Posted by Matt

You might want to go back and read my earlier account of the fundamental forces and what we mean by "electroweak symmetry breaking." Briefly, the current theory we have of particle physics that's valid up to the energy scales we can test so far at colliders is called "the Standard Model," and all of it is very well-tested except for the Higgs boson. The Higgs was introduced because the Standard Model breaks down completely at a scale somewhere around what we're currently testing, and it's pretty much the simplest thing you could add to the theory to keep it from giving you nonsensical results at those energies. But so far the Higgs hasn't been discovered where people thought it would be, and it introduces all sorts of other problems in the theory.

I said a bit more about this in this post, where I suggested that we should try to understand supersymmetric theories better to get a sense of what sort of strongly interacting possiblities there are for electroweak symmetry breaking. What I'm about to describe is another fairly easy-to-understand example along those lines, albeit not supersymmetric.

(Aside: the Hindustan Times recently published this article about physicists wanting a Linear Collider to find 'God.' Presumably this comes from Leon Lederman's odd dubbing of the Higgs "the God Particle," but it leads to amusing quotes like "nobody has seen God and some even doubt its existence.")

Read on for how we hope to build a realistic model with no Higgs boson. I'm afraid it gets a bit too technical at points, but hopefully the general ideas will be of interest.

Right now I'm working toward starting a project of researching a certain type of Higgsless model. (I say "working toward" because I'm in the stage of reproducing in detail earlier results of Csaba Csaki and others, before I start trying new things.) The idea behind these models is a fairly attractive one, in my opinion.

It all starts with something called the Randall-Sundrum scenario. One fairly comprehensible way to learn a bit about this is from this interview with Lisa Randall at sciencewatch.com. Roughly, the idea is to take a five-dimensional space where the fifth dimension stretches between two four-dimensional "branes." (Note that our universe as we observe it is four-dimensional: three space dimensions, and time.) The geometry of this fifth dimension is "warped," so that as you move along the fifth dimension things shrink in a certain way. It turns out that this can naturally explain why the scale of the electroweak interactions -- the scale of this mysterious Higgs boson that we haven't seen yet -- is so much smaller than the natural scale of gravity. (Phrased a different way, it explains why gravity is so much weaker than the other forces.)

Now, any particle we know about corresponds to a quantum field, and, like the different harmonics on a violin string, there will be different "modes" of this field in the fifth dimension. From the point of view of four-dimensional observers like us, these modes look like independent particles, with increasingly higher mass. These are called "Kaluza-Klein modes," after the people who originally conceived of the idea that there could be more spatial dimensions.

What Csaba and others realized was that this "tower" of additional modes of the W and Z bosons -- the ones that are involved in carrying the electroweak force -- can in some sense play the role of the Higgs boson. (Specifically, they can keep the WW scattering amplitude unitary.) Even better, in the specific five-dimensional "warped" geometry Randall and Sundrum considered, this can be done in a way that's consistent with experimental observations. This was explained in this paper, and more detailed calculations were done in this paper.

This all is very nice, but the Higgs does more than just fix problems with W scattering. It gives masses to fermions! Thus this paper on how to incorporate fermion masses in these Higgsless models. The real challenge proves to be the top quark. It's very heavy -- a top quark has the mass of a gold nucleus! This is huge, when you consider that that's about 175 proton masses. The proton is made of three quarks, but almost all of its mass is binding energy. The up and down quarks in it contribute almost nothing to its mass. The top is just amazingly heavy for a fundamental fermion.

One can achieve a high enough top mass in the Higgsless models by adjusting enough parameters, but the top and the bottom quark are related to each other. It's hard to mess with them independently. So what happens when you try to fix the top in these models is that you tend to mess up the couplings of the bottom quark, which have been experimentally measured.

So, the goal of this project I'm working towards will be to try to solve these problems and produce a fully realistic Higgsless model. This will probably involve adding a new scale in these theories. This isn't so surprising when you consider that these theories are AdS/CFT duals of a theory like walking technicolor, and technicolor generally needs such an extra scale. (See, e.g., these lectures on technicolor by Kenneth Lane.)

One more note, of a more technical nature: some of you might be familiar with recent papers by Howard Georgi, Maxim Perelstein, and others arguing that electroweak corrections to "deconstructed" Higgsless models are in unacceptable disagreement with experiment. These papers don't address the equivalent of bulk fermions, however; the fermions in these are charged under only the gauge groups at the end of the "moose diagram," and so are more like brane fermions. Electroweak corrections in the 5D models seem to be under control, although the whole question hinges on whether that is still true once we include the third generation in a realistic way. Once I get up to speed on all the work that's been done so far, this is what I will have to start computing.

A couple of references, for those with some physics knowledge looking for a way to learn about extra-dimensional scenarios and warped geometry in particular: try Csaba's TASI lectures, and the article on "Holography and Phenomenology" by Nima Arkani-Hamed, Massimo Porrati, and Lisa Randall.

I'll try to find some articles for non-physicists on things like the Randall-Sundrum "brane world" and the Higgs, to supplement this probably confusing and overly digressive sketch.

Posted by Matt at September 8, 2004 11:18 PM
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