Probing the Standard Model flavor structure with hadronic beauty and charm decays

This dissertation investigates hadronic multi-body decays of beauty and charm mesons providing insights into both the CKM sector of the Standard Model and strong interaction dynamics at the hadronic energy scale. First, the resonant substructure of the decay $D^0 \to \pi^+\pi^-\pi^+\pi^-$ is studied. Quantum-entangled $D^0 \bar D^0$ pairs produced in electron-positron collisions are used. The data sample corresponds to an integrated luminosity of $818 \, \text{pb}^{-1}$ recorded by the CLEO-c detector. An amplitude analysis exploiting the full information provided by the five-dimensional phase space is performed to disentangle the various intermediate-state components and measure their relative phases. The global decay-rate asymmetry between $D^0$ and $\bar D^0$ decays is measured and a search for $CP$ asymmetries in the amplitude components is conducted; no evidence for $CP$ violation is found. The fractional $CP$-even content and related hadronic parameters are derived from the amplitude model and found to be consistent with model-independent measurements. These hadronic parameters are crucial input for a future measurement of the $CP$-violating phase $\gamma$ in $B^\pm \to ( D \to \pi^+\pi^-\pi^+\pi^-) K^\pm$ decays, where $D$ represents a superposition of $D^0$ and $\bar D^0$ mesons. With currently existing proton-proton collision data collected by the LHCb experiment, a precision of around $\sigma(\gamma) \approx 12^\circ$ can be achieved, competitive with the most precise single measurement of the CKM angle $\gamma$ to date. Second, hadronic multi-body decays of $B_s$ mesons are studied using proton-proton collision data corresponding to $7 \, \text{fb}^{-1}$ recorded by the LHCb detector. The $B_s- \bar B_s$ oscillation frequency is measured from flavor-specific $B_s \to D_s^- \pi^+ \pi^+ \pi^-$ decays to be $\Delta m_s = (17.7651 \pm 0.0084 (\text{stat}) \pm 0.0058 (\text{syst})) \, \text{ps}^{-1}$, consistent with and significantly more precise than the current world-average value. Mixing-induced $CP$ violation in $B_s \to D_s^\pm K^\mp \pi^\pm \pi^\mp$ decays is explored by means of a time-dependent amplitude analysis. The weak phase difference between $B_s \to D_s^- K^+ \pi^+ \pi^-$ and $\bar B_s \to D_s^- K^+ \pi^+ \pi^-$ decays is determined to be $\gamma = (60 \pm 17(\text{stat+syst}))^\circ$; the most precise measurement of this quantity in the $B_s$ meson system.