Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent base functions with the angular momentum $\ell$. These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys. Rev. A 64, 0421xx (Oct. 2001

Partial Wave Analysis of J/ψ→γ(K+K−π+π−)J/\psi \to \gamma (K^+K^-\pi^+\pi^-)

BES data on $J/\psi \to \gamma (K^+K^-\pi^+\pi^-)$ are presented. The $K^*\bar K^*$ contribution peaks strongly near threshold. It is fitted with a broad $0^{-+}$ resonance with mass $M = 1800 \pm 100$ MeV, width $\Gamma = 500 \pm 200$ MeV. A broad $2^{++}$ resonance peaking at 2020 MeV is also required with width $\sim 500$ MeV. There is further evidence for a $2^{-+}$ component peaking at 2.55 GeV. The non-$K^*\bar K^*$ contribution is close to phase space; it peaks at 2.6 GeV and is very different from $K^{*}\bar{K^{*}}$.Comment: 15 pages, 6 figures, 1 table, Submitted to PL

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

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.

A Measurement of Psi(2S) Resonance Parameters

Cross sections for e+e- to hadons, pi+pi- J/Psi, and mu+mu- have been measured in the vicinity of the Psi(2S) resonance using the BESII detector operated at the BEPC. The Psi(2S) total width; partial widths to hadrons, pi+pi- J/Psi, muons; and corresponding branching fractions have been determined to be Gamma(total)= (264+-27) keV; Gamma(hadron)= (258+-26) keV, Gamma(mu)= (2.44+-0.21) keV, and Gamma(pi+pi- J/Psi)= (85+-8.7) keV; and Br(hadron)= (97.79+-0.15)%, Br(pi+pi- J/Psi)= (32+-1.4)%, Br(mu)= (0.93+-0.08)%, respectively.Comment: 8 pages, 6 figure

The σ\sigma pole in J/ψ→ωπ+π−J/\psi \to \omega \pi^+ \pi^-

Using a sample of 58 million $J/\psi$ events recorded in the BESII detector, the decay $J/\psi \to \omega \pi^+ \pi^-$ is studied. There are conspicuous $\omega f_2(1270)$ and $b_1(1235)\pi$ signals. At low $\pi \pi$ mass, a large broad peak due to the $\sigma$ is observed, and its pole position is determined to be $(541 \pm 39)$ - $i$ $(252 \pm 42)$ MeV from the mean of six analyses. The errors are dominated by the systematic errors.Comment: 15 pages, 6 figures, submitted to PL

Search for the Lepton Flavor Violation Processes J/ψ→J/\psi \to μτ\mu\tau and eτe\tau

The lepton flavor violation processes $J/\psi \to \mu\tau$ and $e\tau$ are searched for using a sample of 5.8$\times 10^7$ $J/\psi$ events collected with the BESII detector. Zero and one candidate events, consistent with the estimated background, are observed in $J/\psi \to \mu\tau, \tau\to e\bar\nu_e\nu_{\tau}$ and $J/\psi\to e\tau, \tau\to\mu\bar\nu_{\mu}\nu_{\tau}$ decays, respectively. Upper limits on the branching ratios are determined to be $Br(J/\psi\to\mu\tau)<2.0 \times 10^{-6}$ and $Br(J/\psi \to e\tau) < 8.3 \times10^{-6}$ at the 90% confidence level (C.L.).Comment: 9 pages, 2 figure

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

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 $\frac{BF(D^+ \to \mu^+ X)}{BF(D^0 \to \mu^+ X)}=2.59\pm 0.70 \pm 0.25$