  We augment standard branching Brownian motion by adding a competitive
interaction between nearby particles. Informally, when particles are in
competition, the local resources are insufficient to cover the energetic cost
of motion, so the particles' masses decay. In standard BBM, we may define the
front displacement at time $t$ as the greatest distance of a particle from the
origin. For the model with masses, it makes sense to instead define the front
displacement as the distance at which the local mass density drops from
$\Theta(1)$ to $o(1)$. We show that one can find arbitrarily large times $t$
for which this occurs at a distance $\Theta(t^{1/3})$ behind the front
displacement for standard BBM.
