Using a simulated data sample of the Belle II detector measurements with an integrated luminosity of $375$ fb$^{-1}$ we performed a study of measurement of branching ratios for two rare $B$ meson radiative decays $B^{\scriptscriptstyle 0}\rightarrow \rho^{\scriptscriptstyle 0}\gamma$ and $B^{\scriptscriptstyle 0}\rightarrow K^{\scriptscriptstyle*0}\gamma$. The obtained branching ratios were then used to determine the value of $\lvert V_{\scriptscriptstyle td}/V_{\scriptscriptstyle ts} \rvert$ ratio of the Cabibbo–Kobayashi–Maskawa matrix elements.
The sample contained simulated data of electron-positron collisions from an upgraded high luminosity Belle II experiment, which will in its future operation period accumulate $50$ ab$^{-1}$ of data.
From the data sample, we first performed na exclusive reconstruction of events for both decay chains. We proceeded with the elimination of background events with the usage of pion veto and machine learning techniques.
We then obtained signal yields from fits to kinematic distributions of events and determined the reconstruction efficiencies, which were found to be $ \epsilon_{\scriptscriptstyle \rho^{\scriptscriptstyle 0}}=9\% $ and $ \epsilon_{\scriptscriptstyle K^{\scriptscriptstyle \ast 0}}=22.7\% $. In comparison to the results from older Belle studies, our reconstruction efficiencies are higher.
The branching ratios determined from the signal yields have values of
$\mathcal{B}(B^{\scriptscriptstyle 0}\longrightarrow\rho^{\scriptscriptstyle 0} \gamma)=(12\pm3)\cdot10^{-7}$ and $\mathcal{B}(B^{\scriptscriptstyle 0}\longrightarrow K^{\scriptscriptstyle \ast0}\gamma)=(4.19\pm0.08)\cdot10^{-5}$, and are within the statistical uncertainty in agreement with theoretical predictions and world average values; in our case the relative statistical uncertainty for the $\rho^{\scriptscriptstyle 0}$ decay mode has a value of 26\% and is comparable with results from older studies with Belle data, while the uncertainty of the $K^{\scriptscriptstyle *0}$ mode branching ratio has a value of 1.9\% and is improved in same comparison.
Finally, we calculated the value of ratio CKM elements
$\left|V_{\scriptscriptstyle td}/V_{\scriptscriptstyle ts}\right|= 0.268\pm 0.041$ which is also in agreement with the world average values, albeit statistical uncertainty is larger descending from results obtained from $\rho^{\scriptscriptstyle 0}$ mode. Nevertheless, we estimate that the statistical uncertainty will be improved by an order of magnitude when the sample of size $50$ ab$^{-1}$ will be used.
We conclude, that in the future, the uncertainty of the ratio $\left|V_{\scriptscriptstyle td}/V_{\scriptscriptstyle ts}\right|$ will be dominated by uncertainties of some of the parameters used to calculate the value of $\left|V_{\scriptscriptstyle td}/V_{\scriptscriptstyle ts}\right|$ that are calculated theoretically or determined from other measurements.
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