Interpretation of neutral charm mesons near threshold as unparticles

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.