  We investigate the effect of unparticle self-interactions at the Large Hadron
Collider (LHC). Especially, we discuss the three-point correlation function,
which is determined by conformal symmetry up to a constant, and study its
relation to processes with four-particle final states. These processes could be
used as a favorable way to look for unparticle physics, and for weak enough
couplings to the Standard Model, even the only way. We find updated upper
bounds on the cross sections for unparticle-mediated 4 gamma final states at
the LHC and novel upper bounds for the corresponding 2 gamma 2l and 4l final
states. The size of the allowed cross sections obtained are comparably large
for large values of the scaling dimension of the unparticle sector, but they
decrease with decreasing values of this parameter. In addition, we present
relevant distributions for the different final states, enabling the possible
identification of the unparticle scaling dimension if there was to be a large
number of events of such final states at the LHC.
