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Section 6: The Weak Force and Flavor Changes

Neither the strong force nor the electromagnetic force can explain the fact that a neutron can decay into a proton, electron, and an (invisible) antineutrino. For example carbon–14, an atom of carbon that has six protons and eight neutrons, decays to nitrogen–14 by switching a neutron to a proton and emitting an electron and antineutrino. Such a radioactive decay (called beta decay) led Wolfgang Pauli to postulate the neutrino in 1930 and Enrico Fermi to develop a working predictive theory of the particle three years later, leading eventually to its discovery by Clyde Cowan, Jr. and Frederick Reines in 1956. For our purposes here, what is important is that this decay is mediated by a new force carrier—that of the weak force.

An example of beta decay.

Figure 19: An example of beta decay.

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As with QED and QCD, the weak force carriers are bosons that can be emitted and absorbed by matter particles. They are the electrically charged W+ and W-, and the electrically neutral Z0. There are many properties that distinguish the weak force from the electromagnetic and strong forces, not the least of which is the fact that it is the only force that can mediate the decay of fundamental particles. Like the strong force, the theory of the weak force first appeared in the 1930s as a very different theory.

Fermi theory and heavy force carriers

Fermi constructed his theory of beta decay in 1933, which involved a direct interaction between the proton, neutron, electron,and antineutrino (quarks were decades away from being postulated at that point). Fermi's theory could be extended to other particles as well, and successfully describes the decay of the muon to an electron and neutrinos with high accuracy. However, while the strength of QED (its coupling) was a pure number, the strength of the Fermi interaction depended on a coupling that had the units of one over energy squared. The value of the Fermi coupling (often labeled GF) thus suggested a new mass/energy scale in nature associated with its experimental value: roughly 250 times the proton mass (or ~250 GeV).

In 1961, a young Sheldon Glashow fresh out of graduate school, motivated by experimental data at the time, and inspired by his advisor Julian Schwinger's work on Yang-Mills theory, proposed a set of force carriers for the weak interactions. They were the W and Z bosons, and had the masses necessary to reproduce the success of Fermi theory. The massive force carriers are a distinguishing feature of the weak force when compared with the massless photon and essentially massless (yet confined) gluon. Thus, when matter is interacting via the weak force at low energies, the virtual W and Z can only exist for a very short time due to the uncertainty principle, making the weak interactions an extremely short-ranged force.

Another consequence of heavy force carriers is the fact that it requires a large amount of energy to produce them. The energy scale required is associated with their mass (Mwc2) and is often called the weak scale. Thus, it was only in the early 1980s, nearly a century after seeing the carriers' effects in the form of radioactivity, that scientists finally discovered the W and Z particles at the UA1 experiment at CERN.

Neutron decay from the inside.

Figure 20: Neutron decay from the inside.

Source: © David Kaplan. More info

Force of change

An equally important difference between the weak force and the others is that when some of the force carriers are emitted or absorbed (specifically, the W+/-), the particle doing the emitting/absorbing changes its flavor. For example, if an up quark emits a W+, it changes into a down quark. By contrast, the electron stays an electron after it emits or absorbs QED's photon. And while the gluon of QCD changes the color of the quark from which it is emitted, the underlying symmetry of QCD makes quarks of different colors indistinguishable. The weak force does not possess such a symmetry because its force carrier, the W, changes one fermion into a distinctly different one. In our example above, the up and down quarks have different masses and electric charges. However, physicists have ample theoretical and indirect experimental evidence that the underlying theory has a true symmetry. But that symmetry is dynamically broken because of the properties of the vacuum, as we shall see later on.

That fact that the W boson changes the flavor of the matter particle has an important physical implication: The weak force is not only responsible for interactions between particles, but it also allows heavy particles to decay. Because the weak force is the only one that changes quarks' flavors, many decays in the Standard Model, such as that of the heavy top quark, could not happen without it. In its absence, all six quark flavors would be stable, as would the muon and the tau particles. In such a universe, stable matter would consist of a much larger array of fundamental particles, rather than the three (up and down quarks and the electron) that make up matter in our universe. In such a universe, it would have taken much less energy to discover the three generations, as we would simply detect them. As it is, we need enough energy to produce them, and even then they decay rapidly and we only get to see their byproducts.

