A composite image from NASA's Chandra X-ray Observatory and Hubble Space Telescope showing the distribution of dark matter (in blue), galaxies (in orange), and hot gas (in green) at the core of a galaxy cluster 2.4 billion light years from Earth. Most of the mass in the cluster comes from dark matter. Image: NASA's Marshall Space Flight Center

Editor's Note: This is the seventh piece in an eight-part series on the search for new physics at CERN.

The discovery of the Higgs boson, announced at CERN on July 4, 2012, completed the Standard Model of particle physics. We physicists had long suspected that the Higgs existed; we spent forty years looking for it. But the LHC was designed with a “no-lose” theorem in mind. Given the design parameters of the LHC, we were confident we would discover something. If the Higgs existed, we were confident the LHC would find it, but even if it did not exist, we knew some new discovery lurked in the energy regime the LHC would probe. Without the Higgs or something to take its place, physics would go very wrong at energies that the LHC could reach. So the LHC was guaranteed to find something new—as much as anything can be guaranteed in science. And so it did: the Higgs boson, with a mass at 125 GeV.

While the Higgs boson was the main promise of the LHC, we also had (and have) great hopes for physics beyond the Standard Model. By their very nature, such possibilities are speculative. I know there is new physics to be found, but, like every other physicist, I don’t know whether the LHC can find it. Still, we have good reasons to think that it can. Even if we are wrong, a negative result—evidence of absence—would be very instructive.

What are we looking for? What might we find? I cannot possibly cover the full range of physics that the LHC might teach us, but I’ll talk about three of the better motivated and—for lack of a better word—popular ideas: additional Higgses, supersymmetric particles, and dark matter.

1. Additional Higgses

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).

With the Higgs discovery, we learned that this story is at least broadly correct. However, the story I told you is the simplest story that fits all the facts. There might well be more than a single field with the properties needed to be “the” Higgs field. Occam’s razor—which tells us not to multiply entities needlessly—might suggest that such additional Higgs fields are superfluous. But Occam’s razor has a terrible track record when it comes to the Standard Model. Why on Earth do we need three copies of every fermion? Or left-handed and right-handed particles requiring a Higgs field to gain mass in the first place? So we should keep an open mind, and at least look for more versions of Higgs-like fields. We can do this in two ways.

The first is to use the same techniques we used to find the 125 GeV Higgs, just at other masses. This is complicated by the fact that, once we add in multiple Higgs fields, the predictions of the theory are less clear. With a single Higgs, we can say exactly how much the Higgs boson couples to every particle. For example, it interacts with heavier fermions more than light ones, and in a very rigid pattern, proportional to their masses (coupling constants fix the masses). With multiple Higgses, though, it is possible for one Higgs to couple to bottom quarks more strongly than it couples to top quarks, despite the fact that top quarks are much heavier. So we have to be careful in this search, and it is much more difficult to either find or exclude new Higgses as we go.

Occam’s razor has a terrible track record when it comes to the Standard Model.

The other way is to study more carefully the one Higgs boson we have found. In the simplest version of the Higgs mechanism, the single Higgs field has a nonzero value and breaks the weak and hypercharge gauge symmetries. If we carefully measure the interactions of the 125 GeV Higgs boson with the W and Z bosons, as well as with the matter fields, we can see whether this single particle fully accounts for these broken symmetries. This is a long, slow process; it requires a huge amount of data. Right now, we can broadly say that our 125 GeV Higgs can account for at least 90 percent of the symmetry breaking, though we have not yet measured with any great detail some of the Higgs boson interactions with the heaviest fermions. (And it is likely we will never be able to directly measure the Higgs interaction with very light fermions, such as electrons, at the LHC.) Getting this 10 percent measurement down to 1 percent or less will take years of work at the LHC, including future upgrades to the high luminosity LHC, which will allow more collisions—thus more data, thus improved measurements.

2. Fixing the Higgs

Another direction of investigation is to tackle directly perhaps the most vexing question for theorists over the last four decades: Why is the Higgs so light?

Granted, for most of those forty years, we didn’t know the mass of the Higgs. But we knew that the Higgs had selected a special energy scale for the Universe: the energy scale of the Higgs field value (246 GeV), which breaks electroweak symmetry. Very roughly, we knew that the mass of the Higgs boson itself was somewhere around this scale—possibly lower, but no more than about a factor of ten higher.

This Higgs field value, which sets the mass of the W and Z bosons and the fermions, was known to be much, much lower than the other important scale of particle physics: the energy scale at which gravity becomes important. (More on this scale soon.) The puzzle for theorists is to explain why everything is so light.

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.

Think again of a vibrating string pulling and pushing on another string close to it and mechanically linked to it. Tuning a guitar changes the tension on the strings; the presence of more strings tied to the same fret could certainly change the note, even if only slightly.

