epsilon 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.Comment: 13 pages, 1 figur
Conformal symmetry of the Lange-Neubert evolution equation
The Lange-Neubert evolution equation describes the scale dependence of the
wave function of a meson built of an infinitely heavy quark and light antiquark
at light-like separations, which is the hydrogen atom problem of QCD. It has
numerous applications to the studies of B-meson decays. We show that the kernel
of this equation can be written in a remarkably compact form, as a logarithm of
the generator of special conformal transformation in the light-ray direction.
This representation allows one to study solutions of this equation in a very
simple and mathematically consistent manner. Generalizing this result, we show
that all heavy-light evolution kernels that appear in the renormalization of
higher-twist B-meson distribution amplitudes can be written in the same form.Comment: 8 page
Baryon octet distribution amplitudes in Wandzura-Wilczek approximation
We study higher twist distribution amplitudes for the SU_F(3) baryon octet.
We identify independent functions for all baryons in the isospin symmetry limit
and calculate the Wandzura-Wilczek contributions to the twist-4 and 5
distributions amplitudes.Comment: 7 page
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