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The First Muons at the Large Hadron Collider

By Michael E. Peskin

The Large Hadron Collider (LHC) is the largest particle accelerator, or scientific equipment for that matter, in the world. Bordering Switzerland and France underground, the LHC will use hadrons to recreate the conditions right after the Big Bang.

March 25, 2011

Michael E. Peskin is a Particle Physics and Astrophysics Faculty at the SLAC National Accelerator Laboratory and co-author of a text book, An Introduction to Quantum Field Theory.

In 2009, the Large Hadron Collider at the European particle physics laboratory CERN recorded its first high-energy collisions. The Large Hadron Collider or LHC is the world’s largest piece of scientific equipment. It includes a ring of magnets in an underground tunnel of 27 km circumference. Each magnet has two tracks, enabling the accelerator to circulate two beams of protons running in opposite directions. Each proton has an energy of 3.5 TeV, that is, roughly 3,500 times the rest energy of the proton computed from E = mc2. At four points around the ring, the proton beams collide head-on. The complex events that produced in these collisions are observed by instruments the size of airplane hangers, within which each cubic centimeter is instrumented with particle detectors. This is an ambitious, technically difficult, and very expensive enterprise. Its purpose is to reveal the laws of physics at distances a factor of 10,000 smaller than the size of an atomic nucleus.

In 2010, the LHC detectors recorded their first substantial sample of data. This was sufficient to observe the known elementary particles, all the way up to the massive top quark, but not yet sufficient to cross the frontier. In the next two years, we expect to receive 100 times more data, allowing access to the rare events generated by quark and gluon scattering at very short distances.

Transverse view of the LHC detector ATLAS, the size of a 10-story building. Image source: ATLAS Experiment © 2011 CERN. (www.atlas.ch/muon.html)

Transverse view of the LHC detector Compact Muon Spectrometer (CMS) showing the systems of magnets used to bend the trajectories of muons in order to measure the muon momentum. CMS is the size of a 5-story building. Image source: CERN. © CERN. (http://public.web.cern.ch/press/PressReleases/Releases2006/PR10.06E.html)

The first sample of LHC data has already generated a sheaf of scientific papers. Here, I would like to show one of these results, the first mass spectrum of muon pairs.

To begin, what is a muon? We are all familiar with the electron, the particle that orbits an atomic nucleus and gives atoms their size and chemical properties. For reasons that we do not understand, Nature gives us two more particles with the exactly the same interactions as the electron but with larger masses. These are the muon, with a mass 200 times larger than that of the electron, and the tau, with a mass 3400 times larger. Each of these particle, like the electron, has an antiparticle of the same mass and the opposite, positive, charge. Both particles decay to electrons and invisible neutrinos. The tau has a lifetime of a tenth of a picosecond, so in an experiment, we see only its decay products. A muon at rest has a lifetime of 2 microseconds. But a particle moving at close to the speed of light can go 600 meters in that time. In addition, Einstein’s special relativity slows the muon’s internal clock, so typical muons produced at the LHC go 100 times farther before they decay. The interactions of muons with matter are relatively weak, so they easily penetrate meters of iron. Muons, then, are seen in the LHC detectors as stable particles making definite, straight tracks that pass through the whole detector. By applying magnetic fields, we can bend these tracks slightly and use the amount of bending to measure the momentum and energy of the muon.

The two largest LHC detectors, called ATLAS and CMS, are designed to optimize the study of muons over a large range in energy. Transverse views of the two detectors[1, 2] are shown in Fig 1. The proton beams enter from the two sides in a direction perpendicular to the plane of the page. The beams collider in the center of each detector. Both detectors have central regions with strong magnetic fields pointing out of the paper. These bend the muons, causing the tracks to curve in the plane of the paper, in one direction for muons, in the opposite direction for antimuons. In CMS, the magnetic field lines return through an iron shell in the outer region of the detector, shown in pink in the figure. The muons bend in the opposite direction as they pass through this shell. The inner momentum measurement is most accurate for low-energy muons, the outer one is most accurate for high-energy muons, so the combination of the two measurements gives high accuracy over the whole range. ATLAS has a special array of magnets in its outer region that create a magnetic field whose lines wrap around the detector. These are shown as the grey circles in the figure. Actually, these are tubes running along the detector parallel to the beam. In this field, the muons bend out of the plane of the paper, forward for muons, backward for antimuons. The effect is the same, giving a uniform accuracy of muon momentum measurement from the lowest values to energies comparable to the beam energies.

