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We analyze KMT-2019-BLG-1339, a microlensing event with an obvious butincompletely 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 lenswith a low mass ratio $q$, the interpretation is subject to two differentdegeneracy types. The first type is the ambiguity in $\rho$, representing theangular source radius scaled to the angular radius of the Einstein ring,$\theta_{\rm E}$, and the other is the $s\leftrightarrow s^{-1}$ degeneracy.The former type, `finite-source degeneracy', causes ambiguities in both $s$ and$q$, while the latter induces an ambiguity only in $s$. Here $s$ denotes theseparation (in units of $\theta_{\rm E}$) in projection between the lenscomponents. We estimate that the lens components have masses $(M_1, M_2)\sim(0.27^{+0.36}_{-0.15}~M_\odot, 11^{+16}_{-7}~M_{\rm J})$ and $\sim(0.48^{+0.40}_{-0.28}~M_\odot, 1.3^{+1.1}_{-0.7}~M_{\rm J})$ according to thetwo solutions subject to the finite-source degeneracy, indicating that the lenscomprises an M dwarf and a companion with a mass around the planet/brown dwarfboundary or a Jovian-mass planet. It is possible to lift the finite-sourcedegeneracy by conducting future observations utilizing a high resolutioninstrument because the relative lens-source proper motion predicted by thesolutions are widely different.

KMT-2019-BLG-1339L: an M Dwarf with a Giant Planet or a Companion Near the Planet/Brown Dwarf Boundary