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Section 10: The Prospect of Grand Unification

Let's put gravity aside for the moment. Although each of the other three fundamental forces has its own very distinctive characteristics, they all share a common structure: They are all mediated by the exchange of particles, each with one unit of spin. Amazingly enough, as we ask more questions about these forces at higher energies, their differences melt away, while their similarities remain.

Unification in the young universe

In this unit, we have frequently used the phrase "at high energies" in connection with force carriers. While the term generally arises in connection with scattering, it also refers to higher temperatures. A gas at a particular temperature consists of particles moving with a specific average momentum; the higher the temperature, the higher the energy of the particles. At earlier cosmological times, the (expanding) universe was much smaller and much hotter. Thus, when we say that the forces act in such-and-such way at high energies, we also mean at high temperatures, or in the early universe.

Quarks and leptons, unified.

Figure 34: Quarks and leptons, unified.

Source: © David Kaplan. More info

At high energies, the three forces "tend toward" each other. As we have seen in previous sections, the electromagnetic coupling is bigger (stronger) at higher energies, while the strong coupling is smaller (weaker). Also at higher temperatures, the Higgs mechanism is no longer in effect (the phase change doesn't happen—the lake doesn't freeze), and thus the W and Z particles are massless, just like the gluons and photon. Thus, above the temperature associated with the Higgs energy, all three forces have massless force carriers. If one calculates the strength of each of the force’s couplings, one finds that their values are coalescing at high energies.

Other things occur at energies above the Higgs mass (which correspond to temperatures above the phase change). First, the electromagnetic and weak forces "unmix." Above that energy, the Ws are not charged under the unmixed electric charge, which is called "hypercharge." Also, under the new hypercharge, the left-handed up and down quarks have the same charge of 1/6, while the left-handed electrons and associated neutrinos have a common charge of -1/2. In addition, all of these particles' masses vanish at high temperature. Thus, some pairs of particles tend to look more and more identical as the temperature increases, thus restoring a kind of symmetry that is otherwise broken by the Higgs mechanism.

The X boson mediates the decay of the proton.

Figure 35: The X boson mediates the decay of the proton.

Source: © David Kaplan. More info

A true unification of the nongravitational forces would involve an extension of what the forces can do. For example, there are force carriers that, when emitted, change a quark from one color to another (gluons), and there are force carriers that change the electron into a neutrino (W-). One could imagine force carriers that change quarks into electrons or neutrinos. Let's call them X particles. As depicted in Figure 35, right-handed down quarks, the electron, and the electron neutrino could then all turn into one another by emitting a spin-1 particle. A symmetry would exist among these five particles if they all had precisely the same properties.

At high temperatures, all the force carriers of the Standard Model have no mass. If the X particle got its mass through another, different Higgs mechanism, it too (at temperatures above that other Higgs mass) would become massless. Thus, a true symmetry—and true unification of forces, could occur at some energy when all force carriers are massless, and the strength of each of the forces (their couplings) are the same.

The possibility of proton decay

These proposed new force carriers have one quite dramatic implication. Just as the Ws can cause the decay of particles, so would the Xs. Both quarks and leptons are now connected by the force and by our new symmetry, allowing a quark to transform into a lepton and vice versa. Therefore, the system permits new processes such as the conversion of a proton to a pion and a positron. But this process is proton decay. If the new force carriers had the same mass and couplings as the W, every atom in the entire observable universe would fall apart in a fraction of a second.

The nearly full water tank of the Super-Kamiokande experiment, which searches for nucleon decay.

Figure 36: The nearly full water tank of the Super-Kamiokande experiment, which searches for nucleon decay.

Source: © Kamioka Observatory, ICRR (Institute for Cosmic Ray Research), The University of Tokyo. More info

Perhaps the proton decays very slowly, thereby saving both the theory and the universe. Physics teams aiming to develop unified theories of forces have sought evidence of proton decay since the 1980s. The most prominent search takes place at the Super-Kamiokande (Super-K) nucleon decay experiment in Hida, Japan. This is the same experiment searching for neutrinos from the Sun, as described in the previous unit. Buried in a deep mine, the experiment uses a stainless-steel tank containing 50,000 tons of water. Photomultiplier tubes and other detectors mounted around the tank identify the so-called Cerenkov light generated when neutrinos scatter charged particles. That light provides clues that can indicate whether a proton has decayed into a positron and a pion.

Super-Kamiokande and other experiments have not discredited the possibility that the proton decays, but they have put severe restrictions on the process. The current lower limit on the mass of the Xs is roughly 1015 GeV. Remarkably, this is roughly around the energy where the couplings get close to each other.

Unification and physics at the LHC

When one takes the low-energy values of the three couplings and theoretically computes them at high scales to see if they unify, the procedure for doing that depends on what particles exist in the theory. If we assume that only the Standard Model particles exist up to very high energies, we find that the couplings run toward each other, but do not exactly meet. But for various reasons, as we will see in the next section, theorists have been looking at theories beyond the Standard Model which predict new particles at the Large Hadron Collider (LHC) energies. One such example is called supersymmetry. It predicts the existence of a host of new particles, superpartners, with the same charges as Standard Model particles, but different spins. In 1991, a new accurate measurement was made of the couplings in the electroweak theory, which allowed for precise extrapolation of the forces to high energies. When those couplings are theoretically extrapolated to high energies in a theory with superpartners just above the mass of the Higgs, one finds that the three couplings meet within the current experimental accuracy. Thus, supersymmetry makes the idea of unification more compelling and vice versa.

In the Standard Model (left), the couplings for the strong, weak and electromagnetic forces never meet, while in Supersymmetry (right), these forces unify near 1015 GeV.

Figure 37: In the Standard Model (left), the couplings for the strong, weak and electromagnetic forces never meet, while in Supersymmetry (right), these forces unify near 1015 GeV.

Source: © David Kaplan. More info

The couplings meet roughly at the energy scale of 1016 GeV. That is comfortably above the lower limit on the new force carriers that would stem from proton decay. In addition, the scale is not too far from the Planck scale below which we expect the appearance of a quantum theory of gravity, such as the string theory that we will encounter in Unit 4. This means that we may be potentially seeing a hint of the unification of all forces, including gravity.


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