How to Make an Apple Pie from Scratch

by Harry Cliff

  This collective motion of the W, Z, and Higgs fields gives rise to an object that can do something remarkable—it can convert antiparticles into particles and vice versa. A sphaleron can act as a matter-making machine; all you need to do is feed some antimatter and a spray of ordinary matter particles will emerge.

  This miraculous ability makes sphalerons the only objects within the framework of the standard model that can break the perfect balance between particles and antiparticles, giving them a uniquely important role in our understanding of the origin of matter. In all other cases, finding a recipe for matter means introducing new exotic particles, but what makes sphalerons so appealing is that you can do it with just the good old W, Z, and Higgs fields. “You don’t need any extra bells and whistles,” as Nick put it.

  The question is, do such bizarre objects really exist in nature, and if so, what would they be like? Well, even though a sphaleron is not a particle, it would look a lot like one. It would have a well-defined position in space, a mass, and a size. What’s more, you can use the equations of the standard model to calculate how big and heavy a sphaleron ought to be. The answers you get are staggering.

  A sphaleron would be about 10-17 meters across—that’s a hundredth of a thousandth of a trillionth of a meter—with a volume a million times smaller than a proton. On the other hand, this fantastically tiny object would have stupendous mass, weighing in at a whopping 9 TeV (trillion electron volts), which is almost ten thousand times heavier than a proton and far, far more massive than the heaviest particle we have ever detected.

  Its minuscule size and gargantuan mass make a sphaleron 10 billion times denser than a proton. To put it another way, a teaspoon of sphalerons would weigh twice as much as the Moon. Such incredible densities are thought to be beyond what even the Large Hadron Collider can create in its most violent particle collisions. What’s more, making a sphaleron isn’t as simple as bashing particles together extremely hard; the energy has to go into the right set of fields in the right order. Trying to make a sphaleron at the LHC is a bit like firing a barrage of tennis balls at an orchestra and expecting to hear Beethoven’s Ninth Symphony. You need W, Z, and Higgs fields to all play together as one, and the chances of that happening randomly in a particle collision are thought to be very slim indeed.

  However, there was a time in the universe when such extreme and yet specific conditions existed—in the first trillionth of a second of the big bang. Back then, the plasma filling the universe was incredibly dense, dense enough to make sphalerons in large numbers. And what’s more, the primordial plasma would have flowed collectively, like currents moving through the ocean, making the chances of getting the W, Z, and Higgs fields all moving together in the right way far more likely than at a particle collider.

  The presence of sphalerons in the early universe provides an almost unique mechanism for producing more matter than antimatter. Indeed, the most promising recipes on offer today for making matter all use sphalerons in one way or another. The trouble is, how do we really know if these things exist in nature?

  Well, for one, sphalerons appear to be an inevitable consequence of electroweak theory, and given that the W, Z, and Higgs were all discovered just as predicted, theorists are fairly confident that sphalerons must exist too. What’s more, despite the initial gloominess over the prospects of detecting them at colliders, some recent theoretical work has shown we may yet have a chance.

  Calculations suggest that random fluctuations in the collisions at the LHC might just allow a sphaleron to form once in a blue moon. They would then immediately decay into a spray of ten different matter particles, a fairly unique signature that physicists at ATLAS and CMS would have a decent chance of spotting among all the other subnuclear detritus.

  An even better prospect might come from collisions between heavy nuclei, like the gold-gold collisions used to study quark-gluon plasma at Brookhaven. These almighty smashups involving hundreds of protons and neutrons generate absolutely stupendous magnetic fields over very short distances, whose powerful pull might be enough to get the W, Z, and Higgs fields all wobbling together in just the right way to make a sphaleron. No one has seen one yet, but maybe, just maybe, the standard model’s most bizarre objects may yet reveal themselves to us. If and when they do, we will have another of the three crucial ingredients for making matter in the early universe.

  A RECIPE FOR QUARKS

  So far, things are going pretty well. The standard model appears to satisfy two of the three Sakharov conditions needed to make more matter than antimatter during the big bang. Sphalerons provide us with a way to convert between particles and antiparticles, while we know from experiments that the weak force breaks the symmetry between quarks and antiquarks. All we need now is a time in the universe’s history when it was out of equilibrium and we could be in business.

  Amazingly, the discovery of the Higgs boson implies that just such an event occurred around a trillionth of a second after the big bang. This was the moment when the Higgs field switched on, giving mass to fundamental particles and changing the basic ingredients of the universe beyond recognition. This crucial event could well be the reason that everything in the universe exists.

  Before the Higgs field switched on, the fundamental particles of nature looked very different from how they do today. The quarks and electrons that would go on to make up ordinary matter had no mass and zipped around at the speed of light, interacting with each other through a single unified electroweak force. However, after around a trillionth of a second the rapidly expanding universe’s temperature dropped below a critical threshold (around 100 GeV), causing the Higgs field to rise to a constant value throughout the entire universe, giving mass to quarks and electrons and causing the electroweak force to break apart into separate electromagnetic and weak forces.

