Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry

We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterise the associated solutions of the SU(\infty) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.Comment: Dedicated to Maciej Przanowski on the occasion of his 65th birthday. Minor corrections. To appear in CQ

Strominger--Yau--Zaslow geometry, Affine Spheres and Painlev\'e III

We give a gauge invariant characterisation of the elliptic affine sphere equation and the closely related Tzitz\'eica equation as reductions of real forms of SL(3, \C) anti--self--dual Yang--Mills equations by two translations, or equivalently as a special case of the Hitchin equation. We use the Loftin--Yau--Zaslow construction to give an explicit expression for a six--real dimensional semi--flat Calabi--Yau metric in terms of a solution to the affine-sphere equation and show how a subclass of such metrics arises from 3rd Painlev\'e transcendents.Comment: 38 pages. Final version. To appear in Communications in Mathematical Physic

Observation of vortex dynamics in arrays of nanomagnets

Vortex dynamics within arrays of square ferromagnetic nanoelements have been studied by time-resolved scanningKerr microscopy (TRSKM),while x-ray photoemission electronmicroscopy has been used to investigate the equilibrium magnetic state of the arrays. An alternating field demagnetization process was found to initialize a distribution of equilibrium states within the individual elements of the array, including quasiuniform states and vortex states of different chirality and core polarization. Repeated initialization revealed some evidence of stochastic behavior during the formation of the equilibrium state. TRSKM with a spatial resolution of ∼300 nm was used to detect vortex gyration within arrays of square nanoelements of 250-nm lateral size. Two arrays were studied consisting of a 9 × 9 and 5 × 5 arrangement of nanoelements with 50- and 500-nm element edge-to-edge separation to encourage strong and negligible dipolar interactions, respectively. In the 5 × 5 element array, TRSKM images, acquired at a fixed phase of the driving microwave magnetic field, revealed differences in the gyrotropic phase within individual elements. While some phase variation is attributed to the dispersion in the size and shape of elements, the vortex chirality and core polarization are also shown to influence the phase. In the 9 × 9 array, strong magneto-optical response due to vortex gyration was observed across regions with length equal to either one or two elements. Micromagnetic simulations performed for 2 × 2 arrays of elements suggest that particular combinations of vortex chirality and polarization in neighboring elements are required to generate the observed magneto-optical contrast.Engineering and Physical Sciences Research Council (EPSRC

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Measurement of the Branching Fraction of the Decay B+→π+π−ℓ+νℓ\boldsymbol{B^{+}\to\pi^{+}\pi^{-}\ell^{+}\nu_\ell} in Fully Reconstructed Events at Belle

We present an analysis of the exclusive $B^{+}\to\pi^{+}\pi^{-}\ell^{+}\nu_{\ell}$ decay, where $\ell$ represents an electron or a muon, with the assumption of charge-conjugation symmetry and lepton universality. The analysis uses the full $\Upsilon(4S)$ data sample collected by the Belle detector, corresponding to 711 fb$^{-1}$ of integrated luminosity. We select the events by fully reconstructing one $B$ meson in hadronic decay modes, subsequently determining the properties of the other $B$ meson. We extract the signal yields using a binned maximum-likelihood fit to the missing-mass squared distribution in bins of the invariant mass of the two pions or the momentum transfer squared. We measure a total branching fraction of ${{\cal B}(B^{+}\to \pi^{+}\pi^{-}\ell^{+}\nu_{\ell})= [22.7 ^{+1.9}_{-1.6} (\mathrm{stat}) \pm 3.5(\mathrm{syst}) ]\times 10^{-5}}$, where the uncertainties are statistical and systematic, respectively. This result is the first reported measurement of this decay.Comment: 23 pages, 19 figure

Measurement of CP violating asymmetries in B^0 -> K^+K^- K^0_S decays with a time-dependent Dalitz approach

We report a measurement of $CP$ violating asymmetries in $B^0(\overline{B}^0) \to K^+ K^- K^0_S$ decays with a time-dependent Dalitz approach. This analysis is based on a data sample of $657\times 10^6$ $B\overline{B}$ pairs accumulated at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. As the result of an unbinned maximum likelihood fit to the selected candidates, the mixing-induced and direct $CP$ violation parameters, $\phi^{\rm eff}_1$ and ${\cal A}_{CP}$ are obtained for $B^0 \to \phi(1020) K^0_S$, $B^0 \to f_0(980) K^0_S$ and other $B^0 \to K^+ K^- K^0_S$ decays. We find four solutions that describe the data. There are \{eqnarray*} \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (32.2 \pm 9.0 \pm 2.6 \pm 1.4)^{\circ}; \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (26.2 \pm 8.8 \pm 2.7 \pm 1.2)^{\circ};\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (27.3 \pm 8.6 \pm 2.8 \pm 1.3)^{\circ}\; {\rm and}\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (24.3 \pm 8.0 \pm 2.9 \pm 5.2)^{\circ}.{eqnarray*}\ The values for the $CP$ violating phase in $B^0\to \phi(1020) K^0_S$ are similar but other properties of the Dalitz plot are quite different for the four solutions. These four solutions have consistent $\phi^{\rm eff}_1$ values for all three $B$ meson decay channels and none of them deviates significantly from the values measured in $B \to (c\bar{c}) K^0$ decays with the currently available statistics. In addition, we find no significant direct $CP$ violation.Comment: submitted to PR