For fermions, including electrons and quarks, this effect turns out to be very small. Indeed, the very baroque nature of fermion mass—involving linking left- and right-handed fields—effectively protects the mass of a fermion from being changed very much by the properties of the other fields. An electron has a small mass, and it stays small even though other particles, like photons and Higgs bosons, interact with the electron field.

However, the Higgs field is a spin-0 field, a very different beast than the spin-1/2 fermions. The Higgs is the only fundamental spin-0 field we know of in the Universe (so far, at least). And it turns out that such fields lack the kind of protection I just described. The Higgs mass feels corrections from every other field that the Higgs interacts with. And these changes are big, as big as the masses of those other fields.

More precisely, the square of the Higgs mass gets a correction equal to the squared mass of every other field that interacts with the Higgs. The physical mass squared (i.e. the square of the mass that we measure), (125 GeV)2 = 15625 GeV2, is in fact the square of the so-called bare mass plus or minus all of these corrections. The sign can be positive or negative because the quantum correction can be either additive or subtractive, depending on the details of the other fields in question.

Now, the other fundamental quantum fields we know about are pretty light: all are close to the Higgs mass. Since their corrections to the Higgs are proportional to their masses, and their masses are close to the Higgs, the impact on the Higgs mass is small. But what if there were very massive quantum fields? They too would affect the Higgs mass, and those corrections could be enormous.

Why might we suspect that very heavy fields exist? Well, we know that our entire framework of quantum field theory falls apart when we try to tackle gravity. So we suspect that there should be—at the very least—new physics and new fields with masses at the energy called the Planck energy.

Think of the Planck energy as the energy you would need to give a fundamental particle to make it collapse into a black hole. That is, it is the largest energy a particle can have before the force of gravity must be taken into account. (Because we don’t have a theory of quantum gravity, we don’t really know how this works, but we do know that beyond the Planck energy we must take it into account.) Since gravity is a very weak force compared to the other fundamental forces (when you pick an object up, the electrostatic forces in your hand counteract the entire gravitational attraction of Earth), you need a lot of energy for this to happen. As a result, the Planck scale is enormous: 1019 GeV. This is a very large amount of energy, the equivalent of about a quarter ton of TNT.

The question that has haunted theorists for decades: Why is everything is so light?

If you haven’t heard of the Planck energy, you may have heard of a related concept, the Planck length. This length, 10-35 meters, is the smallest length over which quantum field theory can be applied. The two concepts—the Planck energy and the Planck length—are related because at lengths smaller than a Planck length, gravity again has to enter the picture. A particle with more than a Planck energy’s worth of mass has fluctuations of its quantum field that are smaller than a Planck length.

Now think about some new particle with a mass at the Planck energy that solves all our problems about getting general relativity and quantum field theory to play nice with each other. That particle is probably going to couple to the Higgs, even if very weakly. And that means it will correct the square of the Higgs mass with a number around (1019 GeV)2 = 1038 GeV2 (that’s a 1 followed by 38 zeroes). Given a correction of that size, how could the Higgs mass be so small? One possibility is that the bare mass of the Higgs is itself something like 1019 GeV, and maybe the large corrections subtract from that bare mass and we end up with the final, measurable mass of the Higgs as (125 GeV)2 = 15625 GeV2, a number much smaller than the square of the Planck scale.

This is possible, but fantastically unlikely. Think of it this way: the square of the physical Higgs mass—the mass that we measure—is a five-digit number. Now let us play a little game. Imagine that you and I randomly write down thirty-eight-digit numbers, corresponding to something on the order of the square of the Planck scale. Then we subtract my number from yours. How many digits will the difference have? Basic probability says that around 80 percent of the time it will have thirty-eight digits; around 98 percent of the time, it will have at least thirty-seven digits; around 99.9 percent of the time, it will have at least thirty-six digits; and so on. By the time we get down to the probability that the difference between our numbers has at least six digits, the answer is basically the same as the probability that we didn’t pick the first thirty-three digits the same—which is so close to 100 percent you have to go out to the thirty-third place to the right of the decimal point to see the difference. In other words, the chance that the difference between our numbers has five or fewer digits is around 1 in 1033. Let that sink in: that’s one in a billion trillion trillion. It is hard to explain in ordinary terms just how rare this is. It would be like getting hit by lightning every year for the next billion billion billion years—except the Earth is only 4.5 billion years old.

What this thought experiment shows is that if you and I randomly wrote down two thirty-eight-digit numbers that turned out to differ from each other by a number close to the square of the Higgs mass, any rational observer would be completely justified in concluding that some sort of subterfuge or coercion must have been at work to get our results to line up so well. Somehow, there must have been a conspiracy preventing the two numbers in question from being truly random.

This is the situation in which we find ourselves when we contemplate the Higgs mass. 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).

