Initially, the Standard model (SM), the most comprehensive theory of fundamental particles and their interactions, is presented. Each interaction is described using the framework of the gauge theory and a Lagrangian is constructed for each of them. The unification of electromagnetic and weak interactions into the electroweak interaction, where symmetry breaking occurs is described in detail. With the Higgs mechanism, masses for gauge bosons, fermions and leptons are generated. A transformation of the states of fermions from the weak (gauge) basis to the mass basis occurs, resulting in flavor mixing which is presented using the CKM matrix.
In the following section, physics beyond the SM, citing neutrino oscillations as an example, which require massive neutrinos, is described. Next, we introduced hypothetical particles, leptoquarks (LQ), which can directly couple leptons, and quarks. Our focus was on the scalar LQ $\tilde{R}_2$, which can couple SM fermions with particles that possess the quantum numbers of the right-handed neutrino, which are absent in the Standard model. Furthermore, we described fundamental quantities in the decays of elementary particles and provided the theoretical background for their calculations.
The main theme of this master's thesis are the decays $B_s^0 \rightarrow$ "invisible", $B^+ \rightarrow K^{+}$ "invisible", and $B^+ \rightarrow K^{+}$ "invisible" in effective theory. For the first decay, we calculated the branching ratios for a scalar operator and a vector operator containing massive right-handed neutrinos, then we incorporated the interaction with LQ $\tilde{R}_2$. Next, we explored the dependece of Yukawa couplings product on the mass of $\tilde{R}_2$. In the cases of $B^+ \rightarrow K^{+}$ "invisible" and $B^+ \rightarrow K^{+}$ "invisible" we first calculated the SM prediction in the effective theory, where "invisible", represents two SM neutrinos. Later, we expanded the selection of operators that include massive right-handed neutrinos and introduced the interaction with LQ. For both decays, we found limits for the masses of LQ $\tilde{R}_2$ and established a connection with the mass of the right-handed neutrino.
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