Long-period giant planets are key to tracing the dynamical evolution and architecture of planetary systems. Their presence in systems with short-period planets offers clues about the origin and migration history of these systems.

Since the early 2000s, we have been conducting a long-term radial velocity monitoring of several tens of Hot Jupiter systems using the CORALIE spectrograph on the 1.2m Euler telescope. We present this unique dataset, spanning over two decades, which reveals several outer companions and long-term RV trends, providing statistical and dynamical constraints on the role of cold giant planets in shaping the orbital evolution of Hot Jupiters.

In parallel, since 2021, we have extended this effort to planets located in the hot Neptunian desert—a region likely sculpted by photoevaporation, tidal effects, or dynamical interactions. Among the systems currently followed, several already show signs of long-period perturbers.

These programs, when combined with the upcoming Gaia DR4 release, will provide a powerful synergy to constrain the period, true mass, and orbital inclination of these outer companions shaping planetary architectures.