Parameter estimation from the transit light curve including gravitational lensing effects

We study transit light curves of exoplanets, incorporating gravitational lensing effects, and explore the possibility of estimating planetary masses using only the transit light curve. We analyze existing data for planets with relatively large orbital distances ($>1$ AU) from Kepler and TESS to evaluate how well their masses can be constrained. For six exoplanets, we derive 2$\sigma$ upper limits of 200-2000 Jupiter masses. We also construct mock data to assess the feasibility of determining masses for exoplanets with larger orbital radii than currently known. Our results show that a precision of $3\times 10^{-6}$ is required to recover the true masses of planets with 10 (5) Jupiter masses at orbital radii of $a=20$ (100) AU. Furthermore, we demonstrate that neglecting gravitational effects can lead to underestimation of exoplanet radii, particularly for planets with large orbital separations. Using mock data with a precision of $2\times 10^{-4}$, assuming a 30 minutes cadence with Kepler for a $K_p=14$ mag star, we find that the estimated radii can be underestimated by 1-20% for 5 and 10 Jupiter-mass planets with $a=$ 10-100 AU. These results highlight the importance of including microlensing effects when modeling transit light curves of wide-orbit planets.