In this short paper, I sum up the ideas of unparticle field theory (UFT). UFT is a scale-invariant theory. Georgi proposed it in 2007. Some slides (of earlier times) by him are available here on the subject. Despite being a wonderful field theory, it lacks experimental evidence. However, indirect shreds of evidence are possible through the following channels

.

There are more channels other than these. (For technicalities of these interactions, refer to papers.) UFT has a parameter  in the field equations. UFT is unlikely (for now) to be observed because it can be integral values, for instance, 1/2. How would the field theory look? 

In the case of  , UFT is just standard model field theory (these scalar theories are scale-invariant). For instance a UFT with the propagator 

 is phase-space (refer to any paper on UFT).  When , the propagator becomes

which is a familiar propagator in SM. There are many more interesting things about UFT that I cover in the paper with results. You should check first (if new to UFT) papers by Georgi, Tzu-Yiang Yuan, and Kingman Cheung. Georgi is also carrying interesting results in Schwinger's problems. 

Recently, a new term was dropped in this area by Hammer and Son. Unnuclear physics is a non-relativistic theory of unparticles. This EFT claims much more experiments than unparticle physics (which is a relativistic version). A recent talk by Dam Son emphasized the phenomenology of unnuclear physics, which is his next paper (to be released this month). A lot is going in this field. However, it is a newborn field, so a lot can't be said.