Higgs Field
Origin of Elementary Mass
Mass Is a Hum
Every elementary particle is a ripple in a field that fills all of space. Light is a ripple in the electromagnetic field, and an electron is a ripple in the electron field. The two kinds of ripple behave very differently. A ripple of light can never stand still. It always runs at the speed of light. Give it less energy and its waves grow longer, but it runs just as fast.
A ripple in the electron field can stay where it is. It is as if every point of that field were tied to its place by a spring: pulled up, it swings back down, past its rest and up again. So the ripple hums in place: the field there swings back and forth at a pitch of its own, about 1.2 × 10²⁰ times a second. No electron at rest can hum any slower. Mass is a form of energy, and the energy of that lowest hum is the electron’s mass. A heavier particle hums at a higher pitch. Light has no lowest note, so it has no mass, and it can never rest.
A popular picture has the Higgs field dragging on particles like water or molasses. It does nothing of the kind. Drag slows things down and takes their energy, and an electron coasting through empty space keeps its speed forever. What the Higgs field does, the theory says, is give the electron’s field a lowest note to hum at.
The Field That Is Never Zero
In empty space most fields hover about zero: never perfectly still, but zero on average. The electric field there averages zero, and so does the electron field. The Higgs field does not. It holds one and the same value everywhere, even in the emptiest space between galaxies. Fields that are tied to it feel that value at every point, and it gives each of them a lowest note. The stronger the tie, the higher the note and the heavier the particle. The top quark has the strongest tie known and weighs about 340,000 times as much as an electron. The photon and the gluon have no tie at all, and no mass.
Why can the electron not simply have a mass of its own? Because of the weak force. Its W bosons act on left-handed electrons and ignore right-handed ones, so only a left-handed electron carries the weak charge they answer to. For a particle, having mass means that as it hums it keeps turning from left-handed to right-handed and back. Each turn would make weak charge vanish or appear, which the laws do not allow. The Higgs field carries weak charge and fills all of space, so it takes up the difference at every turn. The W and Z, the weak force’s own ripples, are heavy for a related reason: they keep meeting the weak charge that fills all of space, and that is why the weak force reaches so short a way. The Higgs field’s value carries no electric charge, so the photon passes through it untouched.
Why is the Higgs field not zero? For it, zero is not the lowest energy. The Higgs field has four parts, so its value is a point in a space of four directions, not a number on a line. Draw its energy over just two of them, a flat map, and you get the shape of the bottom of a wine bottle: a hump in the middle, at zero, and a trough all round it. The field settles in the trough. The theory takes this shape as given; why the energy is shaped this way is not settled.
It was not always so, if universe was once hot enough, as most models of its first moments assume. In that heat the shape was a plain bowl, lowest at zero, and the Higgs field sat at zero on average. The W and Z got no mass from it, and electromagnetism and the weak force had not yet split apart. As universe cooled, a hump rose in the middle of the bowl and pushed the field off zero into the trough. Computer calculations of the theory show that this came smoothly, over a range of temperatures near two million billion degrees, about ten trillionths of a second after the Big Bang. There was no sudden snap and no wall sweeping across space. The scene above shows the simple picture, with a moment when the hump first rises; in the full calculation there is no such moment. Which way round the trough the field went changes nothing anyone can measure, since every point round the trough describes the same world. What matters is how far from zero it lies.
Ringing the Higgs Field
The Higgs field can ripple too, and its ripple is the Higgs boson: the field’s value rocking across the trough and back. The steeper the trough’s walls, the heavier the boson. Ripples round the trough, where the floor is level, make no particle of their own: the W and Z take them in, as a third way of shaking that only a particle with mass can have.
Ringing the field often enough to find its boson took the Large Hadron Collider, near Geneva, where protons meet head-on within a few millionths of a percent of the speed of light. A Higgs boson lasts about 10⁻²² seconds and then turns into other particles, so no detector ever sees it. In the clearest cases it leaves two photons, or four electrons or muons. Light has no tie to the Higgs field, so the two photons come by way of a brief stir in the fields of heavy particles that do, mostly the W boson’s and the top quark’s. Gluons in the colliding protons make the boson the same way, through the top quark’s field. Their energies and directions give back the mass of what made them. Other collisions make such pairs by chance far more often, so the boson shows up only as a small surplus of pairs at one mass. Two of the collider’s giant detectors each found that surplus, at 125 billion electron volts (GeV), about 133 times the mass of a proton.
