Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World - Lisa Randall (2011)



The Standard Model of particle physics, compactly categorizes our current understanding of elementary particles and their interactions (summarized in Figure 40).53 It includes particles like the up and down quarks and the electrons that sit at the core of familiar matter, but it also accommodates a number of other heavier particles that interact through the same forces, but which are not commonly found in nature—particles that we can study carefully only at high-energy collider experiments. Most of the Standard Model’s ingredients, such as the particles the LHC is currently studying, were rather thoroughly buried until the clever experimental and theoretical insights that revealed them in the latter half of the twentieth century.

At the LHC, the ATLAS and CMS experiments are designed to detect and identify Standard Model particles. The real goal, of course, is to go beyond what we already know—to find new ingredients or forces that address outstanding mysteries. But to do so, physicists need to be able to distinguish Standard Model background events and identify the Standard Model particles into which any exotic new particles might decay. Experimenters at the LHC are like detectives who analyze data to piece together clues and ascertain what was there. They will be able to deduce the existence of something new only after they have ruled out everything that is familiar.

Having toured the general-purpose experiments, we will now revisit them in this chapter to better understand how LHC physicists identify individual particles. A bit more familiarity with the particle physics status quo and how Standard Model particles are found will help when we discuss the discovery potential of the LHC in Part IV.


Particles are left-handed or right-handed according to which way they appear to spin about the axis of their direction of motion.


FIGURE 40 ] The elements of the Standard Model of particle physics, with masses shown. Also shown are separate left- and right-handed particles. The weak force that changes particle type acts only on the left-handed ones.


Particle physicists divide the elementary matter particles of the Standard Model into two categories. One type is called leptons, which includes particles such as the electron that don’t experience the strong nuclear force. The Standard Model also includes two heavier versions of the electron, which have the same charge but much bigger masses, and which are called the muon and the tau. It turns out that every Standard Model matter particle has three versions, all with the same charge but with each successive generation heavier than the next. We don’t know why there should be three versions of these particles, all with the same charges. The Nobel Prize—winning physicist Isidor Isaac Rabi, on hearing of the muon’s existence, notably expressed his bafflement with the exclamation, “Who ordered that?”

The lighter leptons are the easiest to find. Although both electrons and photons deposit energy in the electromagnetic calorimeter, because the electron is charged and the photon is not, the electron is readily distinguished from a photon. Only an electron leaves a a track in the inner detector before depositing energy in the ECAL.

Muons too are relatively straightforward to identify. Like all the other heavier Standard Model particles, muons decay so quickly that they aren’t found in ordinary matter, so we rarely find them on Earth. However, muons live long enough to travel to the outer reaches of the detectors before they decay. They therefore leave long clearly visible tracks throughout that experimenters can match up from the inner detector to the outer muon chambers. Because muons are the only Standard Model particle to reach these outer detectors and leave a visible signal, they are easy to pick out.

Though visible, taus are not quite so simple to find. The tau is a charged lepton like the electrons and the muon, but it is even heavier. Like most heavy particles, it too is unstable, which is to say it decays—leaving only other particles in its wake. A tau rapidly decays into a lighter charged lepton and two particles called neutrinos or into a single neutrino along with a particle called a pion that experiences the strong force. Experimenters study these decay products—the particles the initial particle decayed into—to figure out whether a heavy decaying particle was responsible for their presence and if so, what its properties are. Even though the tau doesn’t directly leave a track, all the information the experiments record about the decay products helps identify it and its properties.

The electron, muon, and the even heavier tau lepton have charge—1, the opposite charge of a positively charged proton. Colliders also produce the antiparticles associated with these charged leptons—the positron, antimuon, and antitau. These antiparticles carry charge +1, and leave similar-looking tracks in the detectors. However, because of their opposite charges, they curve in the opposite direction in the presence of a magnetic field.

In addition to the three types of charged leptons just described, the Standard Model also includes neutrinos, which are leptons that don’t carry electric charge at all. Whereas the three charged leptons experience both the force of electromagnetism and the weak nuclear force, neutrinos have zero charge and are therefore impervious to the electric force. Until the 1990s, experimental results indicated that neutrinos had zero mass. One of the most interesting discoveries in that decade was the extremely tiny but nonvanishing masses of neutrinos, which provided important information about the structure of the Standard Model.

