Interpretation of neutral charm mesons near threshold as unparticles

Abstract

The existence of the $X(3872)$ resonance extremely close to the $D^{\ast 0}{\bar{D}}^0$ 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 $X{D}^0$ or $X{D}^{\ast 0}$ in inclusive prompt production at the Large Hadron Collider.

5 pages, 4 figures, title changed, final version

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• Short-distance production of three particles with large scattering length
• Model-independent mass determination of near-threshold states from short-range production
• A First-Quantized Model For Unparticles and Gauge Theories Around Conformal Window