Here we report the localizations and properties of four short-duration GRBs localized by the High Energy Transient Explorer 2 satellite (HETE-2): GRBs 010326B, 040802, 051211 and 060121, all of which were detected by the French Gamma Telescope (Fregate) and localized with the Wide-field X-ray Monitor (WXM) and/or Soft X-ray Camera (SXC) instruments. We discuss eight possible criteria for determining whether these GRBs are short population bursts (SPBs) or long population bursts (LPBs). These criteria are (1) duration, (2) pulse widths, (3) spectral hardness, (4) spectral lag, (5) energy Egamma radiated in gamma rays (or equivalently, the kinetic energy E_KE of the GRB jet), (6) existence of a long, soft bump following the burst, (7) location of the burst in the host galaxy, and (8) type of host galaxy. In particular, we have developed a likelihood method for determining the probability that a burst is an SPB or a LPB on the basis of its T90 duration alone. A striking feature of the resulting probability distribution is that the T90 duration at which a burst has an equal probability of being a SPB or a LPB is T90 = 5 s, not T90 = 2 s, as is often used. All four short-duration bursts discussed in detail in this paper have T90 durations in the Fregate 30-400 keV energy band of 1.90, 2.31, 4.25, and 1.97 sec, respectively, yielding probabilities P(S|T90) = 0.97, 0.91, 0.60, and 0.95 that these bursts are SPBs on the basis of their T90 durations alone. All four bursts also have spectral lags consistent with zero. These results provide strong evidence that all four GRBs are SPBs (abstract continues).
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