# Search for Large Extra Dimensions in Dimuon Production with the D0 Detector

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 = 1012 electron volts.  However, it is commonly thought that gravity’s energy scale is near 1019 GeV = 1027 electron volts, which is often referred to as the Planck scale (MPl).  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 ~1019 GeV, however in the true extra dimensional space the fundamental Planck scale (MS) 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 Chicago, IL.  We searched for the presence of large ED by looking for the production of the type of gravitons described in the previous section.  These gravitons could be produced in the high energy proton-antiproton collisions of the Tevatron.  The energy of these proton-antiproton collisions is 2 TeV.  If gravitons are produced they would quickly decay into SM particles, like muons.  Specifically, we look for events which have two high momentum isolated muons.  The following figure illustrates the proton-antiproton collision which produces a graviton which then quickly decays into two muons.  Also seen in the figure is the angle , which is the angle of the decay muon with respect to the proton-antiproton beam.

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.