Searching for Extra Dimensions

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What extra dimensions, you probably think, having just read
the title. We know very well that the world around us is three-dimensional. We know
East from West, North from South, up from down – what extra dimensions could
there possibly be if we never see them?

Well, it turns out that we do not really know yet how many
dimensions our world has. All that our
current observations tell us is that the world around us is at least
3+1-dimensional. (The fourth dimension is time. While time is very different
from the familiar spatial dimensions, Lorentz and Einstein showed at the
beginning of the 20^{th} 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. It turns out that
for a consistent description of gravity, one needs more than 3+1 dimensions,
and the world around us could have up to 11 spatial dimensions!

How could this be possible? The reason we do not feel these
additional spatial dimensions in our everyday life (if they exist) is because
they are very different from the three dimensions we are familiar with. It
turns out that it is possible that our world is ‘pinned’ to a 3-dimensional
sheet (a so-called ‘brane’) that is located in a higher dimensional space, To
illustrate this, imagine an ant crawling on a sheet of paper in your hand. For
the ant, the ‘universe’ is pretty much two-dimensional, as it cannot leave the
surface of the paper. It only knows North from South and East from West, but up
and down don’t make any sense as long as it has to stay on the sheet of paper.
In pretty much the same way, we could be restrained to a three-dimensional
world, which is in fact a part of a more complicated multi-dimensional
universe!

For
an ant crawling on a sheet of paper the universe is pretty much two-dimensional

These extra spatial
dimensions, if they really exist, are thought to be curled-up, or
“compactified”. In the example with the ant, let’s roll the sheet of paper so
that it forms a cylinder. In this case, if the ant starts crawling in the
direction of curvature, it will eventually come back to the same point it
started from. This is an example of a compactified dimension. If the ant crawls
in a direction parallel to the length of the cylinder, it would never come back
to the same point (we are assuming that the paper cylinder is so long so that
it never reaches the edge). This is an example of a “flat” dimension. According
to string theory then, we live in a
universe where our three familiar dimensions of space are “flat”, but there are
additional dimensions which are curled-up very tightly so that they have an
extremely small radius: 10^{-30} cm or less.

These famous drawings by M.C. Escher illustrate the
idea of a compactified spatial dimension.

© 2000 Cordon
Art B.V.-Baarn-Holland. All rights reserved.

So why would it matter to
us if the universe has more than 3 spatial dimensions, if we can not feel them?
Well, in fact we could “feel” these extra dimensions through their effect on
gravity. While the forces that hold our world together (electromagnetic, weak,
and strong interactions) are constrained to the 3+1-“flat” dimensions, the
gravitational interaction always occupies the entire universe, thus allowing it
to feel the effects of extra dimensions. Unfortunately, since gravity is a very
weak force and since the radius of extra dimensions is tiny, it could be very
hard to see any effects, unless there is some kind of mechanism that amplifies
the gravitational interaction. Such a mechanism was recently proposed by
Arkani-Hamed, Dimopoulos, and Dvali, who realized that the extra dimensions can
be as large as one millimeter, and still we could have missed them in our quest
for the understanding of how the universe works!

If the extra dimensions
were indeed so large, the laws of gravity would be modified at distances
comparable to the size of the extra dimensions. So, why don’t we see this in
experiments? In fact it turns out that we know very well how gravity works for
large distances (Isaac Newton’s famous law that says that gravitational force
between two bodies falls off 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, so their
gravitational interactions are also small and hard to detect. While a new
generation of gravitational experiments that should be capable of probing
Newton’s law at short distances (up to 1 micron) is under way, our current
knowledge about gravity stops at distances of the order of 1 mm. We currently cannot say whether there are,
or are not, possible extra dimensions smaller than 1 mm.

So far so
interesting, but what does this have to do with particle physics and the DØ experiment
at Fermilab? Actually, there is a very direct connection. Since the particles
that we accelerate at Fermilab are very energetic, we can easily probe
distances as small as 10^{-19} cm by studying the products of their
collisions. However, the particles involved in these collisions are very light,
so the gravitational interaction between them is very weak. Fortunately, it
turns out that in the theory proposed by Arkani-Hamed, Dimopoulos, and Dvali,
the gravitational interaction is greatly enhanced if the colliding particles
have sufficiently high energy. This enhancement is due to the so-called
“winding modes” of the graviton – the gravitational force carrier – around the
compactified extra dimensions. If the graviton is energetic enough, it could travel
¾
“wind” its way ¾ around the compactified dimensions
many times. Each time it winds around, it gives rise to a small gravitational
force between the colliding particles. If the number of revolutions that the
graviton makes around the curled extra dimensions is large enough, the
gravitational interaction is tremendously enhanced.

Two
types of the extra-dimensional effects observable at collides. Left: a graviton
escapes from our 3-dimensional world in extra dimensions (Megaverse), resulting
in an apparent energy non-conservation in our three-dimensional world. Right: a
graviton leaves our world for a short moment of time, just to come back and
decay into a pair of photons (the DØ physicists looked for that particular
effect).

As the Fermilab Tevatron is
the highest energy particle accelerator in the world, it is the perfect place
to look for extra dimensions, since the higher the colliding particle energy
is, the stronger enhancement of the gravitational interaction is expected.
Physicists working at the DØ experiment have looked for the effects of
gravitational interactions between pairs of electrons or photons produced in
high-energy collisions. If the gravitational interaction between the two
electrons or two photons is large enough, the properties of such a final state
system would be modified. There will be more pairs produced at high two-body
masses, and also the angular distribution of these particles will be more
uniform than one expects to see if gravity is weak enough to be ignored. When DØ
carefully analyzed the data they collected in 1992-1996, no such enhancements
were found. The data agrees 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. So, no evidence for
extra dimensions was found so far.

A
display of the highest invariant mass (570 GeV) photon-pair event that DØ has
observed in Run I. Two colorful splashes of energy seen in the left and right
“arms” of the detector mark the points where the two photons were intercepted
by the DØ calorimeter. Unfortunately, this event is unlikely to originate from
extra dimensions, due to its angular properties. It is consistent with the rate
that one would expect from known physics processes.

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

Our search for extra
dimensions is not over yet. In fact, it has only just started. We are also
looking for the effects of extra dimensions in collisions that produce
different types of particles, such as quarks. We are also looking for events
where gravitons are produced in the collisions and then leave our
three-dimensional world, travelling off into one of the other dimensions. This
would cause an apparent non-conservation of energy from the point of view of
our three dimensional world. With the next data-taking run scheduled to start
in 2001, and likely to deliver twenty times the data presently accumulated, we
will have a significantly extended sensitivity to large extra dimensions. We
very well might see them!

If we are not so lucky, the
next generation collider, LHC, that is being built at CERN (near Geneva,
Switzerland) will allow us to ultimately probe the theory of large extra
dimensions and either find them or show that the idea is actually wrong. But we
will have to wait six more years or so, before we learn that.

If you have any questions about this research, please
contact Greg Landsberg at Brown University, landsberg@hep.brown.edu.