# $\mathcal{O}(\alpha^2)$ ISR effects with a full electroweak one-loop correction for a top pair-production at the ILC

## TL;DR

This paper provides precise electroweak one-loop corrected predictions for top quark pair production cross sections at the ILC, including initial-state radiation and polarization effects, with detailed analysis of weak corrections and two-loop contributions.

## Contribution

It introduces a comprehensive calculation of $ ext{O}( ext{alpha}^2)$ ISR effects with full electroweak one-loop corrections for top pair production at the ILC, including two-loop initial-state photon emission effects.

## Key findings

- Weak corrections increase the cross section by about 4% at 500 GeV.
- Two-loop initial-state diagrams contribute less than 0.11% correction.
- Running coupling effects are also analyzed.

## Abstract

Precise predictions for an $e^+e^-\rightarrow t\bar{t}$ cross section are presented at an energy region from 400 GeV to 800 GeV. Cross sections are estimated including the beam-polarization effects with full $\mathcal{O}(\alpha)$, and also with effects of the initial-state photon emission. A radiator technique is used for the initial-state photon emission up to two-loop order. A weak correction is defined as the full electroweak corrections without the initial-state photonic corrections. As a result, it is obtained that the total cross section of a top quark pair-production receives the weak corrections of $+4\%$ over the trivial initial state corrections at a centre of mass energy of 500 GeV. Among the initial state contributions, a contribution from two-loop diagrams gives less than $0.11\%$ correction over the one-loop ones at the center of mass energies of from $400$ GeV to $800$ GeV. In addition, an effect of a running coupling constant is also discussed.