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High-magnification microlensing events provide an important channel to detectplanets. Perturbations near the peak of a high-magnification event can beproduced either by a planet or a binary companion. It is known that centralperturbations induced by both types of companions can be generallydistinguished due to the basically different magnification pattern aroundcaustics. In this paper, we present a case of central perturbations for whichit is difficult to distinguish the planetary and binary interpretations. Thepeak of a lensing light curve affected by this perturbation appears to be bluntand flat. For a planetary case, this perturbation occurs when the sourcetrajectory passes the negative perturbation region behind the back end of anarrowhead-shaped central caustic. For a binary case, a similar perturbationoccurs for a source trajectory passing through the negative perturbation regionbetween two cusps of an astroid-shaped caustic. We demonstrate the degeneracyfor 2 high-magnification events of OGLE-2011-BLG-0526 andOGLE-2011-BLG-0950/MOA-2011-BLG-336. For OGLE-2011-BLG-0526, the $\chi^2$difference between the planetary and binary model is $\sim$ 3, implying thatthe degeneracy is very severe. For OGLE-2011-BLG-0950/MOA-2011-BLG-336, thestellar binary model is formally excluded with $\Delta \chi^2 \sim$ 105 and theplanetary model is preferred. However, it is difficult to claim a planetdiscovery because systematic residuals of data from the planetary model arelarger than the difference between the planetary and binary models. Consideringthat 2 events observed during a single season suffer from such a degeneracy, itis expected that central perturbations experiencing this type of degeneracy iscommon.

A New Type of Ambiguity in the Planet and Binary Interpretations of Central Perturbations of High-Magnification Gravitational Microlensing Events