“The Standard Model, as I have explained, requires a Higgs field: a field with a nonzero value everywhere that allows the matter (fermion) fields and W and Z bosons to gain masses and that creates electromagnetism by mixing up the weak and hypercharge forces (breaking their gauge symmetries).”
“To understand this problem, recall two facts about quantum fields. First, the mass of a field tells you its natural frequency. Like a guitar string, the field has a frequency at which it wants to oscillate. If an excitation of the field has the right energy and momentum—adding up to the mass—the field will sustain that oscillation, instead of dying away. So when we say the Higgs mass is 125 GeV, we’re saying that the Higgs field likes to oscillate with a frequency related to this particular energy.”
“Second, fields can couple. Think again of guitar strings: plucking one can induce vibrations in another. Likewise, an excitation in one field can leak over to other fields (indeed, this is how particles are created and annihilated). But the presence of other fields can also meddle with the parameters of a field, including the mass parameter. That is, the existence of other quantum fields in the Universe can make particles heavier or lighter.”
“The natural scale of the Higgs should be near the Planck scale, because of the corrections to the Higgs mass that would come from a particle at the Planck scale. And yet it is not. Thus, we speak of the Naturalness or Hierarchy Problem in the Standard Model: Why is there this vast separation between the Higgs and the Planck scales?”
“Just as we would suspect collaboration if two people picked nearly identical thirty-eight-digit numbers, we suspect that the Universe is somehow conspiring to keep the Higgs mass down. If there were no mechanism—no “conspiracy”—to keep the Higgs mass so small, we would reduce to claiming that there was a ridiculous amount of fine-tuning, allowing the bare mass and the Planck energy corrections to cancel. Theorists have developed many forms that this conspiracy of cancellation could take. The best known is called supersymmetry (often abbreviated SUSY).”
“Supersymmetry is a very elegant solution to the Naturalness problem. It is a straightforward extension of the symmetry arguments that led to our understanding of the forces of Nature as “gauge symmetries.” It has numerous technical and phenomenological arguments going for it, beyond the ones I’ve described here. The main problem with it is that it cannot be a perfect symmetry of Nature. For example, there is no selectron with the same mass as the electron. If there were, we would have found it a long time ago.”
“Other lines of argument lead to the same conclusion: something is missing in the Universe. There needs to be some particle that is not electrically charged (so it doesn’t interact with light), does not interact via the strong nuclear force, and is not any of the known particles in the Standard Model. For example, the ghostly neutrino cannot be dark matter because neutrino masses are tiny and you cannot cram enough of them into a galaxy to make up all the missing mass. In all, there needs to be about five times as much of this dark matter in the Universe as all the normal matter that you and I and every star you can see are made of.”
“The Universe was born in some moment of very high densities and temperatures—the Big Bang. In those early moments, there were no atoms, or even protons, just a dense soup of all the fundamental particles in the Standard Model, smashing into each other, producing new particles and antiparticles, which then quickly smashed into each other, annihilating again. Thinking in terms of fields, there was so much energy available that every field that existed was alive with oscillations, and those oscillations were continually jumping from one field to another.”
“Imagine now some new field, something beyond the Standard Model—the dark matter field. This field too would be singing with energy, and if it were coupled to the fields of the Standard Model, energy would be exchanged between the dark matter and the known particles. Pairs of excitations of this field—new dark matter—could be produced whenever Standard Model particles smashed into each other, and pairs of dark matter could annihilate away into pairs of various Standard Model particles.”
“But the Universe expanded. And as it did so, it cooled. The excitations of all the quantum fields became less and less energetic. If the dark matter field exists and has a large mass, then as the Standard Model fields cool, it will be harder and harder for two excitations of the Standard Model (two particles) to find enough energy in a collision to make a new pair of dark matter particles.”
“Similarly, dark matter would become rarer and rarer in the Universe, and so the odds of two dark matter particles “finding” each other to annihilate away would also drop. Thus, both production and destruction of dark matter would cease—it would have “frozen out,” and the Universe would be left with some relic population of dark matter from those first microseconds after the Big Bang.”
“The amount of dark matter left over would indicate how “easy” it was for two dark matter particles to smash into each other and annihilate. The more strongly coupled the dark matter quantum field, the more often this would happen, even as the Universe got cold and empty as it expanded. So there would be less dark matter today.”
“If you surmise that dark matter happens to interact via the weak nuclear force, and has a mass around the scale of the Higgs mass (the scale where the symmetry of the weak nuclear force is broken), you can predict the amount of dark matter left over from the Big Bang. And (drumroll), under these assumptions you get pretty much exactly the right amount of dark matter we see in the Universe today. Thus we speak of “Weakly Interacting Massive Particles” (WIMPs) and the “WIMP Miracle”: namely, that this weak nuclear force that we already knew was interesting (involving a Higgs boson and everything) also seems to allow a solution to the dark matter problem. Interestingly, one of the attractions of supersymmetry is that it contains particles that are viable candidates for dark matter—combinations of the photino, zino, and higgsinos, which we usually call neutralinos.”
“WIMPs provide one theory about what the right physics might be. Dark matter can be made in other ways as well. But the interesting thing is that right now we have a machine built to produce a lot of particles that have weak nuclear force interactions and masses around 100 or so GeV. Just as the LHC could push enough energy into the Higgs field to make enough particles for ATLAS and CMS to claim discovery, so too it might be able to recreate some aspect of the moments after the Big Bang and start pumping out pairs of dark matter particles.”