Distant trans-Neptunian object candidates from NASA's TESS mission scrutinised: fainter than predicted or false positives?

NASA's Transiting Exoplanet Survey Satellite (TESS) is performing a homogeneous survey of the sky from space in search of transiting exoplanets. The collected data are also being used for detecting passing Solar system objects, including 17 new outer Solar system body candidates located at geocentric distances in the range 80-200 au, that need follow-up observations with ground-based telescope resources for confirmation. Here, we present results of a proof-of-concept mini-survey aimed at recovering two of these candidates that was carried out with the 4.2 m William Herschel Telescope and a QHY600L CMOS camera mounted at its prime focus. For each candidate attempted, we surveyed a patch of sky of over one square degree around its expected coordinates in Sloan r'. The same location was revisited in five consecutive or nearly consecutive nights, reaching S/N > 4 at r' < 23 mag. We focused on the areas of sky around the circumpolar TESS candidates located at equatorial coordinates (07:00:15, +86:55:19), 202.8 au from Earth, and (06:39:47, +83:43:54) at 162.1 au, but we could not recover either of them at r' < 23 mag. Based on the detailed analysis of the acquired images, we confirm that either both candidates are much fainter than predicted or that they are false positives.