New graph-neural-network flavor tagger for Belle II and measurement of $\sin 2{\phi }_1$ in $B^0\to J\mathrm{/}\psi K_{\text{S}}^0$ decays

We present GFlaT, a new algorithm that uses a graph-neural-network to determine the flavor of neutral $B$ mesons produced in $\mathrm{{\rm Y}}(4S)$ decays. It improves previous algorithms by using the information from all charged final-state particles and the relations between them. We evaluate its performance using $B$ decays to flavor-specific hadronic final states reconstructed in a 362 ${\text{fb}}^{-1}$ sample of electron-positron collisions collected at the $\mathrm{{\rm Y}}(4S)$ resonance with the Belle II detector at the SuperKEKB collider. We achieve an effective tagging efficiency of $(37.40\pm 0.43\pm 0.36)\mathrm{\%}$, where the first uncertainty is statistical and the second systematic, which is $18\mathrm{\%}$ better than the previous Belle II algorithm. Demonstrating the algorithm, we use $B^0\to J\mathrm{/}\psi K_{\text{S}}^0$ decays to measure the mixing-induced and direct $CP$ violation parameters, $S=(0.724\pm 0.035\pm 0.009)$ and $C=(-0.035\pm 0.026\pm 0.029)$.