The Search for Extra Dimensions
OR Does Dzero Have Branes?

by Greg Landsberg

Branes are big right now.

They're the vibrating membranes that superstring theorists, including Fermilab's Joe Lykken, have invented over the last five years to describe how our familiar three-dimensional universe might fit into a multidimensional "megaverse,"one with as many as 11--count'em!--dimensions, most of them so curled and compactified that we haven't detected them here on our own little dimensionally challenged 3-D brane.

Superstring theory, with its branes, strings and extra dimensions, represents one consistent way to achieve physicists' long-cherished goal of unifying the theory of gravity--Einstein's theory of general relativity--and the Standard Model--the well-thumbed playbook of particle physics that gives us the electromagnetic, weak and strong forces.

Best of all--almost too good to be true from a particle physics lab's point of view--superstring theory is testable by experiment. DZero's Greg Landsberg, a Fermilab user from Brown University, explains the hunt for evidence of extra dimensions at his experiment at Fermilab's Tevatron.

by Greg Landsberg

Extra dimensions? What extra dimensions? East is east, and west is west, the Bronx is up and the Battery's down. North by Northwest. South. Extra dimensions? Don't we have enough already?

In fact, we do not really know how many dimensions our world has. From our current observations, all we know is that the world around us is at least 3+1-dimensional. (The fourth dimension is time. While time is different from the familiar spatial dimensions, Lorentz and Einstein showed at the beginning of the 20th century that space and time are intrinsically related.) The idea of additional spatial dimensions comes from string theory, the only self-consistent quantum theory of gravity so far. This theory tells us that a consistent description of gravity requires more than 3+1 dimensions, and that indeed the world around us could have up to 11 spatial dimensions.

Eleven? How is this possible?

If extra dimensions exist, we do not feel them in our everyday life because they are very different from the three dimensions we know. According to superstring theory, it is possible that our world is'pinned' to a 3-dimensional sheet (a so-called "brane") that is itself located in a higher-dimensional space.

Imagine an ant crawling on a sheet of paper. For the ant, the "universe"is for all intents and purposes two-dimensional, since it cannot leave the surface of the paper. The ant knows north from south and east from west, but up and down have no meaning as long as it has to stay on the paper. In much the same way, we may be restrained to a three-dimensional world that is in fact part of a more complicated multidimensional universe.

Theorists tell us that these extra spatial dimensions, if they exist, are curled up, or "compactified."In the example with the ant, we could imagine rolling the sheet of paper to form a cylinder. If the ant crawled in the direction of curvature, it would eventually come back to the point where it started--an example of a compactified dimension. If the ant crawled in a direction parallel to the length of the cylinder, it would never come back to the same point (assuming a cylinder so long so that the ant never reaches the edge)--an example of a "flat"dimension. According to superstring theory, we live in a universe where our three familiar dimensions of space are "flat,"but there are additional dimensions, curled up so tightly so they have an extremely small radius: 10-30 cm or less.

Does it matter to us if the universe has more than three spatial dimensions, if we cannot feel them? In fact, fascinatingly, we might actually "feel"these extra dimensions through their effect on gravity. While the forces that hold our world together (the electromagnetic, weak and strong interactions) are constrained to the 3+1 "flat"dimensions, the gravitational interaction occupies the entire "megaverse,"allowing it to feel the effects of extra dimensions. However, since gravity is a very weak force and the radius of extra dimensions is tiny, it would be extremely hard to see any effects--unless there is some kind of mechanism that amplifies the gravitational interaction. Just such a mechanism was recently proposed by theorists Nima Arkani-Hamed of SLAC, Savas Dimopoulos at Stanford and Georgi Dvali of New York University. They realized that the extra dimensions might be as large as one millimeter and still have been overlooked in experimentalists' quest for the understanding of how the universe works.

If the extra dimensions were indeed as large as a millimeter, the laws of gravity would be modified at distances comparable to the size of the extra dimensions. Why, then, don't we see such an effect in experiments?

We know very well how gravity works for large distances (Newton's famous law says that the gravitational force between two bodies decreases as the square of distance between them). However, no one has tested how well this works for distances less than about 1 mm. It is complicated to study gravitational interactions at small distances. Objects positioned so close to each other must be very small and very light, making their gravitational interactions also small and hard to detect. Although a new generation of gravitational experiments to probe Newton's law at short distances (up to a few microns) is under way, our current knowledge of gravity stops at distances of about 1 mm. We do not know whether there are, or are not, possible extra dimensions smaller than 1 mm.

Here's where DZero comes in

So far so good, but what does this have to do with particle physics and Fermilab's DZero experiment? In fact, there is a direct connection. The particles that we accelerate at Fermilab are very energetic, and we can easily probe distances as small as 10-19 cm by studying the products of their collisions. The bad news is that, because the particles in these collisions are so light, the gravitational interaction between them is extremely weak. The good news is that, in the theory proposed by Arkani-Hamed, Dimopoulos and Dvali, the gravitational interaction is greatly enhanced if the colliding particles have a high enough energy. This enhancement is due to the so-called "Kalusa-Klein"modes of the graviton--the gravitational force carrier--in which the graviton winds around the compactified extra dimensions. If the graviton were energetic enough, it could travel--"wind"its way--around the compactified dimensions many times. Each time it wound around, it would give rise to a small gravitational force between the colliding particles. If the graviton made enough revolutions around the curled extra dimensions, the gravita-tional interaction would be tremendously enhanced.

As the highest energy particle accelerator in the world, the Tevatron is the perfect place to look for extra dimensions: the higher the colliding particle energy, the stronger the expected enhancement of the gravitational interaction. Physicists working at DZero have looked for the effects of gravita-tional interactions between pairs of electrons or photons produced in high-energy collisions. If the gravitational interaction between the two electrons or two photons were large enough, the properties of such a final-state system would be modified. There would be more pairs produced at high two-body masses, and the angular distribution of these particles would be more uniform than expected if gravity were weak enough to be ignored.

When DZero experimenters carefully analyzed the data they collected in 1992-1996, they found no such enhancements. The data agree very well with the predictions from known physics processes, and the gravitational interaction does not seem to play any significant role at the energies that we are able to reach. No evidence for branes has been found at DZero so far.

We've only just begun

Although DZero experimenters have not seen extra dimensions, they were able to set stricter limits on their size than those set so far by gravitational experiments or accelerator experiments at lower energy machines. These new limits also place significant constraints on Arkani-Hamed, Dimopoulos and Dvali's theory.

The search for extra dimensions is not over. In fact, it has only just begun. Our colleagues across the ring at DZero's sister experiment, CDF, are searching their data for evidence of extra dimensions, and we look forward to their results. The collaborations are looking for the effects of extra dimensions in collisions that produce different types of particles, such as quarks. They are also seeking events where gravitons are produced in the collisions and then leave our three-dimensional world, traveling off into one of the other dimensions. Such a departure would cause an apparent nonconservation of energy from the point of view of our three-dimensional world.

With the next Tevatron run scheduled to start in 2001 and likely to deliver 200 times the data presently accumulated, Fermilab's collider experiments will have a significantly extended sensitivity to large extra dimensions. They might very well see them!

If they are not so lucky, the next generation Large Hadron Collider now being built at CERN in Europe will allow physicists to probe the theory of large extra dimensions and either find them or show that the idea is wrong. But we will have to wait six more years or so, before we learn that.