In this master thesis, we study the $B \rightarrow \nu \nu (\gamma)$ decay, where $B \in \{B_s, B_d\}$ meson decays into two neutrinos and a potential soft photon, and the $B \rightarrow \nu \nu \gamma$ decay with an observable photon in the framework of the Standard Model with $n=3$ additional chiral right-handed neutrinos. In this model neutrinos in the mass basis are Majorana fermions. We parametrize the mass matrices in the neutrino sector with a newly derived parametrization which naturally generalizes the well known Casas-Ibara parametrization. The differential decay widths of the $B \rightarrow \nu_C \nu_D$ and $B \rightarrow \nu_C \nu_D \gamma$ decay modes are derived for the general case (with $n$ additional neutrinos). The branching ratios of the $B \rightarrow \nu \nu (\gamma)$ and $B \rightarrow \nu \nu \gamma$ decays are investigated within the assumption that the photon detectors cover the full solid angle around the decay point of the $B$ meson. The more general case is commented on at the end of the thesis: we find that the contribution of the $B \rightarrow \nu \nu (\gamma)$ decay to $B$ meson decays with non-observable decay products can be completely negligible. The results presented in this work qualitatively apply also to other decays of pseudoscalar neutral flavored mesons to two neutrinos and a potential (soft) photon.
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