  Distinct gap features in the nearest protoplanetary disk, TW Hya (distance of
59.5$\pm$0.9 pc), may be signposts of ongoing planet formation. We performed
long-exposure thermal infrared coronagraphic imaging observations to search for
accreting planets especially within dust gaps previously detected in scattered
light and submm-wave thermal emission. Three nights of observations with the
Keck/NIRC2 vortex coronagraph in $L^\prime$ (3.4-4.1$\mu$m) did not reveal any
statistically significant point sources. We thereby set strict upper limits on
the masses of non-accreting planets. In the four most prominent disk gaps at
24, 41, 47, and 88 au, we obtain upper mass limits of 1.6-2.3, 1.1-1.6,
1.1-1.5, and 1.0-1.2 Jupiter masses ($M_J$) assuming an age range of 7-10 Myr
for TW Hya. These limits correspond to the contrast at 95\% completeness (true
positive fraction of 0.95) with a 1\% chance of a false positive within
$1^{\prime\prime}$ of the star. We also approximate an upper limit on the
product of planet mass and planetary accretion rate of
$M_p\dot{M}\lesssim10^{-8} M_J^2/yr$ implying that any putative $\sim0.1 M_J$
planet, which could be responsible for opening the 24 au gap, is presently
accreting at rates insufficient to build up a Jupiter mass within TW Hya's
pre-main sequence lifetime.