Since then the boson has been checked particle by particle. If the Higgs field gives each particle its mass, each particle’s tie to the boson should grow in step with its mass. Measured from the ways the boson is made and the ways it ends, the ties match for the W and Z, the top and bottom quarks and the tau, the electron’s heaviest cousin, within the precision of the measurements. Both detectors have now seen signs of it turning into muons, which are lighter still. The electron’s tie is too weak to measure yet.
If the Higgs Field Were Zero
What would a world be like if the Higgs field sat at zero? In the theory, the electron would have no mass. The size of an atom depends on its electron’s mass: halve the mass and the atom doubles in size. With no mass at all, the electron could not be held in an atom of any size. There would be no atoms, no chemistry and nothing solid.
Protons would still be heavy. Their quarks would lose their small masses, but most of a proton’s mass is the energy of the strong field and of the quarks’ motion in it. If the strong force kept its present strength, calculations put a proton in that world less than a tenth lighter. It might not: the heavier quarks, massless too, would change how its strength grows with distance, and rough estimates then make a proton a few times lighter, though still heavy. The W and Z would not lose all their mass either, as is often said. Even without it, the strong force gives the quark field a steady value throughout empty space, as if quarks and antiquarks were paired everywhere, and that alone hides the weak force’s symmetry, leaving the W and Z nearly three thousand times lighter than they are, or lighter still. The weak force would then reach much farther and grow nearly as strong as the forces inside nuclei.
Radioactive decay could even run backward. Today a free neutron turns into a proton in about fifteen minutes. In the world without the Higgs field, with the quarks’ masses gone, only small effects of the electric and weak forces would tell the two apart, and the proton may come out the heavier. With the weak force so much stronger, it would then turn into a neutron in far less than a millionth of a second. There would be no hydrogen at all. The lightest nucleus would be a lone neutron, which holds no electrons.
Why Is It So Light?
The Higgs boson’s mass is a puzzle. Quantum effects tie it to the heaviest particles it touches. If any exist far above the ones we know, up to the scale where gravity grows strong, they should drag its mass up toward theirs, about 10¹⁶ times heavier than it is. For the mass to come out at 125 GeV, that huge pull has to be cancelled by a starting value that nothing in the theory sets. What cancels is the mass multiplied by itself, and the two must match to about 32 places. Physicists call this the hierarchy problem.
Noise-cancelling headphones do something like it. They play a sound wave shaped exactly against the noise, and the two add up to near silence. Picture the pull of the heaviest particles as one huge wave and the starting value as the other: what is left of their sum is the Higgs mass, multiplied by itself. Change the starting value in its 33rd place, and the mass comes out at 160 GeV instead of 125; three places further up, it is over 3,000; change the first, and it is 10¹⁸ GeV, right back where the pull was taking it. In the headphones, a chip shapes the second wave to match the first. In the theory, nothing does.
Either something unknown makes the cancellation happen, or nothing much heavier exists to pull on it, or nature is simply tuned this finely. Supersymmetry, the most popular answer, gives every particle a heavier partner whose pull cancels its own, and many expected the partners to turn up at the Large Hadron Collider. None has. Other ideas build the Higgs boson out of smaller parts, or add hidden dimensions of space. None has been confirmed.
The Shape Nobody Has Measured
Two things about the wine-bottle shape are known: how far the trough lies from zero, 246 GeV, which sets the masses, and how steep its walls are, which sets the boson’s. The theory predicts the rest of the shape, the hump in the middle included, but nobody has checked it. The first check is how strongly the Higgs field acts on itself, which tests the shape just beside the trough’s floor. The main way to measure that is to make two Higgs bosons at once, which happens about once for every two thousand single ones. The two detectors have combined four years of their data. The answer so far lies anywhere from a little below zero to six times the predicted value. The collider is now shut for an upgrade, and from about 2030 it will make many times more collisions, perhaps enough for a first sign of pairs.
The shape far beyond the trough matters too. Taken at face value, the measured masses of the Higgs boson and the top quark make the energy curve turn down again at enormous values of the field. Then the trough we live in would not be the lowest place, and our empty space could one day tunnel to a deeper one, though most likely only after a time vastly longer than the age of universe. Heavier particles not yet found could change the curve, so the question is open.
