Constraints on Planetary Companions in the Magnification A=256 Microlensing Event: OGLE-2003-BLG-423

We develop a new method of modeling microlensing events based on a Monte Carlo simulation that incorporates both a Galactic model and the constraints imposed by the observed characteristics of the event. The method provides an unbiased way to analyze the event especially when parameters are poorly constrained by the observed lightcurve. We apply this method to search for planetary companions of the lens in OGLE-2003-BLG-423, whose maximum magnification A_max=256+-43 (or A_max=400+-115 from the lightcurve data alone) is the highest among single-lens events ever recorded. The method permits us, for the first time, to place constraints directly in the planet-mass/projected-physical-separation plane rather than in the mass-ratio/Einstein-radius plane as was done previously. For example, Jupiter-mass companions of main-sequence stars at 2.5 AU are excluded with 80% efficiency.