The mass distribution in an assembling super galaxy group at $z=0.37$
  We present a weak gravitational lensing analysis of supergroup SG1120$-$1202,
consisting of four distinct X-ray-luminous groups, that will merge to form a
cluster comparable in mass to Coma at $z=0$. These groups lie within a
projected separation of 1 to 4 Mpc and within $\Delta v=550$ km s$^{-1}$ and
form a unique protocluster to study the matter distribution in a coalescing
system.
  Using high-resolution {\em HST}/ACS imaging, combined with an extensive
spectroscopic and imaging data set, we study the weak gravitational distortion
of background galaxy images by the matter distribution in the supergroup. We
compare the reconstructed projected density field with the distribution of
galaxies and hot X-ray emitting gas in the system and derive halo parameters
for the individual density peaks.
  We show that the projected mass distribution closely follows the locations of
the X-ray peaks and associated brightest group galaxies. One of the groups that
lies at slightly lower redshift ($z\approx 0.35$) than the other three groups
($z\approx 0.37$) is X-ray luminous, but is barely detected in the
gravitational lensing signal. The other three groups show a significant
detection (up to $5 \sigma$ in mass), with velocity dispersions between
$355^{+55}_{-70}$ and $530^{+45}_{-55}$ km s$^{-1}$ and masses between
$0.8^{+0.4}_{-0.3} \times 10^{14}$ and $1.6^{+0.5}_{-0.4}\times 10^{14} h^{-1}
M_{\odot}$, consistent with independent measurements. These groups are
associated with peaks in the galaxy and gas density in a relatively
straightforward manner. Since the groups show no visible signs of interaction,
this supports the picture that we are catching the groups before they merge
into a cluster.
