Exploring the presence of a fifth force at the Galactic Center

Aims: The presence of a Yukawa-like correction to Newtonian gravity is investigated at the Galactic Center, leading to a new upper limit for the intensity of such a correction. Methods: We perform a Markov Chain Monte Carlo analysis using the astrometric and spectroscopic data of star S$2$ collected at the Very Large Telescope by GRAVITY, NACO and SINFONI instruments, covering the period from $1992$ to $2022$. Results: The precision of the GRAVITY instrument allows us to derive the most stringent upper limit at the Galactic Center for the intensity of the Yukawa contribution ($\propto \alpha e^{-\lambda r}$) to be $\mathrm{\mid }\alpha \mathrm{\mid }<0.003$ for a scale length $\lambda =3\cdot {10}^{13}\mathrm{m}(\sim 200\mathrm{A}\mathrm{U})$. This improves by roughly one order of magnitude all estimates obtained in previous works.