Although neutrinos are very light and therefore well within the energy reach of colliders, they are impossible to directly detect at the LHC because they have no electric charge and therefore interact only weakly—so weakly that although more than 50 trillion neutrinos from the Sun pass through you every second, you really have no idea until someone tells you.

In spite of their invisibility, the physicist Wolfgang Pauli conjectured neutrinos existed as a “desperate way out” to explain where the energy went when neutrons decay. Without the neutrino carrying off some of the energy, it appeared that energy conservation was violated by this process, since the proton and the electron that were detected after the decay didn’t add up to the same energy as the neutron that went in. Even well-established physicists such as Niels Bohr were willing at the time to sacrifice their principles and accept that energy could be lost. Pauli was more faithful to known physical premises and conjectured instead that energy is indeed conserved, but experimenters just couldn’t see the charge-neutral particle that carried the remaining energy off. He turned out to be right.

Pauli named his then-hypothetical particle the neutron, but the name has since been used for other purposes—namely, the neutral partner of the proton that sits inside a nucleus. So Enrico Fermi, the Italian physicist who developed the theory of the weak interactions but is perhaps best known for helping develop the first nuclear reactor, gave it the cutish name neutrino, which in Italian means “little neutron.” It’s of course not a little neutron, but—like a neutron—it carries no electric charge. And a neutrino is indeed much lighter than a neutron.

As with all the other types of Standard Model particles, three types of neutrinos exist. Each charged lepton—the electron, muon, and tau—has an associated neutrino that it interacts with via the weak nuclear force”54

We have already seen how to find electrons, muons, and taus. So the remaining experimental question about leptons is how experimenters find neutrinos. Because neutrinos have no electric charge and interact so weakly, they escape the detector without leaving any trace at all. How does anyone at the LHC tell they were there?

Momentum (which is velocity times mass when particles move slowly but is more like energy moving in a particular direction when the particle travels near the speed of light) is conserved in all directions. As with energy, we have never found any evidence that momentum can be lost. So if the momentum of the particles measured in the detector is less than the momentum that went in, some other particle (or particles) must have escaped, carrying away the missing momentum in the process. This type of logic led Pauli to deduce the existence of neutrinos in the first place (in his case in nuclear beta decay), and to this day it’s how we learn of the existence of weakly interacting particles that seem to be invisible.

At hadron colliders, experimenters measure all the momentum transverse to the beam and calculate if something is missing. They focus on momentum transverse to the beam since a lot of momentum is carried away by particles that head down the beam pipe and is therefore too difficult to keep track of. The momentum perpendicular to the initial protons is much simpler to measure and account for.

Since the initial collision has essentially zero total momentum transverse to the beam, so too should the final state. So if measurements don’t agree with expectations, experimenters can “detect” that something is missing. The only remaining question is how to distinguish which of the many potential noninteracting particles it was. For Standard Model processes, we know neutrinos will be among the undetected elements. Based on the neutrino’s known weak force interactions that we will get to shortly, physicists calculate and predict the rate at which neutrinos should be produced. In addition, physicists already know what the decay of a W boson should look like—for example, an isolated electron or muon whose transverse momentum carries energy comparable to half the W mass is fairly unique. So using momentum conservation and theoretical input, neutrinos can be “found.” Clearly, there are fewer identifying tags on these particles than ones we see directly. Only a combination of theoretical considerations and missing energy measurements can tell us what was there.

It’s important to keep such ideas in mind when we consider new discoveries. Similar considerations apply for other novel particles without any charges, or with charges so weak that they can’t be directly detected. Only a combination of missing energy and theoretical input can be used in those cases to deduce what was there. That’s why hermeticity—detecting as much momentum as possible—is so important.


We’ve now considered leptons (electrons, muons, taus, and their associated neutrinos). The remaining category of particles in the Standard Model have the name hadrons—particles that interact through the strong nuclear force. This category includes all particles made from quarks and gluons, such as protons and neutrons and other particles called pions. Hadrons have internal structure—they are bound states of quarks and gluons held together by the strong nuclear force.

However, the Standard Model doesn’t list the many possible bound states. It lists the more fundamental particles that get bound together into hadronic states—namely, the quarks and gluons. In addition to the up and down quarks that sit inside protons and neutrons, heavier quarks called charm and strange and top and bottom exist as well. As with the charged and neutral leptons, the heavier quarks have charges identical to their lighter counterparts—the up and down quarks. The heavier quarks are also not readily found in nature. Colliders are needed to study them too.

