November 07, 2004

Fun in the fifth dimension.

I've been spending a great deal of time on research lately. We are trying to build a realistic physics model that has no Higgs boson. As I've written about before, the Higgs is a particle in the Standard Model (SM) of particle physics that we have never actually observed in an experiment. Chances are that, if the current Fermilab experiments don't find it (or something very much like it), the next LHC experiments will. But there is always a chance that they won't.

In the case that the Higgs is not found, and nothing looking like the Higgs (what we call a "scalar boson") is found, physicists are going to have a lot of explaining to do. The conventional wisdom is that, since the approximate symmetry of nature called the "electroweak" symmetry is not exact ("broken," we call it), there must be a Higgs at the energy scale the next experiments will probe.

Well, we're putting together a model without any such scalar boson (at least, not at energies where the next experiments will see it). It's not the most aesthetically pleasing model in the world, and the chances that this exact model represents the real world are very small, but it's good to have at least one example as a sort of proof-of-concept. We can hope that the lessons we learn from it might give us a better general idea of what Higgsless models are like.

For those of you who want the details, look at the last paper of the others I am working with (Giacomo Cacciapaglia, Csaba Csaki, Christophe Grojean, and John Terning): "Curing the Ills of Higgsless Models: the S Parameter and Unitarity." As I don't want to talk too much about the details of research in progress before we have written our paper, I'll stick mostly to the outline of future work at the end of that paper. I've drawn a picture to try to get some of the idea across.

Here's a (very schematic) picture of what we're doing:

I apologize for my limited skill at drawing these things on a computer, but maybe the idea will get across. In this model, we have a five-dimensional universe (four spatial dimensions, one time). The new fifth dimension is represented as the horizontal direction in this picture; you should imagine that each slice (such as any one of the parallelograms drawn in blue) has three spatial dimensions. Some of these slices are special; they are the ones shown, and are called "branes." Branes are real physical objects, that are very heavy, which lie in the extra dimension. Particles can either be stuck on a brane, or propagate through the space between branes.

In our model, some particles (the gauge bosons, which carry forces) exist across the entire five-dimensional space. The black and red lines in the picture are examples. Other particles (the fermions, which make up matter) lie between only two of the branes. The blue and green lines in the picture are examples. The green blob on the Planck brane at the end of the green line represents a "brane-localized fermion"; it is stuck on the brane, but it mixes with the bulk fermion represented by the green line, so that in some sense we see them as the same particle. The lines here represent the "wave function" of the particle in the extra dimension; roughly, places where this is peaked are places the particle is most likely to be found. For instance, the red line represents a heavy boson (what we call a "KK mode" or "Kaluza-Klein mode") that tends to be found mostly near the "TeV brane" on the right. The other particles that have fairly flat lines will be found anywhere in the fifth-dimensional space. How strongly particles interact is related to the extent to which their "wave functions" overlap in the fifth dimension. Thus, for instance, the heavy boson marked in red will not interact much with the fermion in blue, which is living in the opposite side of the middle (Planck) brane from where the red wave function is peaked. Similarly, the heavy boson in red will not interact much with the fermion marked in green, because this fermion has a large piece stuck on the brane (the green blob in the picture) and that is far away from where the red line is peaked.

The shapes of all these wave functions are determined by the boundary conditions, which specify what they do on the branes. For instance, on one brane a certain function might be constrained to be zero, which means the line is anchored in place on that brane. Alternatively, the derivative of the function might be constrained to be zero on that brane, which roughly means the line is allowed to slip around on the brane so long as it is flat there.

All of this might look rather ad hoc, but in fact the boundary conditions we have to use for the fields all come from a sensible set of rules that are based on the idea that the symmetries of the theory can be different in different places. On the Planck brane we put the usual "Standard Model" symmetries; on the TeV branes we break electroweak symmetry by boundary conditions, which thus in some sense fulfill the usual role of the Higgs boson. Other parts of the Higgs boson's role are taken over by the KK modes, which can affect the way the gauge bosons interact but which mostly do not affect the fermions, since these are localized elsewhere. Certain effects are also dependent on the size of the "bulk" that is involved, so by making the bulk on the left-hand side of the picture smaller than the one on the right, we can accomplish other important effects.

All this is necessarily very vague, and for those who want details you can consult our paper when we have finished it. I hope that to some extent this picture gives you an idea of how what we're doing works. There are all sorts of related models under discussion in which extra dimensions can have important (and sometimes surprising) effects on physics. One can either take these seriously -- that is, believe that there really are extra dimensions that are within reach of the next generation of colliders -- or take them as tools for building four-dimensional (three space, one time) models with unusual properties that one can see how to arrange in the five-dimensional picture but that are not obvious in the four-dimensional picture. This is the "effective theory" picture (again, roughly speaking; in fact "effective theory" has a pretty precise meaning).

(Is this at all comprehensible? Feedback or questions are very much welcomed. I don't want to discuss details of research on this blog until it's eventually posted on, but queries about extra dimensions or branes or particle physics in general are welcome.)

Posted by Matt at November 7, 2004 06:22 PM
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