Распады $B_c^+$ мезона и поиск редкого распада $B^0_s \to \mu^+ \mu^-$ в эксперименте ATLAS

The PhD thesis is dedicated to a study of heavy hadrons in the ATLAS experiment at the Large Hadron Collider. It presents a measurement of the branching ratios of the $B_c^+$ meson decays, $B_c^+\to J/\psi D_s^+$ and $B_c^+\to J/\psi D_s^{*+}$, using another $B_c^+$ decay, $B_c^+\to J/\psi \pi^+$, for normalization. Polarization of daughter particles in the $B_c^+\to J/\psi D_s^{*+}$ decay is also measured. The study was performed with data collected by ATLAS in $pp$ collisions at centre-of-mass energies $\sqrt{s} = 7$ and 8 TeV in 2011--2012. The thesis also describes a study on search for the $B^0_s\to \mu^+\mu^-$ rare decay with ATLAS data of $pp$ collisions at $\sqrt{s} = 7$~TeV. An upper limit on the decay branching ratio is set. Author's principal contribution to this study was developing a method to estimate a background from neutral $B$ meson decays to a pair of light charged hadrons ($B\to hh^\prime$).