Measurement of the properties of $B^+\rightarrow\rho^+\rho^0$ decays at Belle~II

This experimental particle-physics thesis reports measurements of properties of $B^+\rightarrow\rho^+\rho^0$ decays for the determination of the quark-mixing matrix angle \newline \mbox{$\alpha=\text{arg}(-(V_{td}V^*_{tb})/(V_{ud}V^*_{ub}))$}, a fundamental parameter of quark dynamics. The analysis uses the full data set of electron-positron collisions at the $\Upsilon(4S)$ resonance produced by the energy-asymmetric SuperKEKB collider and collected by the Belle~II experiment until June 2022. Belle~II is an hermetic solenoidal magnetic spectrometer, surrounded by particle-identification detectors, calorimeter, and muon detectors, designed to reconstruct the decay products of 10 GeV electron-positron collisions. The sample corresponds to 387 million pairs of bottom-antibottom mesons. The analysis is developed using simulated and control-data samples. Only when all procedures are established the analysis is applied to the sample of signal candidates in data. Data are enriched in $B^+\rightarrow\rho^+\rho^0$ events by a multivariate statistical-learning selection that suppresses the most prominent source of background by minimizing the expected statistical variance of the quantities of interest. A multidimensional fit of sample composition identifies statistically the signal and determines the angular distributions of its decay products. Special care is devoted to keep the systematic uncertainties under control: the main contribution comes from mismodelings of the angular distributions in signal-rich regions. The central values are hidden as the analysis is still under internal collaboration review. 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} $\mathcal{B}(B^+\rightarrow\rho^+\rho^0)~=~([\text{xx}]^{+1.40}_{-1.39}~(\textrm{stat})\pm [1.39]~(\textrm{syst}))\times 10^{-6}$, \end{center} the fraction of longitudinally polarized $B^+\rightarrow\rho^+\rho^0$ decays, \begin{center} $f_L~=~[\text{xx}]^{+0.017}_{-0.015}~(\textrm{stat})\pm [0.008]~(\textrm{syst})$, \end{center} and the ${\it CP}$-violating charge-asymmetry, \begin{center} $A_{\it CP}~=~[\text{xx}]\pm 0.062~(\textrm{stat})\pm [0.041]~(\textrm{syst})$. \end{center} The statistical uncertainties are competitive with the current world-best results. The systematic uncertainties are reported in brackets as they are still preliminary.