Worlds Next Door: A Candidate Giant Planet Imaged in the Habitable Zone of \acenA.\\ I. Observations, Planet Orbital and Physical Properties, and Exozodi Upper Limits

We report on coronagraphic observations of the nearest solar-type star \acenA using the MIRI instrument on the \emph{James Webb} Space Telescope. The proximity of \acen (1.34 pc) means that the star's habitable zone is spatially resolved at mid-infrared wavelengths so that sufficiently large planets or quantities of exozodiacal dust would be detectable via direct imaging. With three epochs of observation (August 2024, February 2025 and April 2025) we achieve a sensitivity sufficient to detect $T_{\rm eff}\approx$ 250 K (1~$R_{\rm Jup}$) planets between 1\arcsec--2\arcsec\ and exozodiacal dust emission at the level of $>$2$\times$ the brightness of our own zodiacal cloud, for a S/N = 5 detection threshold. The lack of exozodiacal dust emission sets an unprecedented limit: a factor of $\sim$10-100 more sensitive than measured toward any other stellar system to date. In August 2024, we detected a F$_\nu$(15.5 \mum) = 3.5~mJy point source at a separation of 1.5\arcsec\ from \acenA. Because the August epoch had only one successful observation at a single roll angle, it is not possible to claim that \sone is a bona fide planet. Our analysis confirms that \sone is neither a background nor a foreground object. The failure to recover \sone in the February and April 2025 epochs implies either that \sone is an artifact (disfavored by various tests) or that \sone is real but has been carried by its orbital motion to an unfavorable location for detection. Assuming that \sone is the counterpart of the object, $C1$, seen by the VLT/NEAR program, we obtain four families of dynamically stable orbits (two prograde, two retrograde) consistent with the one detection and the two non-detections. The key median properties of these orbit families include a semi-major axis of 1.7~au or 2.2~au (corresponding to a 2.1~yr and 3~yr period, respectively), eccentricity of $\approx$0.4, and a mutual inclination of 48$^\circ$ (prograde) or 130$^\circ$ (retrograde) with respect to the \acenAB binary orbital plane (typical uncertainty of $\pm10^\circ$). A 225~K and $\approx$1.1~\rj\ planet with a mass between 90--150~\mearth (consistent with radial velocity limits) fits the $S1+C1$ photometry. Alternatively, the $S1+C1$ photometry is consistent with a Saturn radius ($\approx$0.85~\rj) planet surrounded by a Saturn-like ring system, which would be responsible for the majority of the MIRI F1550C emission. This paper is first in a series of two papers: Paper II (Sanghi \& Beichman et al. 2025, submitted) discusses the data reduction strategy and the robustness of \sone as a planet candidate, as opposed to an image artifact, in post-processing.