We analyze KMT-2019-BLG-1339, a microlensing event with an obvious but incompletely resolved brief anomaly feature around the peak of the light curve. Although the origin of the anomaly is identified to be a companion to the lens with a low mass ratio , the interpretation is subject to two different degeneracy types. The first type is the ambiguity in , representing the angular source radius scaled to the angular radius of the Einstein ring, , and the other is the degeneracy. The former type, `finite-source degeneracy’, causes ambiguities in both and , while the latter induces an ambiguity only in . Here denotes the separation (in units of ) in projection between the lens components. We estimate that the lens components have masses $(M_1, M_2)\sim (0.27^{+0.36}{-0.15}~M\odot, 11^{+16}{-7}~M{\rm J})\sim (0.48^{+0.40}{-0.28}~M\odot, 1.3^{+1.1}{-0.7}~M{\rm J})$ according to the two solutions subject to the finite-source degeneracy, indicating that the lens comprises an M dwarf and a companion with a mass around the planet/brown dwarf boundary or a Jovian-mass planet. It is possible to lift the finite-source degeneracy by conducting future observations utilizing a high resolution instrument because the relative lens-source proper motion predicted by the solutions are widely different.

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