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Section 7: Electroweak Unification and the Higgs

While the W particles are force carriers of the weak force, they themselves carry charges under the electromagnetic force. While it is not so strange that force carriers are themselves charged—gluons carry color charges, for example—the fact that it is electromagnetic charge suggests that QED and the weak force are connected. Glashow's theory of the weak force took this into account by allowing for a mixing between the weak force and the electromagnetic force. The amount of mixing is labeled by a measurable parameter, .

Unifying forces

The full theory of electroweak forces includes four force carriers: W+, W-, and two uncharged particles that mix at low energies—that is, they evolve into each other as they travel. This mixing is analogous to the mixing of neutrinos with one another discussed in the previous unit. One mixture is the massless photon, while the other combination is the Z. So at high energies, when all particles move at nearly the speed of light (and masses can be ignored), QED and the weak interactions unify into a single theory that we call the electroweak theory. A theory with four massless force carriers has a symmetry that is broken in a theory where three of them have masses. In fact, the Ws and Z have different masses. Glashow put these masses into the theory by hand, but did not explain their origin.

The Z particle at SLAC.

Figure 24: The Z particle at SLAC.

Source: © SLAC National Accelerator Laboratory. More info

The single mixing parameter predicts many different observable phenomena in the weak interactions. First, it gives the ratio of the W and Z masses (it is the cosine of ). It also gives the ratio of the coupling strength of the electromagnetic and weak forces (the sine of ). In addition, many other measurable quantities, such as how often electrons or muons or quarks are spinning one way versus another when they come from a decaying Z particle, depend on the single mixing parameter. Thus, the way to test this theory is to measure all of these things and see if you get the same number for the one parameter.

Testing of the electroweak theory has been an integral part of particle physics experimental research from the late 1980s until today. For example, teams at LEP (the Large Electron-Positron collider, which preceded the Large Hadron Collider (LHC) at CERN) produced 17 million Z bosons and watched them decay in different ways, thus measuring their properties very precisely, and putting limits on possible theories beyond the Standard Model. The measurements have been so precise that they needed an intensive program on the theoretical side to calculate the small quantum effects (loop diagrams) so theory and experiment could be compared at similar accuracy.

A sickness and a cure

While the electroweak theory could successfully account for what was observed experimentally at the time of its inception, one could imagine an experiment that could not be explained. If one takes this theory and tries to compute what happens when Standard Model particles scatter at very high energies (above 1 TeV) using Feynman diagrams, one gets nonsense. Nonsense looks like, for example, probabilities greater than 100%, measurable quantities predicted to be infinity, or simply approximations where the next correction to a calculation is always bigger than the last. If a theory produces nonsense when trying to predict a physical result, it is the wrong theory.

A "fix" to a theory can be as simple as a single new field (and therefore, particle). We need a particle to help Glashow's theory, so we'll call it H. If a particle like H exists, and it interacts with the known particles, then it must be included in the Feynman diagrams we use to calculate things like scattering cross sections. Thus, though we may never have seen such a particle, its virtual effects change the results of the calculations. Introducing H in the right way changes the results of the scattering calculation and gives sensible results.

Scattering of W particles in Feynman diagrams.

Figure 25: Scattering of W particles in Feynman diagrams.

Source: © David Kaplan. More info

In the mid-1960s, a number of physicists, including Scottish physicist Peter Higgs, wrote down theories in which a force carrier could get a mass due to the existence of a new field. In 1967, Steven Weinberg (and independently, Abdus Salam), incorporated this effect into Glashow's electroweak theory producing a consistent, unified electroweak theory. It included a new particle, dubbed the Higgs boson, which, when included in the scattering calculations, completed a new theory—the Standard Model—which made sensible predictions even for very high-energy scattering.

