We present the analysis of four candidate short duration binary microlensing events from the 2006-2007 MOA Project short event analysis. These events were discovered as a byproduct of an analysis designed to find short timescale single lens events that may be due to free-floating planets. Three of these events are determined to be microlensing events, while the fourth is most likely caused by stellar variability. For each of the three microlensing events, the signal is almost entirely due to a brief caustic feature with little or no lensing attributable mainly to the lens primary. One of these events, MOA-bin-1, is due to a planet, and it is the first example of a planetary event in which stellar host is only detected through binary microlensing effects. The mass ratio and separation are q = 4.9 +- 1.4 x 10^{-3} and s = 2.10 +- 0.05, respectively. A Bayesian analysis based on a standard Galactic model indicates that the planet, MOA-bin-1Lb, has a mass of m_p = 3.7 +- 2.1 M_{Jup}, and orbits a star of M_* = 0.75{+0.33 -0.41} M_solar at a semi-major axis of a = 8.3 {+4.5 -2.7} AU. This is one of the most massive and widest separation planets found by microlensing. The scarcity of such wide separation planets also has implications for interpretation of the isolated planetary mass objects found by this analysis. If we assume that we have been able to detect wide separation planets with a efficiency at least as high as that for isolated planets, then we can set limits on the distribution on planets in wide orbits. In particular, if the entire isolated planet sample found by Sumi et al. (2011) consists of planets bound in wide orbits around stars, we find that it is likely that the median orbital semi-major axis is > 30 AU.
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