Hadrons (which interact via the strong force) look very different from leptons (which don’t) in particle collisions. That is primarily because quarks and gluons have such strong interactions that they never appear in isolation. They are always in the middle of a jet that might contain the original particle, but will always include a bunch of others that also experience the strong force. Jets don’t contain single particles, but a spray of strongly interacting particles “protecting” the initial one, as can be seen in Figure 41. Even if not present in the initial event, the strong interactions will create many new quarks and gluons from the quark or gluon that initiated the jet in the first place. Proton colliders produce a lot of jets since protons themselves are made of strongly interacting particles. Such particles produce sprays of many additional strongly interacting particles that travel alongside them. They also sometimes create quarks and gluons that go off in different directions and form their own independent jets.

The quote I used in Warped Passages from the “Jet Song” in West Side Story actually describes hadronic jets quite well:

You’re never alone,

You’re never disconnected!

You’re home with your own:

When company’s expected,

You’re well protected.


cross section view


side view

FIGURE 41 ] Jets are sprays of strongly interacting particles that develop around quarks and gluons. The picture shows their detection in trackers and the hadronic calorimeter. (Modified version of photo courtesy of CERN)

Quarks—and most gang members—won’t be found on their own, but in the midst of related strongly interacting companions.

Jets generally leave visible tracks, since some of the particles in jets are charged. And when a jet reaches the calorimeters, it deposits its energy. Careful experimental studies, as well as analytic and computer calculations, help experimenters deduce the properties of the hadrons that created the jets in the first place. Even so, strong interactions and jets make quarks and gluons more subtle. You don’t measure the quark or gluon itself, but the jet in which it resides. That makes most quark and gluon jets indistinguishable from each other. They all deposit lots of energy and leave many tracks. (See Figure 42 for a schematic of how detectors identify key Standard Model particles.)


images  Neutral particle path

images  Charged particle track

images  Lower-res charged particle track

images    Energy recorded

images     Particle shower

FIGURE 42 ] A summary of how Standard Model particles are distinguished in the detectors. Neutral particles don’t register in the trackers. Both charged and neutral hadrons can leave small deposits in the ECAL but deposit most of their energy in the HCAL. Muons go through to the outer detector.

Even after measuring a jet’s properties, telling which of the different quarks or gluons initiated the jets is challenging if not impossible. The bottom quark—which is the heaviest quark with the same charge as the down (as well as the heavier strange) quark—is an exception to the rule. The reason the bottom quark is special is that it decays more slowly than the other quarks. Other unstable quarks decay essentially immediately after they are produced, so their decay products appear to start their tracks at the interaction point where the protons collided. Bottom quarks, on the other hand, last long enough (about one and a half picoseconds, or enough time to travel about a half millimeter at the light speed at which they travel) to leave a track a noticeably large distance from the interaction point. The inner silicon detectors detect this displaced vertex, as illustrated in Figure 43.


FIGURE 43 ] Hadrons made of bottom quarks live long enough to leave a visible track in the detector before decaying into other charged particles. This can leave a kink in the silicon vertex detectors, which can be used to identify bottom quarks. The ones here came from top quark decays.

When experimenters reconstruct a track from a bottom quark decay, it doesn’t extend back to the initial interaction point in the center of the event. Instead the track seems to originate from the place in the inner tracker where the bottom quark decayed, leaving a kink in tracks that is the juncture between the bottom quark that came in and the decay product that came out.55 With the fine segmentation of the silicon detectors, experimenters can view detailed tracks in the region close to the beam, and successfully identify bottom quarks a significant fraction of the time.

The other type of quark that is distinctive from an experimental vantage point is the top quark, which is special because it is so heavy. The top quark is the heaviest of the three quarks that have the same charge as the up quark (the other one is called charm). Its mass is about 40 times heavier than the differently charged bottom quark and more than 30,000 times the mass of the up quark, which has the same charge as the top.

