Knocking on Heaven's Door - Lisa Randall [138]
By putting charge into the vacuum, the Higgs mechanism breaks the symmetry associated with the weak force. And it does so at a particular scale. The scale is set by the distribution of charges in the vacuum. At high energies, or equivalently—via quantum mechanics—small distances, particles won’t encounter any weak charge and therefore behave as if they have no mass. At small distances, or equivalently high energies, the symmetry therefore appears to be valid. At large distances, however, the weak charge acts in some respects like a frictional force that would slow the particles down. Only at low energies, or equivalently large distances, does the Higgs field seem to give particles mass.
And this is exactly as we need it to be. The dangerous interactions that wouldn’t make sense for massive particles apply only at high energies. At low energies particles can—and must, according to experiments—have mass. The Higgs mechanism, which spontaneously breaks the weak force symmetry, is the only way we know to accomplish this task.
Although we have not yet observed the particles responsible for the Higgs mechanism that is responsible for elementary particle masses, we do have experimental evidence that the Higgs mechanism applies in nature. It has already been seen many times in a completely different context—namely, in superconducting materials. Superconductivity occurs when electrons pair up and these pairs permeate a material. The so-called condensate in a superconductor consists of electron pairs that play the same role that the Higgs field does in our example above.
But rather than carry weak charge, the condensate in a superconductor carries electric charge. The condensate therefore gives mass to the photon that communicates electromagnetism inside the superconducting material. The mass screens the charge, which means that inside a superconductor, electric and magnetic fields do not reach very far. The force falls off very quickly over a short distance. Quantum mechanics and special relativity tell us that this screening distance inside a superconductor is the direct result of a photon mass that exists only inside the superconducting substrate. In these materials, electric fields can’t penetrate farther than the screening distance because in bouncing off the electron pairs that permeate the superconductor, the photon acquires a mass.
The Higgs mechanism works in a similar fashion. But rather than electron pairs (carrying electric charge) permeating the substance, we predict there is a Higgs field (that carries weak charge) that permeates the vacuum. And instead of a photon acquiring mass that screens electric charge, we find the weak gauge bosons acquire mass that screens weak charge. Because weak gauge bosons have nonzero mass, the weak force is effective only over very short distances of subnuclear size.
Since this is the only consistent way to give gauge bosons masses, physicists are fairly confident that the Higgs mechanism applies in nature. And we expect that it is responsible not just for the gauge boson masses, but for the masses of all elementary particles. We know of no other consistent theory that permits the Standard Model weakly charged particles to have mass.
This was a difficult section with several abstract concepts. The notions of a Higgs mechanism and a Higgs field are intrinsically linked to quantum field theory and particle physics and are remote from phenomena we can readily visualize. So let me briefly summarize some of the salient points. Without the Higgs mechanism, we would have to forfeit sensible high-energy predictions or particle masses. Yet both of these are essential to the correct theory. The solution is that symmetry exists in the laws of nature, but can be spontaneously broken by the nonzero value of a Higgs field. The broken symmetry of the vacuum allows Standard Model particles to have nonzero masses. However, because spontaneous symmetry breaking is associated with an energy (and length) scale, its effects are relevant only at low energies