Measurements of Branching Fractions and Time-dependent CP Violating Asymmetries in B0→D(∗)±D∓B^{0} \to D^{(*)\pm}D^{\mp} Decays

We report measurements of branching fractions and time-dependent CP asymmetries in $B^{0} \to D^{+}D^{-}$ and $B^{0} \to D^{*\pm}D^{\mp}$ decays using a data sample that contains $(772 \pm 11)\times 10^6 B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We determine the branching fractions to be $\mathcal{B}(B^{0} \to D^{+}D^{-})=(2.12 \pm 0.16 \pm 0.18)\times 10^{-4}$ and $\mathcal{B}(B^{0} \to D^{*\pm}D^{\mp}=(6.14 \pm 0.29 \pm 0.50)\times 10^{-4}$. We measure CP asymmetry parameters $\mathcal{S}_{D^{+}D^{-}} = -1.06_{-0.14}^{+0.21} \pm 0.08$ and $\mathcal{C}_{D^{+}D^{-}} = -0.43 \pm 0.16 \pm 0.05$ in $B^{0} \to D^{+}D^{-}$ and $\mathcal{A}_{D^{*}D} = +0.06 \pm 0.05 \pm 0.02$, $\mathcal{S}_{D^{*}D} = -0.78 \pm 0.15 \pm 0.05$, $\mathcal{C}_{D^{*}D} = -0.01 \pm 0.11 \pm 0.04$, $\Delta\mathcal{S}_{D^{*}D} = -0.13 \pm 0.15 \pm 0.04$ and $\Delta\mathcal{C}_{D^{*}D} = +0.12 \pm 0.11 \pm 0.03$ in $B^{0} \to D^{*\pm}D^{\mp}$, where the first uncertainty is statistical and the second is systematic. We exclude the conservation of CP symmetry in both decays at equal to or greater than $4\sigma$ significance.Comment: 7 pages, 2 figure

Measurement of CP violating asymmetries in B^0 -> K^+K^- K^0_S decays with a time-dependent Dalitz approach

We report a measurement of $CP$ violating asymmetries in $B^0(\overline{B}^0) \to K^+ K^- K^0_S$ decays with a time-dependent Dalitz approach. This analysis is based on a data sample of $657\times 10^6$ $B\overline{B}$ pairs accumulated at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. As the result of an unbinned maximum likelihood fit to the selected candidates, the mixing-induced and direct $CP$ violation parameters, $\phi^{\rm eff}_1$ and ${\cal A}_{CP}$ are obtained for $B^0 \to \phi(1020) K^0_S$, $B^0 \to f_0(980) K^0_S$ and other $B^0 \to K^+ K^- K^0_S$ decays. We find four solutions that describe the data. There are \{eqnarray*} \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (32.2 \pm 9.0 \pm 2.6 \pm 1.4)^{\circ}; \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (26.2 \pm 8.8 \pm 2.7 \pm 1.2)^{\circ};\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (27.3 \pm 8.6 \pm 2.8 \pm 1.3)^{\circ}\; {\rm and}\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (24.3 \pm 8.0 \pm 2.9 \pm 5.2)^{\circ}.{eqnarray*}\ The values for the $CP$ violating phase in $B^0\to \phi(1020) K^0_S$ are similar but other properties of the Dalitz plot are quite different for the four solutions. These four solutions have consistent $\phi^{\rm eff}_1$ values for all three $B$ meson decay channels and none of them deviates significantly from the values measured in $B \to (c\bar{c}) K^0$ decays with the currently available statistics. In addition, we find no significant direct $CP$ violation.Comment: submitted to PR

Search for Time-Dependent CPT Violation in Hadronic and Semileptonic B Decays

We report a new sensitive search for CPT violation, which includes improved measurements of the CPT-violating parameter z and the total decay-width difference normalized to the averaged width DeltaGamma_d/Gamma_d of the two Bd mass eigenstates. The results are based on a data sample of 535 x 10^6 BBbar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. We obtain Re(z) = [+1.9 +/- 3.7 (stat) +/- 3.3 (syst)] x 10^{-2}, Im(z) = [-5.7 +/- 3.3 (stat) +/- 3.3 (syst)] x 10^{-3}, and DeltaGamma_d/Gamma_d = [-1.7 +/- 1.8 (stat) +/- 1.1 (syst)] x 10^{-2}, all of which are consistent with zero. This is the most precise single measurement of these parameters in the neutral B-meson system to date.Comment: 7 pages, 3 figures, 2 tables, LaTeX; addition of supplemental information, corrections of typos, results unchange

Evidence for the Suppressed Decay B- -> DK-, D -> K+pi-

The suppressed decay chain B- -> DK-, D -> K+pi-, where D indicates a anti-D0 or D0 state, provides important information on the CP-violating angle phi_3. We measure the ratio R_{DK} of the decay rates to the favored mode B- -> DK-, D -> K-pi+ to be R_{DK} = [1.63^{+0.44}_{-0.41}(stat)^{+0.07}_{-0.13}(syst)] x 10^{-2}, which indicates the first evidence of the signal with a significance of 4.1sigma. We also measure the asymmetry A_{DK} between the charge-conjugate decays to be A_{DK} = -0.39^{+0.26}_{-0.28}(stat)^{+0.04}_{-0.03}(syst). The results are based on the full 772 x 10^6 B anti-B pair data sample collected at the Upsilon(4S) resonance with the Belle detector.Comment: 6 pages, 2 figures, 2 tables, accepted by Physical Review Letter