The SUSY Trilepton Signature

March 31, 1998

Our current understanding of what the universe is made of and how its fundamental constituents behave is largely described in the Standard Model (SM) . This model, which has to date been very successful, describes the universe as being made up of leptons, for example electrons and muons, and quarks, which make up protons and neutrons. A property of leptons and quarks which interests us for this discussion is a quantity called spin. Quarks and leptons have spin=1/2 and are called fermions. All fermions have half integral spin, e.g.. 1/2, 3/2, 5/2 and so on. The spin of a particle is one of the properties that tells us how the particle behaves and interacts with other particles. Leptons and quarks can interact with each other via three types of forces: the strong force between quarks, which holds protons together; the weak force between leptons and quarks, which is responsible for the radioactive decay of heavy elements like Uranium; and the more familiar electromagnetic force between electrically charged quarks and leptons. There is a fourth force of nature, gravity, with has yet to be included in the SM. These forces come about by the exchange of another type of particle called a gauge boson. Bosons are particles that have integral spin, spin = 0, 1, 2 and so on. Gauge bosons in the SM have spin = 1. The last piece of the SM is the Higgs boson (spin=0) which is a particle that is believed to be responsible for giving the other particles of the SM their mass through interactions with the Higgs.

As stated the SM has been very successful; however, there are some problems with it. First, the mass of the Higgs particle is not given by the SM; it's only very loosely constrained by theory. There are also some interactions in the SM which are not well behaved unless the Higgs mass is light enough; for example, the SM gives reaction rates for certain interactions that are too large. However, there is no natural way in the SM to ensure a light mass Higgs.

One popular solution to this problem is to extend the SM to a larger set of particles. The new additional particles of this extended set are like the particles of the SM except they differ in their spin by a value of 1/2. They also differ in the value of their mass. This is to say for every SM particle there is a complementary particle with the same qualities of its SM partner except it differs in spin by 1/2 and has a different mass. For example for the electron with spin = 1/2, there would be a particle that is like the electron in every way except it has spin=0, and it is much heavier than the electron. This symmetry between the new particles and the SM particles, namely the fermion <==> boson symmetry has been called SUperSYmmetry or SUSY. It is the interaction of these new SUSY particles with the Higgs bosons that allow a natural way of ensuring a light enough Higgs mass. The SuperSymmetric partners to the SM particles are generally heavier because the symmetry has been broken. Otherwise, they would have the same mass as the SM particles, and we would have seen them in nature or have produced them abundantly in high energy collisions, for example, between protons and anti-protons at Fermilab. But the fact that we have yet to see these particles indicates that they are likely to be quite heavy, or perhaps their interaction with SM particles is very weak.

If SUSY particles exist and are produced in high energy collisions, they would create some very distinct signals in our detector. One such signal, which is the subject of this discussion, is the detection of three leptons (electrons or muons). A depiction of the production of a pair of SUSY particles and their subsequent decay to three leptons is shown in the following picture.

What we see in this picture from left to right is first the coming together (annihilation) of a quark and anti-quark (q' with line above it) to produce a virtual W boson. The quark comes from the colliding proton, and the anti-quark comes from the colliding anti-proton. What we mean by virtual , denoted by the asterisk, is that in effect the mass of the virtual particle is smaller or larger than mass we expect the particle to typically have. For example, W bosons, which are bosons that carries the Weak force, are mostly produced with a mass of about 80 GeV/c² which is the mass of about 85 protons or something like the mass of a calcium atom. However, sometimes the W boson is created with a mass that is significantly larger or smaller. In this way it is possible for the W boson to break up (decay) into particles whose masses sum to something much greater than 80 GeV/c².

