In NLO the symmetry breaking, which is proportional to the $\beta$-function, arises only in the off-diagonal part (in the basis of Gegenbauer polynomials) of the anomalous dimension matrix $\hat \gamma$, not in the coefficient function. So, we are able to make the predictions for the NLO coefficient functions without restrictions.

To overcome difficulties with gauge invariance and Lorentz decomposition of the hadronic tensor for the DVCS, we deal, in what follows, only with appropriate projections of the latter: $${\cal F}^{\mit\Gamma} ( \omega, \zeta )
=
i {\cal P}^{\mit\Gamma}_{\mu\nu}
\int d^4 z e^{iqz}
\langle h' |
T \left\{ J_\mu (0) J_\nu (z) \right\}
| h \rangle ,$$ where ${\cal P}^V_{\mu\nu} = g_{\mu\nu}$ corresponds to unpolarized scattering and ${\cal P}^{A}_{\mu\nu} = i \epsilon_{\mu\nu Qp}/(Qp)$ to polarized case. Here $1/\omega = -Q^2/2(Qp)$ and $Q = q - \Delta$.

On the one hand the amplitude for DVCS can be represented in the factorized form as convolution of the non-forward distribution (\[definition\]) and the perturbative coefficient function $$\label{DVCS}
{\cal F}^{\mit\Gamma} ( \omega, \zeta ) = \int d x
\sum_{i=Q,G} {^i T^{\mit\Gamma}}( \omega, x, \zeta, Q^2 | \alpha_s )
{^i {\cal O}^{\mit\Gamma}} ( x, \zeta ).$$ For the hand-bag diagram[^4] we have to LO in the 