TOI-1728b: The Habitable-zone Planet Finder confirms a warm super Neptune orbiting an M dwarf host.

We confirm the planetary nature of TOI-1728b using a combination of ground-based photometry, near-infrared Doppler velocimetry and spectroscopy with the Habitable-zone Planet Finder.TOI-1728 is an old, inactive M0 star with \teff{} $= 3980^{+31}_{-32}$ K, which hosts a transiting super Neptune at an orbital period of $\sim$ 3.49 days. Joint fitting of the radial velocities and TESS and ground-based transits yields a planetary radius of $5.05_{-0.17}^{+0.16}$ R$_{\oplus}$, mass $26.78_{-5.13}^{+5.43}$ M$_{\oplus}$ and eccentricity $0.057_{-0.039}^{+0.054}$. We estimate the stellar properties, and perform a search for He 10830 \AA absorption during the transit of this planet and claim a null detection with an upper limit of 1.1$\%$ with 90\% confidence. A deeper level of He 10830 \AA ~ absorption has been detected in the planet atmosphere of GJ 3470b, a comparable gaseous planet. TOI-1728b is the largest super Neptune -- the intermediate subclass of planets between Neptune and the more massive gas-giant planets -- discovered around an M dwarf. With its relatively large mass and radius, TOI-1728 represents a valuable datapoint in the M-dwarf exoplanet mass-radius diagram, bridging the gap between the lighter Neptune-sized planets and the heavier Jovian planets known to orbit M-dwarfs. With a low bulk density of $1.14_{-0.24}^{+0.26}$ g/cm$^3$, and orbiting a bright host star (J $\sim 9.6$, V $\sim 12.4$), TOI-1728b is also a promising candidate for transmission spectroscopy both from the ground and from space, which can be used to constrain planet formation and evolutionary models.