  Gaps in circumstellar disks can signal the existence of planetary perturbers,
making such systems preferred targets for direct imaging observations of
exoplanets. Being one of the brightest and closest stars to the Sun, the
photometric standard star Vega hosts a two-belt debris disk structure. Together
with the fact that its planetary system is being viewed nearly face-on, Vega
has been one of the prime targets for planet imaging efforts. Using the vector
vortex coronagraph on Keck/NIRC2 in Ms-band at 4.67 $\mu$m, we report the
planet detection limits from 1 au to 22 au for Vega with an on-target time of
1.8 h. We reach a 3 Jupiter mass limit exterior to 12 au, which is nearly an
order of magnitude deeper than existing studies. Combining with existing radial
velocity studies, we can confidently rule out the existence of companions more
than ~8 Jupiter mass from 22 au down to 0.1 au for Vega. Interior and exterior
to ~4 au, this combined approach reaches planet detection limits down to ~2-3
Jupiter mass using radial velocity and direct imaging, respectively. By
reaching multi-Jupiter mass detection limits, our results are expected to be
complemented by the planet imaging of Vega in the upcoming observations using
the James Webb Space Telescope to obtain a more holistic understanding of the
planetary system configuration around Vega.
