  The STAR collaboration reports the first measurements of the transverse
momentum asymmetry $A_J$ of di-jet pairs in central gold-gold collisions and
minimum bias proton-proton collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC. We
focus on anti-$k_T$ di-jets with a leading jet $p_T>20$ GeV/$c$ and a
subleading jet $p_T>10$ GeV/$c$, with a constituent cut of 2 GeV/$c$, which
reduces the effect of the underlying heavy-ion background. We examine the
evolution of $A_J$ while reclustering these same di-jets with a lower
constituent cut of 200 MeV/$c$.
  For the low $p_T$ constituent cut with a resolution parameter of $R=0.4$, the
balance between the di-jets is restored to the level of p+p collisions which
indicates the lost energy observed for di-jets with a constituent cut of
  $p_T ^{\text{Cut}}>2$ GeV/$c$ is recovered. Further variations of $R$ and the
constituent \pT-cutoff indicate that the lost energy is redistributed in the
form of soft particles, accompanied by a broadening of the jet structure.
