In this thesis, the measurement of double-spin asymmetry for
electron production from heavy flavor decays was performed in a
Relativistic Heavy Ion Collider (RHIC) in the PHENIX experiment at
Brookhaven National Laboratory to measure the polarized parton
distribution function of gluon in the small Bjorken x region
(x~0.01). For this experiment, for the first time a Hadron Blind
Detector (HBD), which is a position-sensitive gas Cherenkov counter
with Gas Electron Multiplier whose surface is evaporated by CsI,
was employed. This HBD contributes to reducing the background from
electron pairs produced by real and virtual photon conversion.
Furthermore, the author develops a new analysis method for the
background reduction, and the signal-to-background ratio is
improved by a factor of roughly 2.0. Using the combination of the
HBD and a new analysis method, the double-spin asymmetry of the
electron production with transverse momentum ranging 0.5 < pT
< 3.0 GeV/c is measured and confirmed to be zero-consistent
within the limit of the statistical uncertainty of about 1%. This
result identifies the constraint of the gluon polarization in the
small Bjorken x region, a worldwide first.
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