  In unparticle physics, operators of the conformal sector have
self-interactions, and these are unsuppressed for strong coupling. The 3-point
interactions are completely determined by conformal symmetry, up to a constant.
We do not know of any theoretical upper bounds on this constant. Imposing
current experimental constraints, we find that these interactions mediate
spectacular collider signals, such as $pp -> U -> UU -> \gamma \gamma \gamma
\gamma$, $\gamma \gamma ZZ$, $ZZZZ$, $\gamma \gamma l^+ l^-$, $ZZ l^+ l^-$, and
$4l$, with cross sections of picobarns or larger at the Large Hadron Collider.
Self-interactions may therefore provide the leading discovery prospects for
unparticle physics.
