\otimes x^j \\
&\Rightarrow& F( z, x, \zeta )
= - {^{QG}\!K^A} (z , x , \zeta) \ln \frac{Q^2}{\mu^2}
+ \left[ 1  - {\cal D} \ln (1 - z \omega) \right]
{^{QG}\!K^A} (z , x , \zeta). \nonumber\end{aligned}$$

By adding the results of Eqs. (\[nondiagonal\]) and (\[nondiagonal2\]) together and subtracting the solution (\[Phi\]) of the evolution equation for $\beta = 0$, we finally come to the coefficient function in the ${\overline{\rm MS}}$ scheme: $${^G T_{(1)}^A}( \omega, x, \zeta, Q^2 ) =
{^Q T_{(0)}} ( \omega, y ) \otimes
\biggl\{
{^{QG}\!K^A} ( y, x, \zeta )\, \ln \frac{Q^2}{\mu^2}
+ \left[ \ln \left( 1 - y \omega \right) - 1 \right]
{^{QG}\!K^A} ( y, x, \zeta )
\biggr\}.$$

As an outcome of the same but a little bit more involved analysis for the quark scattering amplitude we get: $$\begin{aligned}
\label{unpolQCF}
{^Q T_{(1)}^A}( \omega, x, \zeta, Q^2 ) \!\!\!&=&\!\!\!
{^Q T_{(0)}} ( \omega, y ) \otimes
\biggl\{
{^{QQ}\!K^A} ( y, x, \zeta )\,
\ln \frac{Q^2}{\mu^2}
- \frac{3}{2} \left[ {^{Q}\!K^b} ( y, x, \zeta ) \right]_+
+ \frac{3}{2} \delta (y - x) \nonumber \\
&+& \ln \left( 1 - y \omega \right)
{^{QQ}\!K^A} ( y, x, \zeta )
- \left[ {^{Q}\!G} ( y, x, 