from the known (complex) virtual coefficient ${\cal
C}^H_{virt}(M_H^2)$ of single Higgs production [@Spira:1995rr; @Graudenz:1992pv; @Harlander:2005rq; @Anastasiou:2009kn; @Aglietti:2006tp][^4], $${\cal C}_{virt}(Q^2) = \left. {\cal C}^H_{virt}(M_H^2)\right|_{M_H^2 \to
Q^2} \, .$$ In the HTL, this virtual coefficient (before renormalization) approaches the expression $${\cal C}_{virt} (Q^2) \to \frac{\Gamma(1-\epsilon)}{\Gamma(1-2\epsilon)}
\left(\frac{4\pi\mu_0^2 (1-i\bar\epsilon)}{-Q^2}\right)^\epsilon \left\{
-\frac{3}{2\epsilon^2} + \frac{3}{4} - \frac{\pi^2}{4} \right\}$$ with the ’t Hooft scale $\mu_0$, where the (infinitesimal) regulator $\bar\epsilon$ defines the proper analytical continuation of this expression. This result has to be followed by the renormalization of the strong coupling $\alpha_s$ and the top mass $m_t$ that will be discussed in Section \[sc:renorm\]. In addition, we have subtracted the HTL to obtain the pure top-mass effects at NLO (relative to the massive LO expression $F_\triangle$) to ensure that in the end the results of the program [Hpair]{} [@hpair] can be added back. This last step will be discussed in Section \[sc:renorm\], too.

### One-particle-reducible diagrams

The one-particle-reducible contribution is depicted in Fig. \[fg:gghhvirt\] (middle diagram), where a second diagram with the initial gluons interchanged has to be added. These will constitute the $\hat t$- and $\hat u$-channel parts where the second is related to the first just by the interchange $\hat t\leftrightarrow \hat
u$ \[see $C_{\triangle\triangle}$ 