The full paper is available here.

**The Question**

The Standard
Model (SM) of particle physics is an extraordinary accomplishment of
scientific thought. It explains what the
universe is made of and how the material in the universe interacts to produce
the effects we see. However, the SM does
not contain an explanation for the force we are most familiar with in our
day-to-day lives, gravity! The troubling issue between the SM and
gravitational theory can be illustrated by asking the question, why are
gravity’s “quantum” interactions so much smaller than SM
interactions? Or another way of asking
the same question, why is gravity’s energy scale vastly bigger than that
of the SM? Note that a given
theory’s interaction strength is inversely proportional to its inherent
energy scale. These questions can be
quantified by looking at the different energy scales within the two theories. The SM processes occur at energy scales
around 1 TeV = 10^{12} electron volts. However, it is commonly thought that
gravity’s energy scale is near 10^{19} GeV
= 10^{27} electron volts, which is often referred to as the Planck
scale (M_{Pl}). This 15 order of magnitude difference in
energy scales is referred to as the hierarchy problem of
particle physics.

**A Possible Solution**

A solution to the question posed above was presented in 1998 by a group of
physicists, Arkani-Hamed, Dimopoulos,
and Dvali (ADD).
In their paper they suggest that the seemingly unreachable Planck energy
scale may be in fact much lower, i.e. within the reach of current and planned
future colliders.
They postulated that SM particles are confined to a three-dimensional
surface which is embedded in a higher dimensional “multiverse”,
which consists of the three standard plus *n* extra
dimensions (ED). However, they
theorize that gravitons
can propagate in the entire multiverse. One consequence is from the point of view of
the SM three-dimensional world, extra dimensional gravitons can have very large
masses. Furthermore, the size of ED in
the ADD model is much larger than either the Planck or SM length, which is
basically one over the energy scale, and may be as large as ~1 mm. Since gravitons are free to propagate in
these large ED, the gravitational interaction would appear suppressed relative
to our three-dimensional world. This is
due to the large extra volume gravity permeates. Consequently, this gives the illusion that
the Planck scale is ~10^{19} GeV, however in
the true extra dimensional space the fundamental Planck scale (M_{S})
can be as low as ~1 TeV, thus eliminating the
hierarchy problem.

**The Search **

The analysis presented here utilizes data from Run II of the Tevatron accelerator complex located at Fermi National Accelerator Laboratory near

The muons are identified by hits in the detector’s muon chambers as well as an associated track in the tracking detector. The following figure shows the information used for this study.

a) The mass versus cos() of the two muons as predicted by SM. If no invisible particles are produced, this quantity corresponds to the mass of the mother particle.

b) The mass versus cos() of the two muons as predicted by SM and a possible LED signal.

c) The mass versus cos() of the two muons as seen in the experiment.

The term describes the “strength” of the possible large ED
effects. The fundamental Planck scale is
related to by the following equation:. The factor *F* is different depending on the model of
large ED studied, however this factor has values typically around one. The quantity 246 pb^{-1} is basically
a measure of the number of events in our data sample which contains about
17,000 events. The next plot shows the
mass spectrum for the two muons. Open circles are from data, solid histogram
is the SM prediction, and the dashed histograms are for possible large ED
signal.

**The Result**

By comparing the plots above, we see that there is no statistically significant excess of events seen in the possible, high mass, signal region. One might point out that there are two data events that look like signal (masses greater than 600 GeV), however if you sum up the number of events predicted by the SM in this region it is fully consistent with two! While we do not see any evidence for large ED gravitons decaying into two high momentum muons, we can still set limits on the “strength” of large ED effects in dimuon production. The limits found are summarized in the following table.

This table shows that the fundamental Planck scale must be
bigger than 0.85-1.27 TeV (depending on the choice of
the factor *F*). For the dimuon
final state, these results represent the most stringent to date.

If you have questions about this analysis, please contact the primary authors Ryan J. Hooper and Greg Landsberg.