The supersymmetric solution asserts that these massive contributions from heavy fields that add to the Higgs mass are exactly canceled by the contributions of some new set of fields. According to supersymmetric theories (there are many), every field in the Universe has a partner that is identical in every respect, other than somehow giving an opposite sign contribution to the Higgs mass.

This effect is achieved by partnering each field with a new field that has a spin that differs by half a unit of spin. This guarantees that the Higgs mass corrections are equal and opposite. This would apply to the hypothetical new particles at the Planck energy, but it also would apply to the known particles of the Standard Model. The spin-1/2 electron thus gains a supersymmetric electron partner that is spin-0. This “scalar” electron is called the “selectron.” Similarly, there are smuons for the muons, staus for the taus, sneutrinos for the neutrinos, and squarks for the quarks—sups, sdowns, scharms and so on. The spin-1 W, Z, and photon get spin-1/2 partners: the wino, zino, and photino. The gluon gets the gluinos. The spin-0 Higgs itself gets its own partner, the higgsino. The cancellations of supersymmetry also protect the mass of these new spin-0 particles from running off to the Planck scale, as was the concern with the Higgs to begin with.

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.

But that’s not a deal breaker for theoretical physicists. We’ve seen broken symmetries before: the Higgs breaks the symmetry of the hypercharge and weak forces, after all. If supersymmetry is broken at an energy similar to the scale of the Higgs field value, then all the new superpartners to the Standard Model particles would have masses near that scale, and the corrections to the Higgs mass would still be small. Unlike the tendency of the Higgs mass to run off to the Planck scale if given the chance, this new supersymmetry scale does not (we think) get huge corrections that drive it to the highest energies possible. The Naturalness Problem would be solved.

I think it is safe to say that, going into the LHC era, supersymmetry with superparticle masses around a few hundred GeV was the odds-on favorite for the new physics beyond the Higgs. In fact, many thought that it was likely that the Higgs itself would be one of the later particles discovered. Gluinos and squarks would be strongly interacting, like their super-partners the gluons and quarks. That means that when you bash two protons together at high energy, you should create huge numbers of them—at least, if the squarks and gluinos are relatively light. The Higgs, on the other hand, interacts through weakly interacting forces, and is therefore produced in relatively paltry numbers. The gluinos and squarks first, went the thinking, then the difficult-to-see Higgs much later.

That didn’t happen. Gluinos and squarks, if they exist and decay in the way we think they would, must be much heavier than we thought they should be. Not 300–400 GeV, but over 800 GeV (and maybe over 2000 GeV, depending on the details of the model). Some of the other hypothetical superpartners can be lighter, but in general, there must be a significant split between the energy scale of the Higgs (now known to be 125 GeV) and the energy scale of supersymmetry (unknown, but maybe over 1000 or 2000 GeV).

Remember, supersymmetry was a solution to a problem: Why are there two scales in physics (the Higgs scale and the Planck scale)? The further the scale of supersymmetry gets from the Higgs, the less it answers this question, and in fact starts becoming its own, new problem: Why are there three scales in physics (Higgs scale, Planck scale, and supersymmetry scale)?

Perhaps the Universe just has no problem with two random thirty-eight-digit numbers that agree at the first thirty-three places.

For my own part, I haven’t completely given up on supersymmetry. It is a compelling idea. However, it is starting to seem likely that, if supersymmetry exists, it is not the supersymmetry predicted by the previous generation of physicists. Similar things can be said about many of the other (non-supersymmetric) solutions to the Naturalness Problem. The theoretical framework might be sound, but the actual implementation must be different in important ways—otherwise we should have found new particles at the LHC by now. Either that, or we have fundamentally misunderstood something about how the Higgs field interacts. Or the Universe just has no problem with two random thirty-eight-digit numbers that agree at the first thirty-three places.

3. The Dark Universe

The Naturalness Problem suggests there should be something new at the LHC: it would offend theorists’ sense of propriety if there weren’t. But, as I said, maybe the Universe just doesn’t care about the Naturalness Problem. That would tremendously unsatisfying, and I don’t believe for a second that it is the case, but maybe that’s the case. Do I really have any better argument that there’s new physics to be found out there?

Yes. In fact, I have pretty much ironclad evidence that the Standard Model is not the end of the story. We may not discover the solution at the LHC, but we face an immense problem that needs to be solved.

