We search for the rare decay $B^{+}\to K^{+}\nu \overline{\nu }$ in a $362{\mathrm{fb}}^{-1}$ sample of electron-positron collisions at the $\mathrm{\Upsilon }(4S)$ resonance collected with the Belle II detector at the SuperKEKB collider. We use the inclusive properties of the accompanying $B$ meson in $\mathrm{\Upsilon }(4S)\to B\overline{B}$ events to suppress background from other decays of the signal $B$ candidate and light-quark pair production. We validate the measurement with an auxiliary analysis based on a conventional hadronic reconstruction of the accompanying $B$ meson. For background suppression, we exploit distinct signal features using machine learning methods tuned with simulated data. The signal-reconstruction efficiency and background suppression are validated through various control channels. The branching fraction is extracted in a maximum likelihood fit. Our inclusive and hadronic analyses yield consistent results for the $B^{+}\to K^{+}\nu \overline{\nu }$ branching fraction of $[2.7\pm 0.5(\mathrm{stat})\pm 0.5(\mathrm{syst})]\times {10}^{-5}$ and $[{1.1}_{-0.8}^{+0.9}(\mathrm{stat}{)}_{-0.5}^{+0.8}(\mathrm{syst})]\times {10}^{-5}$, respectively. Combining the results, we determine the branching fraction of the decay $B^{+}\to K^{+}\nu \overline{\nu }$ to be $[2.3\pm 0.5(\mathrm{stat}{)}_{-0.4}^{+0.5}(\mathrm{syst})]\times {10}^{-5}$, providing the first evidence for this decay at 3.5 standard deviations. The combined result is 2.7 standard deviations above the standard model expectation.

We discuss selected and important features of hadronic molecules as one of several promising forms of exotic hadrons near thresholds. Using examples of D D ¯ * systems such as X(3872) and Z _c , emphasis is put on the roles of the one pion exchange interaction between them and their coupling to intrinsic quark states. Thus hadronic molecules emerge as admixtures of the dominant long-range hadron structure and short-range quark structure. For the pion exchange interaction, properties of the tensor force are analyzed in detail. More coupled channels supply more attractions, and heavier constituents suppress kinetic energies, providing more chances to form hadronic molecules of heavy hadrons. Throughout this article, we show details of basic ideas and methods.

We investigate the hidden-charm pentaquarks as superpositions of ${\mathrm{\Lambda }}_c{\overline{D}}^{(*)}$ and ${\mathrm{\Sigma }}_c^{(*)}{\overline{D}}^{(*)}$ (isospin $I=1/2$) meson-baryon channels coupled to a $uudc\overline{c}$ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can consistently explain the masses and decay widths of $P_c^{+}(4312)$, $P_c^{+}(4440)$ and $P_c^{+}(4457)$ with the dominant components of ${\mathrm{\Sigma }}_c\overline{D}$ and ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ with spin-parity assignments $J^P=1/2^{-}$, $3/2^{-}$ and $1/2^{-}$, respectively. We analyze basic properties of the $P_c$’s such as masses and decay widths, and find that the mass ordering is dominantly determined by the quark dynamics while the decay widths by the tensor force of the one-pion exchange.

In order to understand the structure of X(3872), the $$c\bar {c}$$ charmonium core state that couples to the $$D^0 \bar {D}^{\ast 0}$$ and $$D^+ D^{\ast -}$$ molecular states is studied. The strengths of the couplings between the charmonium state and the hadronic molecular states are determined so as to reproduce the observed mass of X(3872). The attraction between D and $$\bar {D}^{\ast }$$ is determined so as to be consistent with the observed $$Z_b^{\pm ,0}$$(10 610) and $$Z_b^{\pm ,0}$$(10 650) masses. Isospin symmetry breaking is introduced by the mass differences between the neutral and charged D mesons. The structure of X(3872) that we have obtained is not just a $$D^0 \bar {D}^{\ast 0}$$ hadronic molecule but a charmonium–hadronic molecule hybrid state. It consists of about 6% $$c\bar {c}$$ charmonium, 69% isoscalar $$D \bar {D}^\ast $$ molecule, and 26% isovector $$D \bar {D}^\ast $$ molecule. This explains many of the observed properties of X(3872), such as isospin symmetry breaking, the production rate in the $$p \bar {p}$$ collision, the non-existence of the $$\chi _{c1}(2P)$$ peak predicted by the quark model, and the absence of charged X. The same picture can be applied to other heavy two-meson S-wave systems, where the states predicted by the quark model are not observed above the thresholds.

We studied LaAlO${}_3$/SrTiO${}_3$ interfaces for varying LaAlO${}_3$ thickness by core-level photoemission spectroscopy. In Ti $2p$ spectra for conducting “$n$-type” interfaces, Ti${}^{3+}$ signals appeared, which were absent for insulating “$p$-type” interfaces. The intensity of the Ti${}^{3+}$ signals was significantly higher than that expected for the transport carrier densities, indicating that part of the carriers at the interfaces are localized. The Ti${}^{3+}$ signals increased with LaAlO${}_3$ thickness, but started well below the critical thickness of 4 unit cells for metallic transport. Core-level shifts with LaAlO${}_3$ thickness were much smaller than predicted by the polar catastrophe model. We attribute these observations to surface defects and/or adsorbates providing charges to the interface even below the critical thickness.

We present a measurement of the differential shapes of exclusive $B\to D^{*}\ell {\overline{\nu }}_{\ell }$ ($B=B^{-},{\overline{B}}^0$ and $\ell =e$, $\mu$) decays with hadronic tag-side reconstruction for the full $711{\mathrm{fb}}^{-1}$ Belle dataset. We extract the Caprini-Lellouch-Neubert (CLN) and Boyd-Grinstein-Lebed (BGL) form factor parameters and use an external input for the absolute branching fractions to determine the Cabibbo-Kobayashi-Maskawa matrix element and find $|V_{cb}{|}_{\mathrm{CLN}}=(40.2\pm 0.9)\times {10}^{-3}$ and $|V_{cb}{|}_{\mathrm{BGL}}=(40.7\pm 1.0)\times {10}^{-3}$ with the zero-recoil lattice QCD point $\mathcal{F}(1)=0.906\pm 0.013$. We also perform a study of the impact of beyond zero-recoil lattice QCD calculations on the $|V_{cb}|$ determinations. Additionally, we present the lepton-flavor universality ratio $R_{e\mu }=\mathcal{B}(B\to D^{*}e{\overline{\nu }}_e)/\mathcal{B}(B\to D^{*}\mu {\overline{\nu }}_{\mu })=0.993\pm 0.023\pm 0.023$, the electron and muon forward-backward asymmetry and their difference $\mathrm{\Delta }{A}_{FB}=0.028\pm 0.028\pm 0.008$, and the electron and muon $D^{*}$ longitudinal polarization fraction and their difference $\mathrm{\Delta }{F}_L^{D^{*}}=0.030\pm 0.025\pm 0.007$. The uncertainties quoted correspond to the statistical and systematic uncertainties, respectively.