[Paper Review] Full $\mathcal{O}(\alpha)$ electroweak radiative corrections to $t \bar{t} \gamma$ and $e^-e^+\gamma$ productions at ILC with GRACE-Loop

P. H. Khiem, Y. Kurihara+11 more|arXiv (Cornell University)|Mar 26, 2014

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper presents full one-loop electroweak radiative corrections to top quark pair and Bhabha-like processes at the International Linear Collider (ILC), computed using the GRACE-Loop framework. It finds that electroweak corrections significantly impact the top quark forward-backward asymmetry and total cross section, with weak corrections reaching −16% at 1 TeV, and that radiative corrections are crucial for precision luminosity monitoring and top quark physics at ILC energies.

ABSTRACT

The full $\mathcal{O}(\alpha)$ electroweak radiative corrections to $t \bar{t} \gamma$ and $e^-e^+\gamma$ productions at the International Linear Collider (ILC) are presented in this paper. The computation is performed with the help of GRACE-Loop system. In the physical results, we discuss on the cross section, electroweak corrections, and the top quark forward-backward asymmetry ($A_{FB}$) which are the function of the center-of-mass energy.

Motivation & Objective

• To compute full one-loop electroweak radiative corrections for t¯tγ and e−e+γ production at the ILC with high precision.
• To assess the impact of these corrections on the top quark forward-backward asymmetry (AFB), a key observable for new physics searches.
• To evaluate the importance of radiative corrections for precision measurements and luminosity monitoring at future e+e− colliders.
• To validate the calculations using gauge and renormalization scheme independence tests in the GRACE-Loop framework.

Proposed method

• The GRACE-Loop system is employed to compute one-loop amplitudes with on-shell renormalization and non-linear gauge fixing, ensuring gauge independence.
• The calculation includes all contributing diagrams: tree-level, virtual one-loop, and real bremsstrahlung contributions (soft and hard photons).
• The system implements an axial gauge for external photons to reduce numerical cancellations and improve stability in small-angle and high-energy regions.
• Cross-sections and asymmetries are evaluated across a range of center-of-mass energies from 360 GeV to 1 TeV, with kinematic cuts applied to final-state particles.
• Consistency is verified via independence tests: ultraviolet cutoff (CUV), fictitious photon mass (λ), hard photon energy cut (kc), and five gauge parameters (˜α, ˜β, ˜κ, ˜δ, ˜ǫ), all showing stability to 19 digits.
• Input parameters include standard model values: α−1 = 137.0359895, MZ = 91.187 GeV, MW = 80.3759 GeV, MH = 120 GeV, and top quark mass mt = 172.0 GeV.

Experimental results

Research questions

• RQ1 How do full O(α) electroweak corrections affect the total cross section of t¯tγ production at ILC energies?
• RQ2 To what extent do electroweak corrections modify the top quark forward-backward asymmetry (AFB) in t¯tγ production compared to the tree-level prediction?
• RQ3 How significant are radiative corrections for e−e+γ production, particularly in the context of luminosity monitoring at ILC?
• RQ4 Are the calculated amplitudes stable under variations of gauge parameters, UV cutoff, and photon energy cuts, confirming numerical reliability?
• RQ5 How do QED and weak corrections compare in magnitude and energy dependence across the ILC energy range?

Key findings

• The total cross section for e−e+ → t¯tγ peaks near √s ≈ 550 GeV and decreases with increasing center-of-mass energy.
• QED corrections dominate at low energies, contributing up to ~10% at 360 GeV, but diminish rapidly at higher energies.
• Weak corrections in the α-scheme reach −16% at 1 TeV, indicating a significant non-QED contribution to the amplitude.
• The electroweak-corrected top quark forward-backward asymmetry (AFB) is smaller than the tree-level value, highlighting the importance of full corrections for precision measurements.
• The AFB in t¯tγ production exceeds that in t¯t production for √s ≥ 400 GeV, a clear signature observable at ILC.
• Radiative corrections to e−e+γ production are substantial, decreasing from −2% at 250 GeV to −20% at 1 TeV, and visible in invariant mass distributions near MZ and in the high-mass tail.