  This event is known as the “electroweak phase transition,” and crucially, for our story, it satisfies the third and final Sakharov condition—a time when the universe was out of equilibrium. Combined with the experimental discovery that charge-parity symmetry (the symmetry between matter and antimatter) is broken by the weak force and the theoretical prediction of the existence of sphalerons that can convert antimatter into matter (and vice versa), the electroweak phase transition could have been the moment when nature’s scales were tipped in ordinary matter’s favor, ultimately giving rise to the material universe.

  How could this have happened? Well, as the term “phase transition” suggests, this was a moment when the universe underwent a rapid change of state, similar to more familiar phase transitions like steam cooling to form liquid water or water freezing into ice. Making matter during the electroweak phase transition depends on exactly how the phase transition happened—specifically, whether it was smooth and even or sudden and uneven.

  A smooth and even transition is no use for making matter, as sphalerons would have converted particles into antiparticles and antiparticles into particles at the same rate, preserving the perfect balance between matter and antimatter. However, if the electroweak phase transition happened unevenly, then making more matter than antimatter becomes possible.

  There’s no getting away from the fact that this process is a little complicated, but we are talking about the recipe for everything here. I’ll take it step by step.

  As the universe cools, the Higgs field turns on in some places before others, causing bubbles to form in the searing-hot plasma that fills the universe. Inside these bubbles where the Higgs field is on, quarks and electrons have gained mass and the weak and electromagnetic forces have come into existence. Outside these bubbles, the Higgs field is still off, particles have no mass, and there is still a single unified electroweak force.

  You can picture these bubbles as like droplets of liquid water condensing out of a cloud of steam; just as light reflects off the surface of a water droplet, quarks and antiquarks reflect off these bubbles. Some of the
quarks and antiquarks zooming about in the external plasma will collide with a bubble, either passing inside or bouncing off back into the surrounding plasma.

  Thanks to the fact that the weak force breaks charge-parity symmetry—that is, it interacts with particles and antiparticles slightly differently—the chances of an antiquark bouncing off the bubble walls are slightly higher than for a quark, while a quark has a better chance of passing into the bubble. As a result, more antiquarks end up outside the bubbles while there are more quarks inside. There are still equal numbers of quarks and antiquarks overall, but they’re now unevenly distributed.

  This is where sphalerons play their starring role in the story. Sphalerons can’t exist inside the bubbles where the Higgs field has switched on, but outside the bubbles where the Higgs field is off they are being produced all the time. The fact that there are sphalerons outside the bubbles but not inside is crucial. Outside the bubbles, sphalerons gobble up the extra antiquarks and convert them into quarks, while the excess quarks inside the bubbles are safely out of the sphalerons’ reach and stay as they are. The result is that, for the first time in the (admittedly still extremely brief) history of the universe, there are now more quarks than antiquarks.

  While all this is going on, the bubbles are getting bigger and bigger, swallowing the newly made quarks and saving them from being turned back into antiquarks by the sphalerons. A tiny instant after the phase transition began, these bubbles start to collide with one another, merging into bigger and bigger regions until eventually the entire universe has been filled with the new “Higgs on” state. This kills off the sphalerons, preventing any more conversions and freezing the imbalance between quarks and antiquarks forever. This tiny imbalance is enough to give matter the edge during the great annihilation, around a microsecond later, leaving just enough to form everything we see in the world around us.

  This rather miraculous process is known as “electroweak baryogenesis,”*3 which is just a fancier and more compact way of saying “making quarks when the Higgs field turned on.” One thing that makes it extremely appealing is that it is experimentally testable. That may seem like a low bar for a scientific theory, but as we’ll see, many of the ideas that we encounter as we move closer and closer to the big bang are more or less impossible to test directly due to the vast energies involved. The electroweak phase transition, on the other hand, took place when the temperature of the universe was around 100 GeV, well within the collision energy of the LHC, which can smash protons together at 14,000 GeV. That means that the LHC should be able recreate the particles and phenomena that were involved and test whether it really was how matter got made in the early universe.

  1. The Higgs field starts turning on, forming bubbles.

  2. Charge-parity violation means more antiquarks bounce off the bubbles than quarks, creating an excess of antiquarks outside the bubbles.

  3. Sphalerons outside the bubbles convert antiquarks into quarks.

  4. Bubbles expand and merge, leaving more quarks than antiquarks.

  However, the idea immediately runs into some problems if we only use the ingredients provided by the standard model. A major stumbling block is that the amount of matter-antimatter asymmetry that we’ve measured so far seems to be way too small to get the process to work. What that effectively means is that the probabilities for quarks and antiquarks to bounce off those Higgsy bubbles would be too similar, and you wouldn’t get a big enough excess of quarks building up inside the bubbles.

  Another serious issue has to do with the electroweak phase transition itself. Now that we know the mass of the Higgs boson, theorists can plug it into their models and calculate how the phase transition would have happened. What you find is that instead of taking place unevenly in bubbles, the phase transition would have happened evenly and smoothly throughout all of space, and without bubbles to separate quarks from antiquarks the whole process becomes impossible.

