Unparticle Self-Interactions and Their Collider Implications
  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. 
Jonathan L. Feng, Arvind Rajaraman and Huitzu Tu