To see the problem, let’s step back from the LHC and Geneva—very far back. Consider the Milky Way galaxy as a whole. If you get away from the lights of civilization, you can see the Milky Way at night as a glowing indistinct band stretching across the heavens. If you look with a telescope, you’ll discover that this band is full of stars. Hundreds of billions of stars. The band of the Milky Way is one of the spiral arms of the Milky Way galaxy, and the LHC, Earth, and the Sun are embedded in it. Since we’re in the middle of the Milky Way, we typically don’t have a great view of it, but here is a striking image of it from Australia:

The central band of the Milky Way behind the Pinnacles in Nambung National Park in western Australia. Image copyright: Michael Goh

Besides the Milky Way, the Universe includes hundreds of billions of other similar galaxies. One of our closest galactic neighbors, Andromeda, is also a spiral galaxy. The spiral arms of Andromeda and of the Milky Way suggest motion: the galaxies look like they are spinning. And indeed they are; the Sun is orbiting at 220 kilometers per second around the center bulge of the Milky Way. It just takes a long time to complete one galactic year. (The Sun will complete one orbit of the Milky Way every 250 million years or so.) So on human timescales, we see the spirals as frozen in space.

However, we can measure the speed at which the stars are moving, just as we measured the speed of the Sun moving in our own Milky Way. And what we find is that the stars are moving much too fast. To see what this means, consider two figure skaters holding hands and then spinning around each other at high speeds. If they go too fast, they will lose grip, and go flying off. To stay spinning on a circle requires a force: for the skaters, it is the contact forces when they grab each other. For the protons on the ring of the LHC, it is the magnetic forces of the superconducting magnets. For the Earth going around the Sun, it is the gravitational force from the Sun on the Earth. For the stars in the Milky Way (and in the other spiral galaxies), it is the force of gravity from all the other stars in the galaxy.

The problem is, if you estimate the mass of all the stars and gas in a galaxy using the light they give off, you get a gravitational force far too small to hold the Sun (or any of the other stars in the beautiful spiral arms) on their course. Something else in the galaxy, something invisible, must be holding the whole thing together. We call this mysterious stuff “dark matter.” Dark matter—matter that does not interact with light—is literally holding the galaxy together.

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.

Therefore, dark matter is strong evidence of new physics—something beyond the Standard Model. To be fair, some physicists think to explain what holds a galaxy together we need to modify gravity, not introduce a new particle. I find their arguments unconvincing, but in any event, modifying gravity is also new physics. Something remains for us to find.

So why should we expect to find the dark matter at the LHC? After all, if the primary property of dark matter is its darkness—its lack of interaction with the Standard Model—why should we expect to find it in the rubble of smashed protons?

It is completely conceivable that we won’t. But we think we might, and it is worth looking. Let me explain why. Again, keep in mind that the story I’m about to tell you is not experimentally confirmed physics. It’s a theory, an idea of what might be, and we have to find evidence that either rules it in or out. (Confession: I specialize in the study of dark matter. So the possibility of finding dark matter at the LHC is incredibly exciting for me.)

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.

Many arguments lead to the same conclusion: something is missing in the Universe.

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.

Searching for dark matter at the LHC is difficult. Dark matter is invisible to every layer of the ATLAS and CMS detectors. To find it, you have to look where all the visible matter went, and see if there is an imbalance in the momentum suggesting that something you didn’t see went the other direction. As a result, nearly every failure mode of the LHC detectors looks like dark matter: a particle slipping through the cracks, or measuring too much energy, or too little. However, experimentalists have proved themselves to be very good at their jobs. They cannot find every possible type of dark matter a theorist like myself can dream up, but they can find one of the most compelling possibilities.

4. Mysteries

There are many other mysteries that particle physicists want to know the answer to, and I have not even begun to touch on all of them. Among the problems the LHC could potentially answer are: Why are there three generations of fermions? Why is there more matter than antimatter? Why and how do neutrinos get their (tiny) mass? Even if nothing unusual in the LHC data is found, those problems will still be out there, demanding solutions.

In a few days, the ATLAS and CMS experiments will announce their most recent set of results at the International Conference on High Energy Physics (ICHEP), held this year in Chicago. They will weigh in definitively on the statistical anomaly at 750 GeV that I explained at the start of this series. Either the puzzle will remain and grow, suggesting new physics, or it will disappear as many other anomalies have in the history of particle physics. Regardless of the outcome, I will end this series after the ICHEP conference, letting you in on the news.

Peter Higgs wrote his paper predicting the Higgs particle in 1964. The first planning meeting for the LHC was in 1984. The Higgs was discovered in 2012. That is a long time to wait. But the Higgs isn’t the end of the story, and no matter the ICHEP results, they will not be the end of the story either. Theorists have had a long time to think of possible solutions to the problems that confound us, but without data, we cannot tell which solutions are right—if any are. Indeed, one notable feature of the strange anomaly that kicked off this series is that it does not fit into any of the huge library of “possible things to discover at the LHC” we theorists had come up with. The capacity of the Universe to surprise, amaze, and confound us is always greater than we can imagine.

I hope the Universe has a surprise for us in August, but either way, I hope you have learned about the sort of physics we study at the LHC and similar experiments, what we have accomplished, what we still have to discover, and why it is so incredibly exciting—when you learn that you were right, yes, but also when you learn that you were totally wrong.