A mechanism for mass

The way the Higgs field gives masses to the W and Z particles, and all other fundamental particles of the Standard Model (the Higgs mechanism), is subtle. The Higgs field—which like all fields lives everywhere in space—is in a different phase than other fields in the Standard Model. Because the Higgs field interacts with nearly all other particles, and the Higgs field affects the vacuum, the space (vacuum) particles travel through affects them in a dramatic way: It gives them mass. The bigger the coupling between a particle and the Higgs, the bigger the effect, and thus the bigger the particle's mass.

In our earlier description of field theory, we used the analogy of waves traveling across a lake to represent particles moving through the vacuum. A stone thrown into a still lake will send ripples across the surface of the water. We can imagine those ripples as a traveling packet of energy that behaves like a particle when it is detected on the other end. Now, imagine the temperature drops and the lake freezes; waves can still exist on the surface of the ice, but they move at a completely different speed. So, while it is the same lake made of the same material (namely, water), the waves have very different properties. Things attempting to move through the lake (like fish) will have a very different experience trying to get through the lake. The change in the state of the lake itself is called a phase transition.

Figure 26: The Higgs mechanism is analogous to a pond freezing over.

Source: © David Kaplan. More info

This situation with the Higgs has a direct analogy with the freezing lake. At high enough temperatures, the Higgs field does not condense, which means that it takes on a constant value everywhere, and the W and Z are effectively massless. Lower temperatures can cause a transition in which the Higgs doublet condenses, the W and Z gain mass, and it becomes more difficult for them to move through the vacuum, as it is for fish in the lake, or boats on the surface when the lake freezes. In becoming massive, the W and Z absorb parts of the Higgs field. The remaining Higgs field has quantized vibrations that we call the Higgs boson that are analogous to vibrations on the lake itself. This effect bears close analogy with the theory of superconductivity that we will meet in Unit 8. In a sense, the photon in that theory picks up a mass in the superconducting material.

Not only do the weak force carriers pick up a mass in the Higgs phase, so do the fundamental fermions—quarks and leptons—of the Standard Model. Even the tiny neutrino masses require the Higgs effect in order to exist. That explains why physicists sometimes claim that the Higgs boson is the origin of mass. However, the vast majority of mass in our world comes from the mass of the proton and neutron, and thus comes from the confinement of the strong interactions. On the other hand, the Higgs mechanism is responsible for the electron's mass, which keeps it from moving at the speed of light and therefore allows atoms to exist. Thus, we can say that the Higgs is the origin of structure.

Closing in on the Higgs

There is one important parameter in the electroweak theory that has yet to be measured, and that is the mass of the Higgs boson. Throughout the 1990s and onward, a major goal of the experimental particle physics community has been to discover the Higgs boson. The LEP experiments searched for the Higgs to no avail and have put a lower limit on its mass of 114 Giga-electron-volts (GeV), or roughly 120 times the mass of the proton. For the Standard Model not to produce nonsense, the Higgs must appear in the theory at energies (and therefore at a mass) below 1,000 GeV.

Simulation of a Higgs event at the LHC.

Figure 27: Simulation of a Higgs event at the LHC.

Source: © ATLAS Experiment, CERN. More info

However, there have been stronger, more indirect ways to narrow in on the Higgs. When LEP and other experiments were testing the electroweak theory by making various measurements of the mixing angle, the theory calculations needed to be very precise, and that required the computing of more complicated Feynman diagrams. Some of these diagrams included a virtual Higgs particle, and thus the results of these calculations depend on the existence of the Higgs.

Though the effects of virtual Higgs bosons in Feynman diagrams are subtle, the experimental data is precise enough to be sensitive to the mass to the Higgs. Thus, though never seen, as of 2010, there is a prediction that the Higgs boson mass must be less than roughly 200 times the proton mass. With a successful high-energy run of the Large Hadron Collider, and with the support of a full analysis of data from the Tevatron experiments at Fermilab, we should know a lot about the Higgs boson, whether it exists, and what its mass is by 2015.


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