Possible existence of Ep-Lp and Ep-Eiso correlations for Short Gamma-Ray
  Bursts with a factor 5 to 100 dimmer than those for Long Gamma-Ray Bursts
  We analyzed correlations among the rest frame spectral peak energy $E_{\rm
p}$, the observed frame 64ms peak isotropic luminosity $L_{\rm p}$ and the
isotropic energy $E_{\rm iso}$ for 13 Short Gamma Ray Burst (SGRB) candidates
having the measured redshift $z$, $T_{\rm 90}^{\rm obs}/(1+z)<2$ sec and well
determined spectral parameters. A SGRB candidate is regarded as a misguided
SGRB if it is located in the 3-$\sigma_{\rm int}$ dispersion region from the
best-fit function of the $E_{\rm p}$--$E_{\rm iso}$ correlation for Long GRBs
(LGRBs) while the others are regarded as secure SGRBs possibly from compact
star mergers. Using 8 secure SGRBs out of 13 SGRB candidates, we tested whether
$E_{\rm p}$--$E_{\rm iso}$ and $E_{\rm p}$--$L_{\rm p}$ correlations exist for
SGRBs. We found that $E_{\rm p}$--$E_{\rm iso}$ correlation for SGRBs($E_{\rm
iso} =10^{51.42 \pm 0.15}{\rm erg s^{-1}} ({E_{\rm p}}/{\rm 774.5 keV})^{1.58
\pm 0.28}$) seems to exist with the correlation coefficeint $r=0.91$ and chance
probability $p=1.5\times10^{-3}$. We found also that the $E_{\rm p}$--$L_{\rm
p}$ correlation for SGRBs($L_{\rm p} = 10^{52.29 \pm 0.066}{\rm erg s^{-1}}
({E_{\rm p}}/{\rm 774.5 keV})^{1.59 \pm 0.11}$) is tighter than $E_{\rm
p}$--$E_{\rm iso}$ correlation since $r=0.98$ and $p=1.5\times10^{-5}$. Both
correlations for SGRBs are dimmer than those of LGRBs for the same $E_{\rm p}$
by factors $\sim$100 ($E_{\rm p}$--$E_{\rm iso}$) and $\sim$ 5($E_{\rm
p}$--$L_{\rm p}$). Applying the tighter $E_{\rm p}$--$L_{\rm p}$ correlation
for SGRBs to 71 bright BATSE SGRBs, we found that pseudo redshift $z$ ranges
from 0.097 to 2.258 with the mean $<z>$ of 1.05. The redshifts of SGRBs
apparently cluster at lower redshift than those of LGRBs ($<z>\sim 2.2 $),
which supports the merger scenario of SGRBs.
