the former. This physical process is similar to that obtained in the Dipole Model: the wave function describes the photon splitting and its subsequent sprouting. Preventing an unnecessary calculation, one needs only to take into account two of the diagrams, since the other ones lead to the same contributions.

Computing the imaginary part of the amplitude defined in Eq.(\[cut-rule\]), the product of the amplitudes in the left- and right-hand side is given by $$\begin{aligned}
 \nonumber
{\cal{A}}_{L} {\cal{A}}_{R} &=& (4 \pi)^{3} \, \alpha^{2}_{s} \, \alpha \, \sum_{q} e^{2}_{q} \, \left( \frac{\epsilon_{\mu}\epsilon^{*}_{\nu}}{k^{4}r^{2}} \right) \frac{V^{ba}_{\delta\sigma}}{N_{c}} (t^{b}t^{a}) \, 4 p_{\lambda}p^{\sigma} \\
&\times& 2 \, \left\{ \frac{\textrm{Tr} \left[ ({\not{\hbox{\kern-1.5pt $q$}}}- {\not{\hbox{\kern-.3pt $l$}}}) \gamma^{\mu} {\not{\hbox{\kern-.3pt $l$}}}\gamma^{\lambda} ({\not{\hbox{\kern-1.5pt $k$}}}+ {\not{\hbox{\kern-.3pt $l$}}}) \gamma^{\sigma} {\not{\hbox{\kern-.3pt $l$}}}\gamma^{\nu} \right]}{l^{4}} + \frac{\textrm{Tr} \left[ ({\not{\hbox{\kern-1.5pt $q$}}}- {\not{\hbox{\kern-.3pt $l$}}}) \gamma^{\lambda} ({\not{\hbox{\kern-1.5pt $k$}}}+ {\not{\hbox{\kern-.3pt $l$}}}- {\not{\hbox{\kern-1.5pt $q$}}}) \gamma^{\mu} ({\not{\hbox{\kern-1.5pt $k$}}}+ {\not{\hbox{\kern-.3pt $l$}}}) \gamma^{\sigma} {\not{\hbox{\kern-.3pt $l$}}}\gamma^{\nu} \right]}{l^{2}(k + l + q)^{2}} \right\},
\label{amp-cut-fhiggs}\end{aligned}$$ where $\epsilon_{\mu}$ and $\epsilon^{*}_{\nu}$ are the polarization vectors of the initial and final photons, respectively, the vector $l^{\mu}$ is the four-momentum of the quark circulating into the fermion loop, and $p^{\mu}$ is the four-momentum of the colliding proton. Mathematically, the traces represent the fermion loop, which can be calculated with a numerical algorithm 