  Recently Sumi et al. (2011) reported evidence for a large population of
planetary-mass objects (PMOs) that are either unbound or orbit host stars in
orbits > 10 AU. Their result was deduced from the statistical distribution of
durations of gravitational microlensing events observed by the MOA
collaboration during 2006 and 2007. Here we study the feasibility of measuring
the mass of an individual PMO through microlensing by examining a particular
event, MOA-2011-BLG-274. This event was unusual as the duration was short, the
magnification high, the source-size effect large and the angular Einstein
radius small. Also, it was intensively monitored from widely separated
locations under clear skies at low air masses. Choi et al. (2012) concluded
that the lens of the event may have been a PMO but they did not attempt a
measurement of its mass. We report here a re-analysis of the event using
re-reduced data. We confirm the results of Choi et al. and attempt a
measurement of the mass and distance of the lens using the terrestrial parallax
effect. Evidence for terrestrial parallax is found at a 3 sigma level of
confidence. The best fit to the data yields the mass and distance of the lens
as 0.80 +/- 0.30 M_J and 0.80 +/- 0.25 kpc respectively. We exclude a host star
to the lens out to a separation ~ 40 AU. Drawing on our analysis of
MOA-2011-BLG-274 we propose observational strategies for future microlensing
surveys to yield sharper results on PMOs including those down to super-Earth
mass.
