\to u \bar{u}) - A_B^{(QED)}(e^+e¯- \to d \bar{d})
,
~~A_4^{(QED)} = A_B^{(QED)}(e^+e¯- \to d \bar{d}) ~ \end{aligned}$$ and inverting Eq. (\[ampllept\]) allows us to obtain $A_j^{(QED)}$ for $e^+e^-$- annihilation into leptons: $$\begin{aligned}
\label{qedlept}
A_1^{(QED)} = 
2A_F^{(QED)}(e^+e¯- \to \mu^+ \mu^-), 
~A_2^{(QED)} = 0, 
~A_3^{(QED)} = - A_4^{(QED)} = A_B^{(QED)}(e^+e¯- \to \mu^+ \mu^-).\end{aligned}$$

Evolution equations for amplitudes $A_j$ in the collinear kinematics
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We would like to discuss now the IREE for the amplitudes introduced earlier. The basic idea for constructing infrared evolution equations for the scattering amplitudes consists in introducing the infrared cut-offs in the transverse momentum space and evolving the scattering amplitudes with respect to them. This method does not involve analyzing the DL contributions of specific Feynman graphs but is based on quite general conceptions such as the analyticity of the scattering amplitudes and the dispersion relations which guarantees its applicability to a wide class of problems (see e.g. Ref. [@flmm] and Refs. therein). The essence of the method is the factorizing the DL contributions of virtual particles with the minimal transverse momenta. The IREE with two cut-offs for the electroweak amplitudes in the hard kinematics (\[hard\]) were obtained in Ref. [@flmm]. In the present section we construct the 