DVCS process).

The scale dependence of the light-ray operators, standing on the left hand side of Eq. (\[definition\]), is governed by the renormalization group equation which is of the generic form ($\bar y \equiv 1 - y$) $$\begin{aligned}
\mu^2\frac{d}{d\mu^2}{\cal O}^{\mit\Gamma} (\lambda , \mu) &=&
\frac{\alpha_s}{2 \pi} \int_{0}^{1} dy \int_{0}^{\bar y} dz
{\cal K}^{\mit\Gamma} (y, z)
{\cal O}^{\mit\Gamma} (\lambda \bar z + \mu z , \mu \bar y + \lambda y).\end{aligned}$$ The evolution kernels for the parity-even ($V$) and parity-odd ($A$) chiral-even light-ray operators are known in the literature [@ji97; @rad96; @RadPRD56; @kern; @BB88]. Here we supplement this list by the kernel for the non-forward transversity ($T$) distribution [@CFS96]: $${\cal K}^T (y, z) = C_F
\left\{ \delta (y) \left[ \frac{1}{z} \right]_+
+ \delta (z) \left[ \frac{1}{y} \right]_+
- \delta (y) - \delta (z) + \frac{3}{2} \delta (y)\delta (z)
\right\}.$$ By exploiting the conversion formula derived in Ref. [@BM97] we can easily write the corresponding evolution equation in the momentum space $$\begin{aligned}
\label{MOMEE}
\mu^2\frac{d}{d\mu^2}{\cal O}^{\mit\Gamma} (x, \zeta) &=&
- \frac{\alpha_s}{2 \pi} \int d x ' K^{\mit\Gamma} (x , x ', \zeta)
{\cal O}^{\mit\Gamma} (x ', \zeta),\end{aligned}$$ with[^2] $$\begin{aligned}
\label{gen-ker-KT}
K^T (x , x ', \zeta)
= C_F \left\{\left[ \frac{x}{x - x'}
\Theta_{11}^0 