---
abstract: 'Electroweak corrections associated with the instability of the top quark to the next-to-next-to-leading logarithmic (NNLL) total top pair threshold cross section in $e^+e^-$ annihilation are determined. Our method is based on absorptive parts in electroweak matching conditions of the NRQCD operators and the optical theorem. The corrections lead to ultraviolet phase space divergences that have to be renormalized and lead to NLL mixing effects. Numerically, the corrections can amount to several percent and are comparable to the known NNLL QCD corrections.'
author:
- 'André H. Hoang and Christoph J. Reißer'
title:  Electroweak Absorptive Parts in NRQCD Matching Conditions 
---

Introduction {#sectionintroduction}
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The line-shape scan of the threshold top pair production cross section $\sigma(e^+e^-\to \gamma^*,Z^*\to t\bar t)$ constitutes a major part of the top quark physics program at the International Linear Collider (ILC) project that is currently being initiated. Because in the Standard Model the top quark width $\Gamma_t\approx 1.5$ GeV is much larger than the typical hadronization energy $\Lambda_{\rm QCD}$, it is expected that the line-shape of the total cross section is a smooth function of the c.m.energy, and that non-perturbative effects are strongly suppressed[@Kuehn1; @Fadin1]. The determination of the top quark mass (in a threshold mass 