50. Planck 2008: day 4

Although I am back to Helsinki for a week already, let me continue my brief review of Planck 2008 talks

Plenary talks of the 4th day were mostly devoted to unparticles and AdS/QCD, with opening talk by Howard Georgi, inventor of unparticles himself. He was talking about his paper (just released) “An unparticle example in 2D” with Eugene Kats (projector did not work in the beginning of his talk, so he had to talk without transparances or PowerPoint presentation, and I was very much impressed how well he did it).

Let me first remind you what is the buzz concering unpartcles. Imagine some scale invariant matter (that is, spectrum of its excitations is scale invariant). One cannot describe such fields (let us call them ) in terms of particles – the possibility of the latter description would imply that the spectral function of excitations (exp. value of the commutator ) has strong peaks at some . Positions of the peak would be related to the mass of the “particles”, while widths of the peaks – to the life time of the “particles”. Scale invariant spectral function therefore means that our particles are interacting so strongly, that their notion is undefined.

This scale invariant matter sector can in principle weakly interact with our Standard Model stuff, and its existence can potentially influence SM scattering, in particular, would lead to events of missing energy and momentum in scattering events. Since unparticles are described by CFT, interactions between them and SM are organized as interactions between SM fields and CFT operators with non-trivial scaling dimensions (Georgi calls them Banks-Zaks fields).

After this short introduction, let me go back to Georgi’s talk… He explicitly introduced an example of the 2D theory with unparticles: Thirring model (massless fermions, 4-fermion interaction; the model is exactly solvable, admits bosonization and is nothing else but CFT) with massive vector bosons. The Thirring model with massive gauge bosons turns also out to be exactly solvable. At higher energies the theory approaches free field limit, while in the IR massive vector bosons are integrated out, only fermions survive, so conformal symmetry gets restored (one has Thirring model unparticles).

As a “SM” stuff, Georgi introduces complex scalar field interacting with Thirring fermions through standard trilinear interaction term, so that we can excite unparticles in collisions .

The physics of scattering turns out to be the following: first of all, there exists the physical scale

where is the mass of gauge bosons and is their interaction with Thirring fermions. At one has energy loss to unparticles, while at one can also excite gauge bosons. enters the overall cross section pretty much in the same way enters cross sections in inclusive QCD processes.

The second talk about unparticles was by John Terning (UC Davis): he discussed AdS/CFT-unparticle interplay. He basically showed that unparticle actions are equivalent to holographic boundary actions for fields in AdS. Clearly, his picture cannot be universal since the class of CFTs is much wider than the class of theories that admit gravity dual.

The talk N3: Antonio Delgado (Notre Dame) has introduced an interaction between Higgs and unarticle stuff of the form

where is the CFT operator with dimension and tried to figure out how it will influence Higgs physics at LHC. The result of the Higgs-unparticle interplay is the
mass gap in the unparticle continuum and a shift in the Higgs mass. In fact, Higgs state can be above (bound state in unparticle continuous spectrum) or below the mass gap. Also, another isolated state, a mix of Higgs and unparticles (Antonio calls it phantom Higgs), can appear in the spectrum near or below the mass gap. Coupling between phantom Higgs, fermions and gauge bosons are reduced.

During the next talk (“A bound on operator dimension in CFT4 and the hierarchy problem” by Riccardo Ratazzi) I decoupled from the audience and missed it almost completely, but the final talk by Tony Gherghetta has grabbed my attention back. Tony was talking about soft-wall AdS/QCD, the subject that definitely deserves a separate post.

To be continued…