used where the manifestly conformaly covariant form of the OPE (\[COPE\]) is hidden. Fortunately, the product of two electromagnetic currents is a renormalization group invariant, so that Eq. (\[DVCS\]) computed in any scheme is equivalent to Eq. (\[COPE\]) derived in the CS scheme.

Since the $\alpha_s$-corrections in Eq. (\[DVCS\]) come from the NLO result for the coefficient function and eigenfunctions of the evolution kernels we are able to predict the former from the combined use of the conformal OPE (\[COPE\]) and the special conformal anomaly which fixes precisely the corrections to the latter. The general conformal decomposition of the non-forward distributions looks like $${^i{\cal O}} (x, \zeta)
= \sum_{k = Q,G} \sum_{j=0}^{\infty}
{^{ik}\phi}_j (x, \zeta | \alpha_s)
\langle h' | {^k{\cal O}}_{jj} | h \rangle ,$$ where the partial conformal waves are generalized, beyond one-loop level, to non-polynomial functions which are the subject of the constraints. For the quark case, which is required for the present application, they have the form $${^{Qk}\phi}_j (x, \zeta | \alpha_s)
= \left\{
\delta_{Qk} \delta (x - y)
+ \frac{\alpha_s}{2\pi} {^{Qk}{\mit\Phi}} (x, y, \zeta)
\right\}
\otimes
\frac{1}{N_j (\nu) \zeta^{j + 1}}
\frac{y}{\zeta} \left( 1 - \frac{y}{\zeta} \right)
C_j^{\nu} \left( 2 \frac{y}{\zeta} - 1 \right),$$ where 