LATEST BELLE II RESULTS ON BEAUTY AND CHARM DECAYS

Precise measurements of each $B\to\pi\pi$ decay is crucial to invoke the isospin sum-rule to disentangle the shift in the value of CKM angle $\phi_{2}$ due to the presence of gluonic penguin [6]. The decay $B^{0}\to\pi^{0}\pi^{0}$ is of particular interest at Belle II, as the final state consists of four photons. The signal yield is extracted from a simultaneous unbinned ML fit to $M_{\rm bc}$, $\Delta E$ and the output of a fast boosted decision tree (FBDT) algorithm based on event topological variables. The procedure is validated using the control sample of $B^{0}\to D^{0}[K^{-}\pi^{+}\pi^{0}]\pi^{0}$. The signal yield is $[14.0^{+6.8}_{-5.6}]$, corresponding to a branching fraction ${\cal B}(B^{0}\to\pi^{0}\pi^{0})=(0.98^{+0.48}_{-0.39}\leavevmode\nobreak\ \pm 0.27)\times 10^{-6}$. This result agrees with the previous measurements.

The decay $B^{0}\to\rho^{+}\rho^{0}$ has two vector mesons in the final state, and is dominated by their longitudinal polarization components. The large width of the $\rho$ meson and neutral pions in the final state lead to large background contamination. The signal yield is determined from an unbinned ML fit to $\Delta E$, FBDT output, reconstructed invariant masses of $\rho^{+}$ and $\rho^{0}$, and their helicity angles. We find $104\pm 16$ signal events which correspond to ${\cal B}(B^{0}\to\rho^{+}\rho^{0})=(20.6\pm 3.2\pm 4.0)\times 10^{-6}$, and the fraction of longitudinal polarization is $[0.936^{+0.049}_{-0.041}\pm 0.021]$.

The $K\pi$ isospin sum rule [7] offers a stringent null test of the SM, and is expressed in terms of direct $CP$ asymmetries and $\cal B$ of the four $B\to K\pi$ decay modes. The experimental uncertainty of the sum rule is currently dominated by the measurements of the decay $B^{0}\to K^{0}\pi^{0}$. We obtain $45^{+9}_{-8}$ signal events for this decay by fitting $\Delta E$ and $M_{\rm bc}$ distributions, which is translated to ${\cal B}(B^{0}\to K^{0}\pi^{0})=(8.5^{+1.7}_{-1.6}\pm 1.2)\times 10^{-6}$. [8]. As this decay is a $CP$ eigen-state, based on the output of flavor tagger [9], we find the decay-time-integrated direct $CP$ asymmetry as $[-0.40^{+0.46}_{-0.44}\pm 0.04]$.

Moments of the photon energy spectrum in the $b\to s\gamma$ transition are important for the determination of $b$–quark mass and its motion inside the $B$ meson. In this analysis [10], we first search for a high-energy photon ($E^{*}_{\gamma}>1.4$ GeV in the CM frame) in the collision events, which should not be arising from a $\pi^{0}$ or an $\eta$ meson decay. The expected spectrum of background events in data is obtained by scaling the Monte Carlo distribution fromthe off-resonance sample and the sidebands. A clear visible excess in data is observed around the expected region of $E^{*}_{\gamma}$ as shown in figure 1.

The decays $B^{+}\to K^{+}\ell^{+}\ell^{-}$ have raised a lot of interest in study of lepton-flavor-universality ratios. These rare decays ( ${\cal B}\sim 10^{-7}$) are challenging to be observed in the early data sample of Belle II. In a recent analysis at Belle II, $8.6^{+4.3}_{-3.9}\pm 0.4$ signal events are observed for the decay $B^{+}\to K^{+}\ell^{+}\ell^{-}$ [11].

The decay $B^{+}\to K^{+}\nu\bar{\nu}$ is theoretically cleaner as there is no contribution from the virtual photon in the diagrams unlike the decays mediated by the $b\to s\ell^{+}\ell^{-}$ transition. The decay $B^{+}\to K^{+}\nu\bar{\nu}$ is experimentally challenging as the final state consists of two neutrinos. At Belle II, a new analysis method has been developed for this search that exploits the topological features of the decay leading to a larger signal reconstruction efficiency. The method has been validated with $B^{+}\to K^{+}J/\psi[\to\mu^{+}\mu^{-}]$, by ignoring the $\mu^{+}\mu^{-}$ from the $J/\psi$ decay to mimic the missing energy from two neutrinos; $K^{+}$ momentum is also modified to correspond to a three-body decay. The signal strength obtained from the fit is $4.2^{+2.9}_{-2.8}{\leavevmode\nobreak\ \rm(stat.)^{+1.8}_{-1.6}}{\leavevmode\nobreak\ \rm(syst.)}$, which corresponds to ${\cal B}=[1.9\pm 1.3{\leavevmode\nobreak\ \rm(stat.)^{+0.8}_{-0.7}}{\leavevmode\nobreak\ \rm(syst.)}]\times 10^{-5}$. This measurement is competitive with the previous results, taking into account of the size of data sample used. As no significant signal is observed, the expected 90% confidence-level (CL) upper limit (UL) on the branching fraction of $2.3\times 10^{-5}$ is derived and the observed UL of $4.1\times 10^{-5}$ is set at 90% CL.

The lifetime measurement of $D^{0}$ meson is performed using $9.6{\leavevmode\nobreak\ \rm fb^{-1}}$ Belle II data recorded in 2019 [13]. Coming from the decay $D^{*+}\to D^{0}\pi^{+}$ in charm-quark pair events, the $D^{0}$ meson is reconstructed in three decay modes: $D^{0}\to K^{-}\pi^{+}$, $D^{0}\to K^{-}\pi^{+}\pi^{0}$ and $D^{0}\to K^{-}\pi^{+}\pi^{+}\pi^{-}$. The $D^{0}$ lifetime is obtained by performing a two-dimensional unbinned ML fit to distributions of proper time and its uncertainty. The average lifetime of $D^{0}$ meson is measured to be $412.3\pm 2.0{\leavevmode\nobreak\ \rm fs}$. With $72{\leavevmode\nobreak\ \rm fb^{-1}}$ of Belle II data, the lifetime measurement of $D^{0}$ is expected to be competitive with the world-averages.

$CP$ violation in the charm sector is an important topic to study at the Belle II experiment. The ultimate aim is to perform a time-averaged Dalitz plot analysis for the decay $D^{*+}\to D^{0}[\to\pi^{+}\pi^{-}\pi^{0}]\pi^{+}$. Currently, the decay has been reconstructed and the signal yield is extracted using a binned ML fit to the distribution of $\Delta M$, difference between the reconstructed invariant masses of $D^{*+}$ and $D^{0}$. The signal yield per ${\rm fb^{-1}}$ is found to be $305\pm 15{\leavevmode\nobreak\ \rm(stat.)}$ [14].