A_j^{(QED)} = A_j^{(QED)}(s, \mu^2) = A_j^{(QED)}(s/ \mu^2), 
~\tilde{A}^{(QED)}_j = \tilde{A}^{(QED)}_j(s, M^2) = 
\tilde{A}^{(QED)}_j(s/ M^2), \\ \nonumber
~\tilde{A}_j = \tilde{A}_j(s, M^2) = \tilde{A}_j(s/ M^2), 
 ~{A'}_j = {A'}_j (s, \mu^2, M^2) = {A'}_j (s/M^2,\eta) ~, \end{aligned}$$ with $$\label{eta}
\eta \equiv \ln(M^2/\mu^2) ~.$$

Our aim is to calculate the amplitudes ${A'}_j$, whereas the amplitudes $A_j^{(QED)}, \tilde{A}^{(QED)}_j$ and $\tilde{A}_j(s/ M^2)$ are supposed to be known. The amplitudes $\tilde{A}_j$ were introduced and calculated in Ref. [@egt]. In order to define amplitudes ${A'}_j, \tilde{A}_j(s, M^2)$, the projection operators of Eq. (\[pr\]) have been used. The use of these operators is based on the fact that the $SU(2)\times U(1)$ symmetry for the electroweak scattering amplitudes takes place at energies much higher than the weak mass scale $M$. On the contrary, the QED amplitudes $A_j^{(QED)}$ and $\tilde{A}^{(QED)}_j$ are not $SU(2)$ invariant at any energy. Nevertheless, it is convenient to introduce “the QED invariant amplitudes” $A_j^{(QED)}, \tilde{A}^{(QED)}_j$ by explicit calculation of the forward and backward QED scattering amplitudes. Then inverting Eq. (\[amplquark\]), we construct the amplitudes $A_j^{(QED)}$ for $e^+e^-$- annihilation into quarks: $$\begin{aligned}
\label{qedquark}
A_1^{(QED)} = 
2 A_F^{(QED)}(e^+e¯- \to d \bar{d}) - A_B^{(QED)}(e^+e¯- \to u \bar{u})
,
~~A_2^{(QED)} = A_B^{(QED)}(e^+e¯- \to u \bar{u}) , \\ \nonumber 
A_3^{(QED)} = 
2A_F^{(QED)}(e^+e¯- 