Top quarks are sufficiently heavy that their decay products leave distinct tracks. When lighter quarks decay, the decay products, like the initial particle, travel so close to the speed of light that they are rushed along together into what appears to be a single jet—even if the jet had its origin in two or more distinct decay products. Unless they are extremely energetic, top quarks, on the other hand, visibly decay into bottom quarks and W bosons (the charged weak gauge bosons) and can be identified by finding both of them. Because the top quark’s heavy mass implies that it interacts most closely with the Higgs particle and other particles involved in weak scale physics that we are hoping to soon understand, the properties of top quarks and their interactions might provide valuable clues to physical theories underlying the Standard Model.


Before we finish discussing how to identify Standard Model particles, the final particles to consider are the weak gauge bosons, the two Ws and the Z, that communicate the weak nuclear force. The weak gauge bosons have the peculiar property that, unlike the photon or gluons, they have nonvanishing mass. The masses associated with the weak gauge bosons that communicate the weak force pose some major fundamental mysteries. The origin of this mass—as with the masses of the other elementary particles this chapter has discussed—is rooted in the Higgs mechanism that we will get to shortly.

Because the Ws and Z are heavy, these gauge bosons decay. This means that the W and Z bosons, as with the top quark and other un-stable heavy particles, can be identified only by finding the particles into which they decay. Because heavy new particles are also likely to be unstable, we’ll use the weak gauge boson decays to exemplify one other interesting property of decaying particles.

W boson interacts with all particles that are sensitive to the weak force (namely, all the particles we have discussed). That gives the W plenty of decay options. It can decay into any charged lepton (the electron, the muon, or the tau) and their associated neutrino. It can also decay into an up and down quark or into a charm and strange quark pair, as illustrated in Figure 44.


FIGURE 44 ] The W boson can decay into a charged lepton and its associated neutrino, or into an up and down quark, or a charm and strange quark. In reality, the physical particles are superpositions of different types of quarks or neutrinos. This allows the W to some-times decay into particles from different generations simultaneously.

Particle masses are also critical in determining allowed decays. A particle can decay only into other particles whose masses add up to a smaller mass than the initial particle. Although the W also interacts with the top and bottom quarks, the top quark is heavier than the W, so this decay isn’t allowed.56

Let’s consider the W decaying into two quarks, since in that case the experimenters measure both decay products (not true for lepton and neutrino since the neutrino is “missing”). Because energy and momentum are conserved, measuring the total energy and momentum of both final state quarks tells us the energy and momentum of the particle that decayed into them, namely, the W.

At this point both Einstein’s special theory of relativity combined with quantum mechanics make the story a bit more interesting. Einstein’s special theory of relativity tells us how mass is related to energy and momentum. Most people know the shorthand E = mc2. This formula holds for particles at rest if m is interpreted as m0, the intrinsic mass of a particle when it’s stationary. Once particles move, they have momentum and the more complete formula E2-p2c2m02c4 comes into play.57 With this formula, the energy and momentum let experimenters deduce the particle’s mass, even when the initial particle has long since disappeared via its decay. Experimenters add up all the momentum and energy and apply this equation. The initial mass is then determined.

The reason quantum mechanics comes into play is more subtle. A particle won’t always seem to have exactly its real and true mass. Because the particle can decay, the quantum mechanical uncertainty relation, which says that it takes infinitely long to precisely measure energy, tells us that the energy for any particle that doesn’t live forever can’t be precisely known. The energy can be off by an amount that will be bigger when the decay is faster and the lifetime shorter. This means that in any given measurement, the mass can be close to—but not precisely—the true average value. Only with many measurements can experimenters deduce both the mass—the value that is most probable and to which the average will converge—and the lifetime, since it is the length of time a particle exists before decaying that determines the spread in measured masses. (See Figure 45.) This is true for the W boson, and also for any other decaying particle.


FIGURE 45 ] Measurements of decaying particles center around their true masses, but allow for a spread of mass values according to their lifetime. The figure shows this for the W gauge boson.

When experimenters piece together what they measure, using the methods this chapter has described, they might find a Standard Model particle. (See Figure 46 for a summary of Standard Model particles and their properties.)58But they might also end up identifying something entirely new. The hope is that the LHC will create new exotic particles that will yield insights into the underlying nature of matter—or even space itself. The next part of the book explores some of the more interesting possibilities.


FIGURE 46 ] A summary of Standard Model particles, organized according to type and mass. The gray circles (sometimes inside the squares) give particle masses. We see the mysterious variety of the elements of the Standard Model.