One-loop QCD interconnection effects in pair production of top quarks

TL;DR

The paper develops a gauge-invariant framework for one-loop non-factorizable QCD corrections to off-shell $t\bar{t}$ production and decay across $e^{+}e^{-}$, $\gamma\gamma$, $q\bar{q}$, and $gg$ initial states, using the leading-pole approximation to separate production and decay subprocesses. It shows that non-factorizable effects arise from semi-soft gluon exchanges and can be expressed in a colour-factorized form involving a universal $\delta_{\text{nf}}$, with explicit currents for the production and decay stages. Numerical results indicate large distortions in the invariant-mass line shapes, but the shift of the Breit–Wigner peak in the top mass is always below $100$ MeV, suggesting that top-mass extraction from the peak is robust to these corrections while full shape analyses may require their inclusion, particularly for singlet-dominated initial states. The findings emphasize the need to account for these corrections in precision electroweak tests and Higgs-mMass constraints, and they provide a groundwork for incorporating higher-order non-factorizable effects in future studies.

Abstract

We calculate the one-loop non-factorizable QCD corrections to the production and decay of pairs of top quarks at various collider experiments. These non-factorizable corrections interconnect the different production and decay stages of the off-shell top-pair production processes. This in particular affects the invariant-mass distributions of the off-shell top quarks, resulting in a shift of the maximum of the distorted Breit-Wigner distributions. Although the non-factorizable corrections can be large, the actual shift in the mass as determined from the peak position of the corrected Breit-Wigner line-shape is below $100\MeV$.

Figures (3)

• Figure 1: The generic structure of the complete $t\bar{t}$-production process $q\bar{q} \to t\bar{t} \to bW^+\bar{b}W^- \to 6\ \hbox{fermions}$ in the LPA. The open circles denote the various production and decay subprocesses. As an example also the non-factorizable semi-soft gluon interaction between the two top-quark decay subprocesses is shown.
• Figure 2: The relative non-factorizable correction $\delta_{nf}(M)$ to the single invariant-mass distribution $d\sigma/dM$. Centre-of-mass energy: $\sqrt{s}=355~\,\mathrm{GeV}$.
• Figure 3: The relative non-factorizable correction $\delta_{nf}(M)$ to the single invariant-mass distribution $d\sigma/dM$. Centre-of-mass energy: $\sqrt{s}=500~\,\mathrm{GeV}$.