Continuing from left to right in the above picture, the virtual W decays to two SUSY particles denoted by W₁ and Z₂ with tilde (~). All SUSY particles in the picture are indicated by the dashed green lines; the SM fermion particles are indicated by the solid blue lines, and the SM bosons are indicated by the red wiggly lines. These two SUSY particles are the SUSY partners of the SM W and Z bosons, sometimes called the Wino and the Zino. Again they are like the SM W and Z bosons, but they have spin=1/2 and are therefore fermions. The two SUSY particles can each decay into a pair of SM leptons plus another SUSY particle denoted by Z₁ with tilde. This last SUSY particle is assumed in our search to be the Lightest SUSY Particle (LSP) and completely stable; it does not decay to anything. We also assume that it does not interact with our detector, so it escapes direct detection. The detached diagram to the right depicts another way these SUSY particles can decay.

We get from the decay of the Wino and Zino three charged leptons and a neutral lepton. The neutral lepton is called a neutrino (indicated by the greek letter nu in the diagram) which does not interact with our detector and therefore escapes being detected directly. We can detect and measure directly the charged leptons, which for our search we require to be either electrons (e) or muons (m). So the signal of interest for the production of a Wino/Zino pair is three charged leptons (eee, eem, emm, mmm) plus missing energy, which we can infer, coming from the two LSPs and the neutrino. The signature depicted in the diagram above is one electron, two muons, and missing energy.

One may ask why is this particular signal for SUSY so interesting. One reason is that there is only one physics process of SM particles that can mimic it. We call processes that can mimic the signal background, similar in concept to background noise. The background process relevant to the SUSY trilepton signal is the production of a SM W and Z boson pair. The rate for this process is quite small; we have yet to identify even one of these events. If we did find a trilepton event from SM W/Z pairs, we would most likely be able to identify it as having a SM Z boson from the energy measurements of the charged leptons. So the trilepton signature is essentially background free, and any signal that we see can be attributed to little else (if anything) other than SUSY. Many theorists feel that it will be through the trilepton signature that SUSY will discovered at Fermilab.

Currently, we have seen no evidence of the trilepton signal in our data; we see no trilepton events. We estimate that we should see no more than about one event from background sources. From this null result, we can set a limit on the production cross section, which relates to how often a particular process occures. The production cross section can be thought of as a probability. It can also be thought of as the effective area presented by the colliding proton and anti-proton to a particular production mechanism. If you take this quantity and multiply it by a measurement of the amount of data that is collected and the efficiency for detecting the trilepton signal, you get an estimate for the number of trilepton events in the given data set that one should see. And when we set a limit on the production cross section, in the absence of any detectable signal, we estimate a maximum possible value for this quantity. If for larger and larger data sets we see no trilepton events, the maximum possible value of the production cross section becomes generally lower and lower.

Our estimate of the limit on the cross section is given in the figure below. It is given as a function of the mass of the wino, because the detection efficiency varies with the mass of the wino; the heavier the wino the greater the detection efficiency.

The red solid line is our limit. The two dashed blue lines are theoretical predictions for the production cross section. The upper blue dashed line is the theoretical maximum value. Most values for the cross section for various SUSY models lie somewhere between the two blue dashed lines; a few models have values below the lower dashed blue line. What is meant here by various SUSY models is that there are many variations of SUSY in the sense that the masses of the SUSY particles can vary from one model to the next. Also the strength of the couplings among SUSY particles and between SUSY and SM particles can vary.

One can interpret the limit for a particular model. If the predicted production cross section at a given wino mass is above the red line then that model is excluded from being a candidate for SUSY. So, for example, of those models that predict values of the production cross section which lie on the upper blue dashed line, we can exclude the models that have wino masses below about 103 GeV/c². This is indicated by the intersection of the red and upper blue lines.

Hopefully, when we gather more data in the next collider run, the trilepton signal will make its appearance ushering in a new era of discovery. For the next run we expect at least 20 times more data than we have now. This will greatly extend our search potential. If no evidence of the trilepton signal appears, then the red line in the above limit plot will move down, and we will exclude higher masses and more SUSY models. In the case of the upper blue curve, we should be able to exclude wino masses to at least 225 GeV/c².

Here is a postscript version of our paper on this subject, which appeared in Physical Review Letters: Phys. Rev. Letters 80, 1591 (1998).

For further information contact Douglas Norman.

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