Many elementary particles decay to a muon and an antimuon. We have known since the 1960’s that protons, neutrinos, and all other particles that interact with the strong or nuclear interaction are built from more elementary particles called quarks. Protons and neutrons are bound states of three quarks; &pi and K mesons are bound states with one quark and one antiquark. Particles made of a quark and an antiquark of the same type are naturally unstable. After enough time (measured in billionths of trillionths of seconds), the quark and antiquark find one another and annihilate. The energy from the annihilation can materialize into any other particle-antiparticle pair, often, into a pair of muons. The muons then fly apart and register as tracks in a detector.

Mass distribution of muon-antimuon system, as measured by ATLAS from their 2010 data sample. Source: ATLAS Experiment © 2011 CERN. (from: https://twiki.cern.ch/twiki/bin/view/AtlasPublic/MuonPerformancePublicPlots)

Mass distribution of muon-antimuon system measured by CMS detectors from their 2010 data sample. Source: CERN, © CERN. (from https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsMUO)

By observing the muon pair, we can identify the particle that it came from. In special relativity, the mass of a particle is proportional to the energy of the particle at rest: E = mc2. We can compute the mass m of a moving particle by measuring both the energy and the momentum. For this case, Einstein’s formula reads
(mc2) = E2 &minus (→pc)2,
where E is the energy in motion, →p is the momentum, and c is the speed of light. Energy and momentum are conserved, so the total energy and total momentum of the muon and antimuon will be the same as that of the original particle. Then, if we have a muon and antimuon pair with energies and momenta (E&minus, →p&minus) and (E+,→p+), the particle that decayed to this pair must have had a mass m given by
m = √{(E&minus + E+)2/c4 &minus (→p&minus +→p+)2/c2}.
The formula above applies to the muon as well, so we can simplify this to
m = √{ 2 m&mu2 + 2 E&minusE+/c4 &minus 2→p &minus . → p+/c2}.

Notice that, for the momenta, we have vector addition. This means that, if the muon and antimuon

An event from CMS showing a muon-antimuon pair (red tracks) with a combined mass close to the expected mass of the Z boson. Image source: CERN © CERN. (from https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResults)

In Fig. 2, I show the plots of muon pair mass that have been produced by the ATLAS and CMS experiments on the basis of their 2010 data[3,4]. These plots show the whole history of particle physics. At low mass, we see the &eta, &rho, and &phi mesons, bound states of the light quarks u, d and s with their antiparticles. The &eta and &rho were discovered in 1961, the &phi in 1963. At intermediate mass values, we see the J/&phi meson, discovered in 1974, a bound state of the heavy c or charmed quark and its antiparticle. Nearby, we see an excited state of this system, called the &psi’. Somewhat higher, there is a peak for the ϒ meson, a bound state of the still heavier b or bottom quark and its antiquark, and subsidiary peaks for the ϒ excited states. These were discovered in 1977. The last prominent peak in the data is not a quark-antiquark bound state but, rather, a particle of a new type. It is the Z boson, one of the elementary quanta of the weak interactions that mediate radioactive decays. The Z is, as far as we know now, a truly elementary particle, with a mass more than 90 times the mass of the proton. This particle was discovered in 1983. Figure 3 shows a Z &rarr &mu&minus &mu+ event recorded by CMS. The straight red tracks are the muons[5]. The wide angle between the two energetic muons indicates that the parent was a very high-mass particle.

Are there more peaks in this plot beyond the Z? As you see, the LHC has not yet given us enough data to answer this question. According to our current knowledge in particle physics, there are no more peaks to be expected. The heaviest known quark, the top quark, has too short a lifetime even to make short-lived bound states like the ϒ. So the conventional expectation would be that the mass plot should be featureless and should decrease beyond the Z.

But this is only the prediction from our current knowledge. This knowledge extends only to masses just a few times the mass of the Z boson. In the next two years, the LHC should give us more than 100 times more data to add to this plot. That will allow us to search for peaks at masses 20 times higher or more – and no one knows what we will find.

Particle physicists will be anxiously scanning these plots as the data accumulates. You can follow them, also, at the public Web sites of the experiments[6, 7]. I encourage you to enjoy the exciting results that will emerge from the LHC.



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