---
abstract: 'The non-radiative scattering amplitudes for electron-positron annihilation into quark and lepton pairs in the TeV energy range are calculated in the double-logarithmic approximation. The expressions for the amplitudes are obtained using infrared evolution equations with different cut-offs for virtual photons and for $W$ and $Z$ bosons, and compared with previous results obtained with an universal cut-off.'
author:
- 'A. Barroso'
- 'B.I. Ermolaev'
- 'M. Greco'
- 'S.M. Oliveira'
- 'S.I. Troyan'
title: 'Electroweak $2 \rightarrow 2$ amplitudes for electron-positron annihilation at TeV energies'
---

Introduction
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Next future linear $e^+e^-$ colliders will be operating in a energy domain which is much higher than the electroweak bosons masses, so that the full knowledge of the scattering amplitudes for $e^+e^-$ annihilation into quark and lepton pairs will be needed. The forward-backward asymmetry for $e^+e^-$ annihilation into leptons or hadrons produced at energies much greater than the $W$ and $Z$ boson masses has been recently considered in Ref. [@egt], where the electroweak radiative corrections were calculated to all orders in the double-logarithmic approximation (DLA). It was shown that the effect of the electroweak DL radiative corrections on the value of the forward-backward asymmetry is quite sizable and grows rapidly with 