  Still, all is not lost. Both of these problems can be fixed as long as there are new quantum fields beyond the ones we’ve found so far. These quantum fields would have to break the CP symmetry between quarks and antiquarks and also change the way the Higgs field behaves to allow bubbles to form as it switched on during the big bang. Encouragingly, these fields should be detectable in experiments.

  The obvious place to look for new quantum fields is the Large Hadron Collider. If they exist, then the LHC should be able to hit them hard enough to make them wobble and create some of the particles that go with them, which could then be spotted by the gigantic ATLAS and CMS experiments. Meanwhile, at LHCb, we’ve spent the last decade searching for new signs of matter-antimatter asymmetry by studying various types of exotic quarks. The “b” in LHCb stands for “beauty,” the name of a heavy cousin of the more familiar down quark that’s found inside protons and neutrons. One of the main goals of LHCb is to study the billions upon billions of beauty quarks produced by the LHC and to see if we can find differences between how the beauty quark and antiquark decay.

  Unfortunately, so far ATLAS and CMS haven’t seen any signs of new particles being created in their collisions, although they may still turn up as the LHC ramps up its collision rate over the next decade. At LHCb we’ve seen plenty of evidence for beauty quarks breaking matter-antimatter symmetry, and more recently we’ve even caught charm quarks (heavy cousins of the up quark) getting in on the symmetry-breaking act. But alas the amount of matter-antimatter asymmetry is still way below the level needed to explain the dominance of matter in the universe.

  If results coming out of the LHC aren’t particularly encouraging for electroweak baryogenesis fans, then things look even gloomier when you consider the results of a totally different, and far less expensive, set of experiments. Rather wonderfully, the strongest arguments against electroweak baryogenesis come from measurements of the shape of the electron, including the decidedly low-frills experiment in the basement of Imperial College that we encountered a while back.

  If new symmetry-breaking quantum fields exist, then they should gather around the electron and squash it from a perfect sphere into something more like a cigar. The fact that the most sensitive electron-shape-measuring experiments in the world have all found the electron to be as round as round can be is starting to put serious pressure on the existence of these new quantum fields.

  So things aren’t looking all that rosy for this particular recipe for making matter. Of course, there is still room for new quantum fields to show up at the LHC or in the ever-more-precise measurements of the electron’s shape being planned for the near future. So while it’s not game over quite yet, theorists are increasingly looking elsewhere to explain the existence of matter in the universe. The most popular alternative involves the most elusive particles that we’ve discovered so far: neutrinos.

  MATTER MADE BY GHOSTS

  Deep under Mount Ikeno in central Japan is one of the most spectacular human-made spaces in the world. Housed a kilometer belowground in an old zinc mine is a soaring cylindrical tank containing 50,000 tons of ultrapure water, big enough to swallow the Statue of Liberty whole. Its walls, floor, and roof are covered with thousands upon thousands of gleaming golden orbs, electrical eyes that watch for faint flickers of light emerging from the dark water, the telltale sign of an arriving neutrino. This is Super-Kamiokande (Super-K), the world’s largest neutrino observatory, and it may have given us a crucial clue to the origin of matter.

  In April 2020, the 150-strong international team that operates Super-K reported the first hint that neutrinos can also break the charge-parity symmetry that relates matter to antimatter. If confirmed by more precise measurements, this is a huge deal. So far, only quarks have been caught breaking charge-parity symmetry through their interaction with the weak force. If neutrinos can do it too, then it opens up a second potential way to make matter in the first instant after the big bang.

 
To understand why Super-K’s result is so significant, we first need to quickly recap what we know about neutrinos. Neutrinos are the most abundant matter particles in the universe, and yet we are almost completely unaware of them thanks to the fact that they have no electric charge and only interact with ordinary atoms through the weak force. As a result, they can pass through solid objects, including planets and stars (not to mention Italian mountain ranges), as if they weren’t there, which sends science writers scouring their thesauruses in search of new spooky adjectives once they’ve used “ghostly” and “elusive” more than a couple of times.*4

  These, ummm, wraithlike neutrinos come in three types or “flavors,” the electron, muon, and tau, each of which is paired up with an electrically charged particle. Fire a beam of electron neutrinos at some atoms with sufficient energy and a few of them will convert into electrons. Do the same thing with muon or tau neutrinos and you’ll get negatively charged particles called, unsurprisingly, “muons” and “taus,” which are heavy, unstable cousins of the electron. Together, the three neutrinos and the electron, muon, and tau particles form a family of six fundamental particles called “leptons.”

  Another thing that we used to believe about neutrinos is that they were completely massless. That is until a major discovery made by Super-K more than twenty years ago. In 1998, scientists there announced they had found evidence of muon neutrinos morphing into tau neutrinos as they traveled through the Earth. This phenomenon is known as “neutrino oscillation,” and all three neutrinos can do it. Produce a beam of pure electron, muon, or tau neutrinos and plonk a detector a few miles away and you’ll discover that a fraction of them have shapeshifted into the other two flavors en route.