25,687 research outputs found
Effects of Luminosity Functions Induced by Relativistic Beaming on Statistics of Cosmological Gamma-Ray Bursts
We study the effects of the beaming-induced luminosity function on statistics
of observed GRBs, assuming the cosmological scenario. We select and divide the
BATSE 4B data into 588 long bursts (T sec) and 149 short bursts
(T sec), and compare the statistics calculated in each subgroup. The
of the long bursts is $ 0.2901\pm 0.0113$, and that of the
short bursts is $0.4178\pm 0.0239$, which is a Euclidean value. For luminosity
function models, we consider a cylindrical-beam and a conic-beam. We take into
account the spatial distribution of GRB sources as well. A broad luminosity
function is naturally produced when one introduces beaming of GRBs. We
calculate the maximum detectable redshift of GRBs, $z_{\rm max}$. The estimated
$z_{\rm max}$ for the cylindrical-beam case is as high as $\sim 14$ for the
long bursts and $\sim 3$ for the short bursts. The large $z_{\rm max}$ value
for the short bursts is rather surprising in that the for
this subgroup is close to the so-called Euclidean value, 0.5. We calculate the
fraction of bursts whose redshifts are larger than a certain redshift ,
i.e. . When we take and apply the luminosity function
derived for the cylindrical-beam, the expected is
for long bursts. When we increase the opening angle of the conic beam to
, decreases to at . We conclude that the beaming-induced luminosity functions are
compatible with the redshift distribution of observed GRBs and that the
apparent Euclidean value of may not be due to the Euclidean
space distribution but to the luminosity distribution.Comment: Accepted for publication in the Astronomical Journal (vol. 548, Feb.
20 2001
Form Factors for Exclusive Semileptonic --Decays
We developed the new parton model approach for exclusive semileptonic decays
of -meson to by extending the inclusive parton model, and by
combining with the results of the HQET, motivated by Drell-Yan process. Without
the nearest pole dominance ans\"atze, we {\bf derived} the dependences of
hadronic form factors on . We also calculated numerically the slope of the
Isgur-Wise function, which is consistent with the experimental results.Comment: 20 pages, RevTex, 2 ps figure files(uuencoded in seperate file
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