  We report the discovery of TOI-4127 b, a transiting, Jupiter-sized exoplanet
on a long-period ($P = 56.39879^{+0.00010}_{-0.00010}$ d), high-eccentricity
orbit around a late F-type dwarf star. This warm Jupiter was first detected and
identified as a promising candidate from a search for single-transit signals in
TESS Sector 20 data, and later characterized as a planet following two
subsequent transits (TESS Sectors 26 and 53) and follow-up ground-based RV
observations with the NEID and SOPHIE spectrographs. We jointly fit the transit
and RV data to constrain the physical ($R_p = 1.096^{+0.039}_{-0.032} R_J$,
$M_p = 2.30^{+0.11}_{-0.11} M_J$) and orbital parameters of the exoplanet.
Given its high orbital eccentricity ($e=0.7471^{+0.0078}_{-0.0086}$), TOI-4127
b is a compelling candidate for studies of warm Jupiter populations and of hot
Jupiter formation pathways. We show that the present periastron separation of
TOI-4127 b is too large for high-eccentricity tidal migration to circularize
its orbit, and that TOI-4127 b is unlikely to be a hot Jupiter progenitor
unless it is undergoing angular momentum exchange with an undetected outer
companion. Although we find no evidence for an external companion, the
available observational data are insufficient to rule out the presence of a
perturber that can excite eccentricity oscillations and facilitate tidal
migration.
