Point Production of a Nonrelativistic Unparticle Recoiling Against a Particle

TL;DR

This paper explores the production rate of nonrelativistic unparticles in a conformal field theory, deriving how their decay and recoil processes depend on energy and symmetry breaking conditions.

Contribution

It provides an exact calculation of unparticle production rates using nonrelativistic conformal field theory, including effects of conformal symmetry breaking by large scattering length.

Findings

Point production rate follows a power-law dependence on energy.

Derived the energy exponent for unparticle decay into recoiling unparticle and particle.

Analyzed the impact of conformal symmetry breaking on two-particle bound states.

Abstract

A nonrelativistic unparticle can be defined as an excitation created by an operator with a definite scaling dimension in a nonrelativistic field theory with an approximate conformal symmetry. The point production rate of an unparticle has power-law dependence on its total energy with an exponent determined by its scaling dimension. We use the exact result for the 3-point function of primary operators in a nonrelativistic conformal field theory to derive the contribution to the point production rate of the unparticle from its decay into another unparticle recoiling against a particle. In the case where the conformal symmetry is broken by a large positive scattering length, we deduce the exponent of the energy in the point production rate of the loosely bound two-particle state recoiling against a particle with large relative momentum.