  We investigate whether the hard X-ray photon index (${\Gamma}$) versus
accretion rate correlation for super-Eddington accreting quasars is different
from that for sub-Eddington accreting quasars. We construct a sample of 113
bright quasars from the Sloan Digital Sky Survey Data Release 14 quasar
catalog, including 38 quasars as the super-Eddington subsample and 75 quasars
as the sub-Eddington subsample. We derive black-hole masses using a
simple-epoch virial mass formula based on the ${\rm H\beta}$ lines, and we use
the standard thin disk model to derive the dimensionless accretion rates
($\dot{\mathscr{M}}$) for our sample. The X-ray data for these quasars are
collected from the Chandra and XMM-Newton archives. We fit the hard X-ray
spectra using a single power-law model to obtain ${\Gamma}$ values. We find a
statistically significant ($R_{\rm S}=0.43$, $p=7.75\times{10}^{-3}$)
correlation between ${\Gamma}$ and $\dot{\mathscr{M}}$ for the super-Eddington
subsample. The ${\Gamma}$-$\dot{\mathscr{M}}$ correlation for the sub-Eddington
subsample is also significant, but weaker ($R_{\rm S}=0.30$,
$p=9.98\times{10}^{-3}$). Linear regression analysis shows that ${\rm
\Gamma}=(0.34\pm0.11){\rm log}{\dot{\mathscr{M}}}+(1.71\pm0.17)$ and ${\rm
\Gamma}=(0.09\pm0.04){\rm log}{\dot{\mathscr{M}}}+(1.93\pm0.04)$ for the super-
and sub-Eddington subsamples, respectively. The ${\Gamma}$-$\dot{\mathscr{M}}$
correlations of the two subsamples are different, suggesting different
disk-corona connections in these two types of systems. We propose one
qualitative explanation of the steeper ${\Gamma}$-$\dot{\mathscr{M}}$
correlation in the super-Eddington regime that involves larger seed photon
fluxes received by the compact coronae from the thick disks in super-Eddington
accreting quasars.
