The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Geometric Phase and Quantum Phase Transition in the Lipkin-Meshkov-Glick model

The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this model. The possibility of the geometric phase or its derivatives as the universal order parameter of characterizing quantum phase transitions has been also discussed.Comment: 6 pages and to be published in Phys.Lett.

Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

Measurements of the observed cross sections for e+e−→e^+e^-\to exclusive light hadrons containing π0π0\pi^0\pi^0 at s=3.773\sqrt s= 3.773, 3.650 and 3.6648 GeV

By analyzing the data sets of 17.3, 6.5 and 1.0 pb$^{-1}$ taken, respectively, at $\sqrt s= 3.773$, 3.650 and 3.6648 GeV with the BES-II detector at the BEPC collider, we measure the observed cross sections for $e^+e^-\to \pi^+\pi^-\pi^0\pi^0$, $K^+K^-\pi^0\pi^0$, $2(\pi^+\pi^-\pi^0)$, $K^+K^-\pi^+\pi^-\pi^0\pi^0$ and $3(\pi^+\pi^-)\pi^0\pi^0$ at the three energy points. Based on these cross sections we set the upper limits on the observed cross sections and the branching fractions for $\psi(3770)$ decay into these final states at 90% C.L..Comment: 7 pages, 2 figure

Partial wave analysis of J/\psi \to \gamma \phi \phi

Using $5.8 \times 10^7 J/\psi$ events collected in the BESII detector, the radiative decay $J/\psi \to \gamma \phi \phi \to \gamma K^+ K^- K^0_S K^0_L$ is studied. The $\phi\phi$ invariant mass distribution exhibits a near-threshold enhancement that peaks around 2.24 GeV/$c^{2}$. A partial wave analysis shows that the structure is dominated by a $0^{-+}$ state ($\eta(2225)$) with a mass of $2.24^{+0.03}_{-0.02}{}^{+0.03}_{-0.02}$ GeV/$c^{2}$ and a width of $0.19 \pm 0.03^{+0.06}_{-0.04}$ GeV/$c^{2}$. The product branching fraction is: $Br(J/\psi \to \gamma \eta(2225))\cdot Br(\eta(2225)\to \phi\phi) = (4.4 \pm 0.4 \pm 0.8)\times 10^{-4}$.Comment: 11 pages, 4 figures. corrected proof for journa

Measurements of the Mass and Full-Width of the ηc\eta_c Meson

In a sample of 58 million $J/\psi$ events collected with the BES II detector, the process J/$\psi\to\gamma\eta_c$ is observed in five different decay channels: $\gamma K^+K^-\pi^+\pi^-$, $\gamma\pi^+\pi^-\pi^+\pi^-$, $\gamma K^\pm K^0_S \pi^\mp$ (with $K^0_S\to\pi^+\pi^-$), $\gamma \phi\phi$ (with $\phi\to K^+K^-$) and $\gamma p\bar{p}$. From a combined fit of all five channels, we determine the mass and full-width of $\eta_c$ to be $m_{\eta_c}=2977.5\pm1.0 ({stat.})\pm1.2 ({syst.})$ MeV/$c^2$ and $\Gamma_{\eta_c} = 17.0\pm3.7 ({stat.})\pm7.4 ({syst.})$ MeV/$c^2$.Comment: 9 pages, 2 figures and 4 table. Submitted to Phys. Lett.

Direct Measurements of Absolute Branching Fractions for D0 and D+ Inclusive Semimuonic Decays

By analyzing about 33 $\rm pb^{-1}$ data sample collected at and around 3.773 GeV with the BES-II detector at the BEPC collider, we directly measure the branching fractions for the neutral and charged $D$ inclusive semimuonic decays to be $BF(D^0 \to \mu^+ X) =(6.8\pm 1.5\pm 0.7)$ and $BF(D^+ \to \mu^+ X) =(17.6 \pm 2.7 \pm 1.8)$, and determine the ratio of the two branching fractions to be $\frac{BF(D^+ \to \mu^+ X)}{BF(D^0 \to \mu^+ X)}=2.59\pm 0.70 \pm 0.25$

Direct Measurements of the Branching Fractions for D0→K−e+νeD^0 \to K^-e^+\nu_e and D0→π−e+νeD^0 \to \pi^-e^+\nu_e and Determinations of the Form Factors f+K(0)f_{+}^{K}(0) and f+π(0)f^{\pi}_{+}(0)

The absolute branching fractions for the decays $D^0 \to K^-e ^+\nu_e$ and $D^0 \to \pi^-e^+\nu_e$ are determined using $7584\pm 198 \pm 341$ singly tagged $\bar D^0$ sample from the data collected around 3.773 GeV with the BES-II detector at the BEPC. In the system recoiling against the singly tagged $\bar D^0$ meson, $104.0\pm 10.9$ events for $D^0 \to K^-e ^+\nu_e$ and $9.0 \pm 3.6$ events for $D^0 \to \pi^-e^+\nu_e$ decays are observed. Those yield the absolute branching fractions to be $BF(D^0 \to K^-e^+\nu_e)=(3.82 \pm 0.40\pm 0.27)$ and $BF(D^0 \to \pi^-e^+\nu_e)=(0.33 \pm 0.13\pm 0.03)$. The vector form factors are determined to be $|f^K_+(0)| = 0.78 \pm 0.04 \pm 0.03$ and $|f^{\pi}_+(0)| = 0.73 \pm 0.14 \pm 0.06$. The ratio of the two form factors is measured to be $|f^{\pi}_+(0)/f^K_+(0)|= 0.93 \pm 0.19 \pm 0.07$.Comment: 6 pages, 5 figure

Study of J/psi decays to Lambda Lambdabar and Sigma0 Sigma0bar

The branching ratios and Angular distributions for J/psi decays to Lambda Lambdabar and Sigma0 Sigma0bar are measured using BESII 58 million J/psi.Comment: 11 pages, 5 figure