Weak charge?

In the case of QED and QCD, the particles carried the associated charges that could emit or absorb the force carriers. QED has one kind of charge (plus its opposite, or conjugate charge), which is carried by all fundamental particles except neutrinos. In QCD, there are three kinds of color charge (and their conjugates) which are only carried by quarks. Therefore, only quarks exchange gluons. In the case of the weak force, all matter particles interact with and thus can exchange the W and Z particles—but then what exactly is weak charge?

The total amount of electric charge is conserved, even in complicated interactions like this one.

Figure 21: The total amount of electric charge is conserved, even in complicated interactions like this one.

Source: © David Kaplan. More info

An important characteristic feature of electromagnetic charge is that it is conserved. This means, for any physical process, the total amount of positive charge minus the total amount of negative charge in any system never changes, assuming no charge enters or leaves the system. Thus, positive and negative charge can annihilate each other, or be created in pairs, but a positive charge alone can never be destroyed. Similarly for the strong force, the total amount of color charge minus the total anti-color charge typically stays the same, there is one subtlety. In principle, color charge can also be annihilated in threes, except for the fact that baryon number—the number of baryons like protons and neutrons—is almost exactly conserved as well. This makes color disappearance so rare that it has never been seen.

Weak charge, in this way, does not exist—there is no conserved quantity associated with the weak force like there is for the other two. There is a tight connection between conserved quantities and symmetries. Thus, the fact that there is no conserved charge for the weak force is again suggestive of a broken symmetry.

Look in the mirror—it's not us

For the weak force, an electron's mirror image is a different type of object.

Figure 22: For the weak force, an electron's mirror image is a different type of object.

Source: © David Kaplan. More info

The weak interactions violate two more symmetries that the strong and electromagnetic forces preserve. As discussed in the previous unit, these are parity (P) and charge conjugation (C). The more striking one is parity. A theory with a parity symmetry is one in which any process or interaction that occurs (say particles scattering off each other, or a particle decaying), its exact mirror image also occurs with the same probability. One might think that such a symmetry must obviously exist in Nature. However, it turns out that the weak interactions maximally violate this symmetry.

As a physical example, if the W- particle is produced at rest, it will—with roughly 10% probability—decay into an electron and an antineutrino. What is remarkable about this decay is that the electron that comes out is almost always left-handed. A left-handed (right-handed) particle is one in which when viewed along the direction it is moving, its spin is in the counterclockwise (clockwise) direction. It is this fact that violates parity symmetry, as the mirror image of a left-handed particle is a right-handed particle.

Spin flipping on the train.

Figure 23: Spin flipping on the train.

Source: © David Kaplan. More info

The electron mass is very tiny compared to that of the W boson. It turns out that the ability of the W- to decay into a right-handed electron depends on the electron having a mass. If the mass of the electron were zero in the Standard Model, the W- would only decay into left-handed electrons. It is the mass, in fact, that connects the left-handed and right-handed electrons as two parts of the same particle. To see why, imagine an electron moving with a left-handed spin. If you were to travel in the same direction as the electron, but faster, then the electron to you would look as if it were moving in the other direction, but its spin would be in the original direction. Thus, you would now see a right-handed electron. However, if the electron had no mass, Einstein's relativity would predict that it moves at the speed of light (like the photon), and you would never be able to catch up to it. Thus, the left-handed massless electron would always look left-handed.

The mixing of the left- and right-handed electrons (and other particles) is again a result of a symmetry breaking. The symmetry is sometimes called chiral symmetry, from the Greek word chiral, meaning hand. The masses of the force carriers, the flavor-changing nature of the weak force, and the masses of all matter particles, all have a single origin in the Standard Model of particle physics—the Higgs mechanism—as we will see in the next section.


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