First observation of the P-wave spin-singlet bottomonium states hb(1P) and hb(2P)

We report the first observations of the spin-singlet bottomonium states h(b)(1P) and h(b)(2P). The states are produced in the reaction e(+)e(-)→h(b)(nP)π(+)π(-) using a 121.4 fb(-1) data sample collected at energies near the Υ(5S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We determine M[h(b)(1P)]=(9898.2(-1.0-1.1)(+1.1+1.0)) MeV/c(2) and M[h(b)(2P)]=(10,259.8±0.6(-1.0)(+1.4)) MeV/c(2), which correspond to P-wave hyperfine splittings ΔM(HF)=(+1.7±1.5) and (+0.5(-1.2)(+1.6)) MeV/c(2), respectively. The significances of the h(b)(1P) and h(b)(2P) are 5.5σ and 11.2σ, respectively. We find that the production of the h(b)(1P) and h(b)(2P) is not suppressed relative to the production of the Υ(1S), Υ(2S), and Υ(3S).     

Singularities of Blaschke normal maps of convex surfaces

We prove that the difference between the numbers of positive swallowtails and negative swallowtails of the Blaschke normal map for a given convex surface in affine space is equal to the Euler number of the subset where the affine shape operator has negative determinant.     

The first halogen-substituted cyclotrigermenes: a unique halogen walk over the three-membered ring skeleton and facial stereoselectivity in the Diels-Alder reaction

Dark red crystals of the halogen-substituted cyclotrigermenes [(tBu3Si)3Ge3X; X = Cl, Br, I] were obtained in good yields by the reaction of [(tBu3Si)3Ge3]+.TTFPB- (TTFPB- = tetrakis(2,3,5,6-tetrafluorophenyl)borate) with potassium halides (KCl, KBr, or KI) in diethyl ether. The crystal structures of the halogen-substituted cyclotrigermenes reveal a cis-bent Ge=Ge double bond, caused by the introduction of the electronegative halogen atom on the sp3 germanium atom of cyclotrigermene. In solution, an intramolecular halogen migration over the three-membered ring skeleton was observed. Facial stereoselectivity in the Diels-Alder reaction of new cyclotrigermenes with 2,3-dimethyl-1,3-butadiene is also reported.     

Observation of D+(s)K- and evidence for D+(s)pi- final states in neutral B decays

We report the first observation of a B meson decay that is not accessible by a direct spectator process. The channel B(0)-->D(+)(s)K- is found in a sample of 85 x 10(6) BB; events, collected with the Belle detector at KEKB, with a branching fraction B(B(0)-->D(+)(s)K-)=(4.6(+1.2)(-1.1)+/-1.3) x 10(-5). We also obtain evidence for the B0-->D(+)(s)pi(-) decay with branching fraction B(B0-->D(+)(s)pi(-))=(2.4(+1.0)(-0.8)+/-0.7) x 10(-5). This value may be used to extract a model-dependent value of |V(ub)|.     

Structure of dichlorine monoxide as studied by microwave spectroscopy. Determination of equilibrium structure by a modified mass dependence method

The microwave spectra of four isotopic species of dichlorine monoxide (OCl₂) have been observed, and the rotational constants have been obtained. The r_m structure for each isotopic species has been determined by Watson's method. The equilibrium structure has been estimated by taking proper averages of r_m structures to be $\text{r}{}_{\mathrm{e}}\text{(OCl) = 1.69587(7)}\text{A}\text{?}$ and ∠_eClOCl = 110.886(6)°. The general applicability and the merit of the present method for estimating the equilibrium structure are pointed out.