of Eq. (\[eq:coeffvirt\])\]. The analytical expression of the coefficient $c_1$ can be related to the top contribution of the process $H\to Z\gamma$ [@Cahn:1978nz; @Bergstrom:1985hp]. The basic building block will be the one-loop contribution of the Higgs coupling to an on-shell and an off-shell gluon that is described, after translating all couplings and masses, by the “effective” Feynman rule,\

(100,100)(20,0) (-120,-560)[![image](./plots/dia_1pr.pdf){width="100.00000%"}]{} (240,58)[$\displaystyle -i \frac{\alpha_s}{\pi v}
\Big[I_1(\tau,\lambda)-I_2(\tau,\lambda)\Big]
\Big[ q_2^\mu q_1^\nu - (q_1 q_2) g^{\mu\nu} \Big] \delta_{ab}\, ,$]{}

\
where the functions $I_{1,2}$ are defined as [@Gunion:1989we] $$\begin{aligned}
I_1(\tau,\lambda) & = & \frac{\tau\lambda}{2(\tau-\lambda)} +
\frac{\tau^2\lambda^2}{2(\tau-\lambda)^2} \left[ f(\tau) - f(\lambda)
\right]
+ \frac{\tau^2\lambda}{(\tau-\lambda)^2} \left[ g(\tau)
- g(\lambda) \right], \nonumber \\
I_2(\tau,\lambda) & = & - \frac{\tau\lambda}{2(\tau-\lambda)}\left[
f(\tau) - f(\lambda) \right],\end{aligned}$$ with $\tau = 4m_t^2/m_H^2$, $\lambda = 4 m_t^2/q_2^2$ and the basic functions $$\begin{aligned}
g(\tau) & = & \left\{ \begin{array}{ll} \displaystyle \sqrt{\tau-1}
\arcsin \frac{1}{\sqrt{\tau}} & \tau \ge 1 \\ \displaystyle
\frac{\sqrt{1-\tau}}{2} \left[ \log \frac{1+\sqrt{1-\tau}}
{1-\sqrt{1-\tau}} - i\pi \right] & \tau < 1 \end{array} \right.\end{aligned}$$ and $f(\tau)$ defined in Eq. (\[eq:ftau\]). Implementing this building block for the two top loops of the one-particle-reducible diagrams, one arrives at the final coefficient $c_1$ of Eq. (\[eq:coeffvirt\]), $$\begin{aligned}
c_1 & = & 2 \Big[ I_1(\tau,\lambda_{\hat t}) -I_2(\tau,\lambda_{\hat
t}) \Big]^2
