The Constraints of Unitary on ππ\pi\pi Scattering Dispersion Relations

A new dispersion relation for the partial wave $\pi\pi$ scattering $S$ matrix is set up. Using the dispersion relation we generalize the single channel unitarity condition, $SS^+=1$, to the entire complex $s$ plane, which is equivalent to the generalized unitarity condition in quantum mechanics. The pole positions of the $\sigma$ resonance and the $f_0(980)$ resonance are estimated based on the theoretical relations we obtained. The central value of the $\sigma$ pole position is $M_\sigma\simeq 410$MeV, $\Gamma_\sigma\simeq 550$MeV, obtained after including the the constraint of the Adler zero condition.Comment: 10 pages with 4 figures, revised version to appear in Phys. Lett.

Dynamical Structure Factor for the Alternating Heisenberg Chain: A Linked Cluster Calculation

We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from a given set of excited states. A linked cluster technique to obtain high order series expansions for these quantities is discussed. We apply these methods to the alternating Heisenberg chain around the dimerized limit ($\lambda=0$), where complete wavevector and frequency dependent spectral weights for one and two-particle excitations (continuum and bound-states) are obtained. For small to moderate values of the inter-dimer coupling parameter $\lambda$, these lead to extremely accurate calculations of the dynamical structure factors. We also examine the variation of the relative spectral weights of one and two-particle states with bond alternation all the way up to the limit of the uniform chain ($\lambda=1$). In agreement with Schmidt and Uhrig, we find that the spectral weight is dominated by 2-triplet states even at $\lambda=1$, which implies that a description in terms of triplet-pair excitations remains a good quantitative description of the system even for the uniform chain.Comment: 26 pages, 17 figure

The κ\kappa resonance in s wave πK\pi K scatterings

A new unitarization approach incorporated with chiral symmetry is established and applied to study the $\pi K$ elastic scatterings. We demonstrate that the $\kappa$ resonance exists, if the scattering length parameter in the I=1/2, J=0 channel does not deviate much from its value predicted by chiral perturbation theory. The mass and width of the $\kappa$ resonance is found to be $M_\kappa=594\pm 79MeV$, $\Gamma_\kappa=724\pm 332MeV$, obtained by fitting the LASS data up to 1430MeV. Better determination to the pole parameters is possible if the chiral predictions on scattering lengths are taken into account.Comment: Minor corrections made on discussions and typos. 1 ref. added version to appear in Nuclear Physics

From Gapped Excitons to Gapless Triplons in One Dimension

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.Comment: 18 pages, 10 figure

The [1,2] Pad\'e Amplitudes for ππ\pi\pi Scatterings in Chiral Perturbation Theory

A detailed analysis to the [1,2] Pad\'e approximation to the $\pi\pi$ scattering 2--loop amplitudes in chiral perturbation theory is made.Comment: Discussions expanded and references are added, version to appear in Physics Letters

A study of charged kappa in J/ψ→K±Ksπ∓π0J/\psi \to K^{\pm} K_s \pi^{\mp} \pi^0

Based on $58 \times 10^6$ $J/\psi$ events collected by BESII, the decay $J/\psi \to K^{\pm} K_s \pi^{\mp} \pi^0$ is studied. In the invariant mass spectrum recoiling against the charged $K^*(892)^{\pm}$, the charged $\kappa$ particle is found as a low mass enhancement. If a Breit-Wigner function of constant width is used to parameterize the kappa, its pole locates at $(849 \pm 77 ^{+18}_{-14}) -i (256 \pm 40 ^{+46}_{-22})$ MeV/$c^2$. Also in this channel, the decay $J/\psi \to K^*(892)^+ K^*(892)^-$ is observed for the first time. Its branching ratio is $(1.00 \pm 0.19 ^{+0.11}_{-0.32}) \times 10^{-3}$.Comment: 14 pages, 4 figure

Measurements of the observed cross sections for exclusive light hadron production in e^+e^- annihilation at \sqrt{s}= 3.773 and 3.650 GeV

By analyzing the data sets of 17.3 pb$^{-1}$ taken at $\sqrt{s}=3.773$ GeV and 6.5 pb$^{-1}$ taken at $\sqrt{s}=3.650$ GeV with the BESII detector at the BEPC collider, we have measured the observed cross sections for 12 exclusive light hadron final states produced in $e^+e^-$ annihilation at the two energy points. We have also set the upper limits on the observed cross sections and the branching fractions for $\psi(3770)$ decay to these final states at 90% C.L.Comment: 8 pages, 5 figur

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 Rare Decays J/Psi --> Ds- e+ nu_e, J/Psi --> D- e+ nu_e, and J/Psi --> D0bar e+ e-

We report on a search for the decays J/Psi --> Ds- e+ nu_e + c.c., J/Psi --> D- e+ nu_e + c.c., and J/Psi --> D0bar e+ e- + c.c. in a sample of 5.8 * 10^7 J/Psi events collected with the BESII detector at the BEPC. No excess of signal above background is observed, and 90% confidence level upper limits on the branching fractions are set: B(J/Psi --> Ds- e+ nu_e + c.c.)<4.8*10^-5, B(J/Psi --> D- e+ nu_e + c.c.) D0bar e+ e- + c.c.)<1.1*10^-5Comment: 10 pages, 4 figure

Measurements of J/psi Decays into 2(pi+pi-)eta and 3(pi+pi-)eta

Based on a sample of 5.8X 10^7 J/psi events taken with the BESII detector, the branching fractions of J/psi--> 2(pi+pi-)eta and J/psi-->3(pi+pi-)eta are measured for the first time to be (2.26+-0.08+-0.27)X10^{-3} and (7.24+-0.96+-1.11)X10^{-4}, respectively.Comment: 11 pages, 6 figure