We investigate the degeneracy in the pattern of central microlensing perturbations of a pair of planetary systems where the planets are located from the primary with projected separations in units of the Einstein radius s and s-1, respectively. From this, we confirm the fact that although alike, the patterns of central perturbations induced by a close (s < 1) planet and a wide (s > 1) planet are not identical and the degree of difference depends on the planet/primary mass ratio and the planet-primary separation. We find that the difference can be greater than 5% for planetary systems with lensing parameters located in the parameter space of (1/1.8 < lsl < 1.8, q > 5 x 10-3), (1/1.3 < lsl < 1/3, q > 1 x 10-3), and (1/1.2 < lsl < 1.2, q > 5 x 10-4), where q represents the planet/primary mass ratio. Although this range occupies a small fraction of the entire parameter space of planetary systems, we predict that the chance of resolving the close/wide degeneracy would not be meager considering that the planet detection efficiency is higher for planets with resonant separations (s ~ 1) and heavier masses. We also find that the differences between the perturbation patterns are basically caused by the effect of the planetary caustic. This explains the tendency of the perturbation difference where (1) the difference increases as the planet/primary mass ratio increases and the separation approaches the Einstein radius, (2) the region of major difference is confined within the region around the line connecting the central and the planetary caustics, and (3) a wide (close) planetary system has a more extended central perturbation region toward the (opposite) direction of the planet.

We propose a diagnostic that can resolve the planet/binary degeneracy of central perturbations in caustic-crossing high-magnification microlensing events. The diagnostic is based on the difference in the morphology of perturbation inside the central caustics induced by a planet and a wide-separation binary companion. We find that the contours of excess exhibit a concentric circular pattern around the caustic center for the binary-lensing case, while the contours are elongated or off-centered for the planetary case. This difference results in the distinctive features of the individual lens populations in the residual of the trough region between the two peaks of the caustic crossings, where the shape of the residual is symmetric for binary lensing while it tends to be asymmetric for planetary lensing. We determine the ranges of the planetary parameters for which the proposed diagnostic can be used. The diagnostic is complementary to previously proposed diagnostics in the sense that it is applicable to caustic-crossing events with small finite-source effect.