Since Howard Georgi taught us how to turn anything into unthing, unparticles have quickly spread to all areas of particle physics. This amazing expansion have been so far consistent with the unthropic principle which says that, in the universe that supports intelligent life, unparticles cannot have any useful application. Nothing is sacred these days, and even the Higgs was recently downgraded to the Unhiggs. Yet in spite of my trademark sarcasm, it seems to me that the Unhiggs may violate the unthropic principle and that the whole idea may turn out to be of some use.
In the good old Standard Model, the Higgs particle fulfills multiple tasks. First of all, it condensates to give mass to the W and Z bosons. But this is just a beginning. The presence of the Higgs particle renders the Standard Model well-behaved - *unitary* - at high energies. A massive W boson has three polarization states - two transverse (to the direction of motion), and one longitudinal. It turns out that the scattering amplitude for the longitudinally polarized W's grows with energy, and at some point it would violate general unitarity bounds of quantum field theory. But the diagrams with the Higgs exchange cancel the dangerous terms in the amplitude and the theory recovers the consistent high-energy behavior. In the particle physics jargon, the Higgs unitarizes WW scattering. Finally, the Higgs contributes to electroweak precision observables. The success of the Standard Model in fitting the LEP and Tevatron data relies to a large extent on assuming loop contributions of a fairly light (less than 200 GeV) Higgs particle.
Since the Higgs does his job so well, living without the Higgs particle is difficult. The Higgsless models make a try. They invoke new heavy spin 1 particles to unitarize WW scattering, but they do much worse in electroweak precision tests. It seems that the Unhiggs is a new possibility. Given the dearth of calculable ideas for electroweak symmetry breaking, any new direction is worth looking at.
In a recent paper, David Stancato and John Terning attempted to get W and Z boson masses from a scalar unparticle Higgs condensation. The first step is to construct a gauge invariant action for the Unhiggs. This is actually quite tricky. Usually, making the action gauge invariant amounts to replacing normal derivatives $\pa$ with covariant derivatives $D = \pa - i A$. But the unparticle nature of the Unhiggs implies that the kinetic term is some non-polynomial function $F(\partial^2)$, rather than the simple $\partial^2$, so that the usual procedure does not apply. Yet there is a trick that makes use of non-local objects called the Wilson lines. The final outcome is a complicated, non-local action: whereas in the normal gauge theory there are vertices with only 3 or 4 gauge bosons legs, in the Unhiggs set-up there exist vertices with an arbitrary number of gauge boson legs.
The paper shows that, even though the interactions are weird, the Unhiggs unitarizes WW scattering. It is not clear yet how well it fares with the electroweak precision tests.
The most serious problem with this approach is that it's unclear what would happen if such unthing is discovered at the LHC. If the Higgs particle is discovered, the Nobel Prize will sure go Peter Higgs who predicted a particle, but he obviously cannot be honored for an unparticle. The three possible scenarios are
1) Unpeter Unhiggs gets a Nobel Prize.
2) Peter Higgs gets the Ignoble Prize
3) There is a fatal error and the universe disappears.
We'll see. Or not.
The paper is here, but be warned that it's unpretty technical.