In this poster, results from the calculation of the decay rate $$Z \rightarrow \psi \bar{\psi},$$ in the absence and presence of a magnetic field are presented.

To incorporate the effect of the external magnetic field, the self-energy function is calculated to one loop using the fermionic propagators modified by the magnetic field. Then, the imaginary part of the self-energy function is calculated, which is directly associated with the decay rate through the Optic Theorem.

The results from this study indicate that the production of fermions, from the decay, is inhibited by the presence of the magnetic field.

Finally, the role of the spin in decay processes in the presence of magnetic fields is studied by comparing the result from this work with others in the field like the $\varphi \rightarrow \varphi^{*} \varphi,$ or $\varphi \rightarrow \psi \bar{\psi},$ decays.

The effects of a constant magnetic field on the decay rate $Z \rightarrow \psi \bar{\psi}$ are studied.

It was found that the presence of the magnetic field inhibits the decay rate compared to the vacuum case.

Different dependence over the transverse momentum to the magnetic field ($p^{\mu}_{\bot}$) and the intensity of the magnetic field ($|eB|$) are studied in a weak field approximation.

The study is compared to others of similar approach in the same energetic regime. This other studies are done over the $\varphi \rightarrow \varphi^{*} \varphi$ and $\varphi \rightarrow \psi \bar{\psi},$ decays.