ON A ZONAL POLYNOMIAL INTEGRAL

A certain multiple integral occurring in the studies of Beherens-Fisher multivariate problem has been evaluated b

On Selberg’s beta integrals

Publisher's version/PDFAskey and Richards (1989) evaluate Selberg’s first and second beta integrals using Aomoto’s (1987) formidable methodology of setting and solving a first order difference equation. Using this methodology they evaluate certain other beta and gamma type integrals. However, Selberg’s first and second beta and gamma type integrals very elegantly fit within the framework of hypercomplex multivariate normal distribution theory developed by Kabe (1984), and hence can be evaluated using the known multivariate normal distribution theory integrals

Very High Energy Gamma Rays from PSR1706-44

We have obtained evidence of gamma-ray emission above 1 TeV from PSR1706-44, using a ground-based telescope of the atmospheric \v{C}erenkov imaging type located near Woomera, South Australia. This object, a $\gamma$-ray source discovered by the COS B satellite (2CG342-02), was identified with the radio pulsar through the discovery of a 102 ms pulsed signal with the EGRET instrument of the Compton Gamma Ray Observatory. The flux of the present observation above a threshold of 1 TeV is $\bf \sim$ 1 $\cdot$ 10$^{-11}$ photons cm$^{-2}$ s$^{-1}$, which is two orders of magnitude smaller than the extrapolation from GeV energies. The analysis is not restricted to a search for emission modulated with the 102 ms period, and the reported flux is for all $\gamma$-rays from PSR1706-44, pulsed and unpulsed. The energy output in the TeV region corresponds to about 10$^{-3}$ of the spin down energy loss rate of the neutron star.Comment: 13 pages, latex format (article), 2 figures include

Measurement of Direct Photon Emission in K^+ -> pi^+ pi^0 gamma Decay

We have performed a measurement of the K^+ -> pi^+ pi^0 gamma decay and have observed 2 X 10^4 events. The best fit to the decay spectrum gives a branching ratio for direct photon emission of (4.7\pm0.8\pm0.3) X 10^{-6} in the pi^+ kinetic energy region of 55 to 90 MeV and requires no component due to interference with inner bremsstrahlung.Comment: 9 pages, 3 figures. To be submitted to PR

Improved Measurement of the K+ to pi+ nu nubar Branching Ratio

An additional event near the upper kinematic limit for K+ to pi+ nu nubar has been observed by Experiment E949 at Brookhaven National Laboratory. Combining previously reported and new data, the branching ratio is B(K+ to pi+ nu nubar)= 1.47 (+1.30, - 0.89) x 10-10 based on three events observed in the pion momentum region 211<P<229 MeV/c. At the measured central value of the branching ratio, the additional event had a signal-to-background ratio of 0.9

On Planetary Companions to the MACHO-98-BLG-35 Microlens Star

We present observations of microlensing event MACHO-98-BLG-35 which reached a peak magnification factor of almost 80. These observations by the Microlensing Planet Search (MPS) and the MOA Collaborations place strong constraints on the possible planetary system of the lens star and show intriguing evidence for a low mass planet with a mass fraction $4\times 10^{-5} \leq \epsilon \leq 2\times 10^{-4}$. A giant planet with $\epsilon = 10^{-3}$ is excluded from 95% of the region between 0.4 and 2.5 $R_E$ from the lens star, where $R_E$ is the Einstein ring radius of the lens. This exclusion region is more extensive than the generic "lensing zone" which is $0.6 - 1.6 R_E$. For smaller mass planets, we can exclude 57% of the "lensing zone" for $\epsilon = 10^{-4}$ and 14% of the lensing zone for $\epsilon = 10^{-5}$. The mass fraction $\epsilon = 10^{-5}$ corresponds to an Earth mass planet for a lensing star of mass \sim 0.3 \msun. A number of similar events will provide statistically significant constraints on the prevalence of Earth mass planets. In order to put our limits in more familiar terms, we have compared our results to those expected for a Solar System clone averaging over possible lens system distances and orientations. We find that such a system is ruled out at the 90% confidence level. A copy of the Solar System with Jupiter replaced by a second Saturn mass planet can be ruled out at 70% confidence. Our low mass planetary signal (few Earth masses to Neptune mass) is significant at the $4.5\sigma$ confidence level. If this planetary interpretation is correct, the MACHO-98-BLG-35 lens system constitutes the first detection of a low mass planet orbiting an ordinary star without gas giant planets.Comment: ApJ, April 1, 2000; 27 pages including 8 color postscript figure