Measurement of the branching fraction, longitudinal polarization fraction, and charge-parity violating asymmetry in $B^+\rightarrow\rho^+\rho^0$ decays at Belle

This is an experimental particle physics thesis aimed at measurements of properties of $B^+\rightarrow\rho^+\rho^0$ decays for the determination of the quark-mixing matrix angle \newline \mbox{$\alpha/\phi_2=\text{arg}(-(V_{td}V^*_{tb})/(V_{ud}V^*_{ub}))$}, a fundamental parameter of quark dynamics. The analysis uses the full data set of electron-positron ($e^+e^-$) collisions produced by the energy-asymmetric KEKB collider at the $\Upsilon(4S)$ resonance collected by the Belle experiment and corresponding to 772 million pairs of bottom-antibottom mesons. Belle is an hermetic magnetic spectrometer surrounded by particle-identification detectors, calorimeters, and muon detectors designed to reconstruct the decay products of 10.58 GeV $e^+e^-$ collisions. The analysis is entirely developed using simulated and control-data samples. Only when all procedures are established the analysis is applied to the signal candidates in data. The principal challenge is to overcome the initial $10^{-6}$ signal-to-background ratio with a selection sufficiently discriminating to isolate an abundant, low-background signal without introducing intractable correlations in the multidimensional fit that determines the parameters of interest. Data are enriched in $B^+\rightarrow\rho^+\rho^0$ events by a multivariate statistical-learning selection that suppresses the most prominent source of background. A multidimensional fit of sample composition then identifies statistically the signal. Special care is devoted to keep the impact of systematic uncertainties under control. A total of approximately 1000 $B^+\rightarrow\rho^+\rho^0$ decays are reconstructed. The fit results, combined with acceptance and efficiency corrections determined from simulation, allow for determining the $B^+\to\rho^+\rho^0$ branching fraction, \begin{center} $\mathcal{B}(B^+\rightarrow\rho^+\rho^0)~=~[\text{xx}]^{+1.20}_{-1.19}~(\textrm{stat})\pm 1.46~(\textrm{syst})$, \end{center} the fraction of longitudinally polarized $B^+\rightarrow\rho^+\rho^0$ decays, \begin{center} $f_L~=~[\text{xx}]\pm 0.025~(\textrm{stat})\pm 0.020~(\textrm{syst})$, \end{center} and the ${\it CP}$-violating charge-asymmetry, \begin{center} $A_{\it CP}~=~[\text{xx}]\pm 0.052~(\textrm{stat})\pm 0.015~(\textrm{syst})$. \end{center} The central values are hidden as the analysis is still under internal collaboration review. The uncertainties are comparable with, or better than, the current world best results. Our results provide a 13$\%$ improvement on the global knowledge of $\alpha/\phi_2$.