  The bulk Lorentz factor of the gamma-ray burst (GRB) ejecta (Gamma_0) is a
key parameter to understand the GRB physics. Liang et al. have discovered a
correlation between Gamma_0 and isotropic gamma-ray energy:
Gamma_0\proptoE_{gamma,iso,52}^{0.25}. By including more GRBs with updated data
and more methods to derive Gamma_0, we confirm this correlation and obtain
Gamma_0~91E_{gamma,iso,52}^{0.29}. Evaluating the mean isotropic gamma-ray
luminosities L_{gamma,iso} of the GRBs in the same sample, we discover an even
tighter correlation Gamma_0~249 L_{gamma,iso,52}^{0.30}. We propose an
interpretation to this later correlation. Invoking a neutrino-cooled
hyperaccretion disk around a stellar mass black hole as the central engine of
GRBs, we derive jet luminosity powered by neutrino annihilation and baryon
loading from a neutrino-driven wind. Applying beaming correction, we finally
derive Gamma_0\proptoL_{gamma,iso}^{0.22}, which is well consistent with the
data. This suggests that the central engine of long GRBs is likely a stellar
mass black hole surrounded by a hyper-accreting disk.
