It is fascinating to read about abstruse Unparticle Physics. But it is very uncommon for an ordinary person to even hear the name "Unparticle Physics". It was first coined and explained by Howard Georgi in 2007 in a short paper. However, it is not a self-contained subject, it involves interesting, challenging, intricate topics like Scale Invariance and Banks-Zaks Field.

A scale-invariant theory is scale conserving theory. If you know the Mandelbrot set, you know they are scale-invariant. But a more simple example would be a circle and a radius. You can zoom in to the circle and still get the same angle ($\theta$). 

That is pretty much the idea of scale invariance. It comes with another invariance called Conformal Invariance. Conformal Invariance preserves the angle in a transformation ignoring the Lorentz transformations. Scale-Invariant theories are also pretty much Conformal Invariant theory. Any high energy theory contains at least two fields, in this scenario, Standard Model and Bank-Zaks Field. The latter field is called theory with non-trivial IR fixed point. Both the fields interact with the exchange of particle $M_{\mu}$, but under the energy $M_{\mu}$ they don't interact, they can, but couplings are suppressed. 

Unparticle Physics has been structured on the $M_{\mu}$ scale. It was wise to use Bank-Zaks operators as Unparticle operators in an Effective Field Theory with below $\Lambda_{\mu}$ energy. The paper shows that it matches onto. For an $O_{BZ}$ operator with mass dimension we have $O_{\mu}$ with low dimensions. 

The propagator for unparticle physics is also quite useful. And the important note is that unparticle stuff ignores the gauge interactions from Standard Model. There are many things one can note from Unparticle Physics. One of them is its "Weirdness". It assumes particles with scale invariance that we haven't seen yet. It is impossible, right now, to test this theory. However, if we ever achieve it, it is going to be tremendous. One can ask, whether particles with conformal invariance exists or such questions.

In another paper, Georgi showed a simple interaction $e^+ e^- \rightarrow \mu^+ \mu^-$. It showed different scales of cross-sections, considering different symmetries and propagators. I will recommend you to check that paper. 

References

1. https://arxiv.org/abs/hep-ph/0703260
2. https://arxiv.org/abs/0704.2457