[en] Experiments are ahead in the race for determining the features of neutral B-mesons. Recent measurements at the LHCb experiment have pushed the uncertainties of the decay width difference ΔΓ in the $B_s-<!--\; ???\; -->{\stackrel{¯<!--\; ??\; -->}{B}}_s$ system to about 6%, whereas the uncertainty of the theory prediction is about a factor of four larger. First results for ΔΓ and the parameter a${}_{fs}$, quantifying the violation of the CP symmetry in $B_s$ and $B_d$ mixing, were already obtained in the Standard Model of particle physics several decades ago. In this thesis we improve on earlier predictions and provide the first next-to-next-to-leading order prediction which stabilizes the dependence on the renormalization scale and reduces uncertainties. The necessary calculations demand attention toward perturbative and non-perturbative aspects of meson physics. Focusing on the former, we carefully construct effective field theories where we complement the physical operators with properly chosen evanescent operators. Furthermore, efficient tools are necessary to compute the thousands of Feynman diagrams.