  The existence of the $X(3872)$ resonance extremely close to the $D^{*0}
\bar{D}^0$ threshold implies that neutral charm mesons have an approximate
nonrelativistic conformal symmetry. Systems consisting of these mesons with
small kinetic energies produced in a short-distance reaction are unparticles in
the sense that they can be created by operators with definite scaling
dimensions in a nonrelativistic conformal field theory. There is a scaling
region in which their energy distribution has power-law behavior with an
exponent determined by the scaling dimension of the operator. The unparticle
associated with two neutral charm mesons produces a peak in the recoil momentum
spectrum of $K^\pm$ in inclusive decays of $B^\pm$ that has been observed. The
scaling dimensions of the unparticles associated with three neutral charm
mesons are calculated. They can be determined experimentally by measuring the
invariant mass distributions for $XD^0$ or $X D^{*0}$ in inclusive prompt
production at the Large Hadron Collider.
