Unparticle realization through continuous mass scale invariant theories

We consider scale invariant theories of continuous mass fields and show how interactions of these fields with the standard model can reproduce unparticle interactions. There is no fixed point or dimensional transmutation involved in this approach. We generalize interactions of the standard model to multiple unparticles in this formalism and explicitly work out some examples, in particular, we show that the product of two scalar unparticles behaves as a normalized scalar unparticle with a dimension equal to the sum of the two composite unparticle dimensions. Extending the formalism to scale invariant interactions of continuous mass fields, we calculate three point functions of unparticles.