\label{eq:1prc1}\end{aligned}$$ with $\lambda_{\hat t} = 4 m_t^2/\hat t$ (and $\lambda_{\hat u} = 4
m_t^2/\hat u$ for the $\hat t\leftrightarrow \hat u$ interchanged contribution accordingly). This expression, inserted in the coefficient $C_{\triangle\triangle}$ of Eq. (\[eq:coeffvirt\]), determines the contribution of the one-particle-reducible diagrams analytically and agrees with the previous calculation of Ref. [@Degrassi:2016vss]. In the HTL, this coefficient approaches the value $c_1\to 2/9$ in accordance with Eq. (\[eq:coeffvirt\]). We have subtracted the HTL with $c_1=2/9$ from the coefficient $C_{\triangle\triangle}$ in order to account for the NLO top-mass effects only so that eventually the results of the program [Hpair]{} [@hpair] can be added back. While the total effect of the one-particle-reducible contributions on the total cross section ranges below the per-cent level, the finite mass effects at NLO contribute less than one per mille.

![\[fg:1prcomp\] *Comparison of the approximation of Ref. [@deFlorian:2017qfk] (blue) for the one-particle-reducible contributions and the HTL (red), both normalized to the full analytical expression. The singularity at about 720 GeV is due to a sign change of the exact expression.*](./plots/1pr_comp.pdf){width="80.00000%"}

Reference [@deFlorian:2017qfk] has proposed an approximation of this one-particle-reducible contribution in terms of the triangle form factor of two on-shell external gluons, $$\begin{aligned}
C_{\triangle\triangle} & = &
\Re e~\frac{\int_{\hat 