New Solutions for Scalar-Isoscalar pi-pi Phase Shifts

The scalar-isoscalar pi-pi phase shifts are calculated in the pi-pi energy range from 600 MeV to 1600 MeV. We use results of the CERN-Cracow-Munich collaboration for the reaction pi^- p --> pi^+ pi^- n on a transversely polarized target at 17.2 GeV/c pi^- momentum. Energy-independent separation of the S-wave pseudoscalar amplitude (pi exchange) from the pseudovector amplitude (a_1 exchange) is carried out. Below the KK threshold we find two solutions for the pi-pi phase shifts, for which the phases increase slower with the effective pi-pi mass than the P-wave phases ("flat" solutions) and two solutions for which the phases increase faster than the P-wave phases ("steep" solutions). Above 1420 MeV both sets of phase shifts increase with energy faster than in the experiment on an unpolarized target. This fact can be related to a presence of the scalar resonance f_0(1500).Comment: 5 pages, 2 figures. Talk given at 7th International Conference on Hadron Spectroscopy (Hadron 97), Upton, NY, 25-30 Aug 199

Non-Gaussianity analysis of GW background made by short-duration burst signals

We study an observational method to analyze non-Gaussianity of a gravitational wave (GW) background made by superposition of weak burst signals. The proposed method is based on fourth-order correlations of data from four detectors, and might be useful to discriminate the origin of a GW background. With a formulation newly developed to discuss geometrical aspects of the correlations, it is found that the method provides us with linear combinations of two interesting parameters, I_2 and V_2 defined by the Stokes parameters of individual GW burst signals. We also evaluate sensitivities of specific detector networks to these parameters.Comment: 18 pages, to appear in PR

Prospects for direct detection of circular polarization of gravitational-wave background

We discussed prospects for directly detecting circular polarization signal of gravitational wave background. We found it is generally difficult to probe the monopole mode of the signal due to broad directivity of gravitational wave detectors. But the dipole (l=1) and octupole (l=3) modes of the signal can be measured in a simple manner by combining outputs of two unaligned detectors, and we can dig them deeply under confusion and detector noises. Around f~0.1mHz LISA will provide ideal data streams to detect these anisotropic components whose magnitudes are as small as ~1 percent of the detector noise level in terms of the non-dimensional energy density \Omega_{GW}(f).Comment: 5 pages, 1 figure, PRL in pres

Locally continuously perfect groups of homeomorphisms

The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case of equivariant homeomorphism group and other examples are also considered.Comment: 14 page

Separation of S- wave pseudoscalar and pseudovector amplitudes in pi^- p---> pi^+ pi^- n reaction on polarized target

A new analysis of S-wave production amplitudes for the reaction $\pi^- p_{\uparrow} \rightarrow \pi^+ \pi^- n$ on a transversely polarized target is performed. It is based on the results obtained by the CERN-Cracow -Munich collaboration in the pion-pion energy range from 600 MeV to 1600 MeV at 17.2 GeV/c $\pi^-$ momentum. Energy-independent separation of the S-wave pseudoscalar amplitude ($\pi$ exchange) from the pseudovector amplitude ($a_{1}$ exchange) is carried out using assumptions much weaker than those in all previous analyses. We show that, especially around 1000 MeV and around 1500 MeV, the $a_{1}$ exchange amplitude cannot be neglected. The scalar-isoscalar $\pi\pi$ phase shifts are calculated using fairly weak assumptions. Below the $K\overline{K}$ threshold we find two solutions for the $\pi-\pi$ phase shifts, for which the phases increase slower with the effective $\pi-\pi$ mass than the P-wave phases. Both solutions are consistent with a broad $f_{0}(500)$ but only one is similar to the well-known "down" solution. We find also the third solution (with a somewhat puzzling behavior of inelasticity) which exhibits a narrow $f_{0}(750)$ claimed by Svec. All the solutions undergo a rapid change at the $K\overline{K}$ threshold. Above 1420 MeV the phase shifts increase with energy faster than those obtained without the polarized-target data. This phase behavior as well as an increase of the modulus of the $a_{1}$-exchange amplitude can be due to the presence of the $f_{0}(1500)$.Comment: 25 Latex pages + 15 Postscript figure