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§ Phase x · The Particle Zoo · Chapter 02

The Standard Model table

By the mid-1970s, after a half-century of cloud chambers, cyclotrons, and counter rates that climbed into the millions per second, the rubble of the particle zoo had been swept into a single sheet of paper. Three columns of quarks, three columns of leptons, four force carriers, and one scalar holding the whole thing together. The table looks, at first glance, like a Periodic Table for the very small. It is in fact something stranger: a complete inventory of every particle that has ever been seen.

If you walk through the lobby of the physics building at almost any research university in the world, you will pass a poster of the Standard Model. It is usually printed in four colors, framed in plastic, and pinned over the coffee machine. Twelve squares of matter, four squares of force, one square for the Higgs. Seventeen tiles in total. That poster is a complete catalog. Every particle that has ever been detected in any experiment, from cosmic-ray showers over Texas to the proton-proton collisions at the Large Hadron Collider, fits inside one of those squares. There are no twenty-third entries, no surprise eighteenth boxes, no asterisks. Half a century of high-energy physics has not added a single new tile to the poster that does not collapse back into one of the seventeen already drawn.

That is a stunning state of affairs. The Periodic Table of the elements, which by 1900 looked similarly complete, turned out to be a façade: each box hid a nucleus, each nucleus hid protons and neutrons, and the protons and neutrons hid quarks. The Standard Model table looks structurally similar, three rows of matter and a column of forces, but as far as we can tell its squares are not façades. Smash a quark hard enough and you do not get something smaller; you get more quarks. Smash an electron and you get an electron, plus photons. The table is, on the best evidence we have, terminal. There is nothing inside any of these boxes. They are points.

The story of how we got here is the story of seventy years of slowly squeezing a sprawling, embarrassing, almost-comical menagerie of mid-century particles into a finite grid. In 1947, when the muon and the pion were the new mysteries of the year, no one would have bet that the catalog would close. By 1964, when Murray Gell-Mann had proposed the quark, the betting had shifted. By the late 1970s, when Sheldon Glashow, Steven Weinberg, and Abdus Salam shared the Nobel Prize for unifying electromagnetism with the weak force, the consensus was that the architecture was nearly complete and only a few more discoveries would close the book. They were right. In 1995 Fermilab found the top quark, in 2000 it found the tau neutrino, and in 2012 CERN found the Higgs. The lid clicked shut.

To make sense of the poster, you need three pieces of vocabulary, all of which we will unpack in this chapter and the next. The first is “fermion.” A fermion is a particle of half-integer spin (spin 1/2 for everything in the table). Fermions are what we ordinarily call “matter”: they take up space, they obey the Pauli exclusion principle, they refuse to share a quantum state with their own kind. Every particle on the left two-thirds of the table is a fermion. The second piece is “boson.” A boson is a particle of integer spin (spin 1 for the force carriers, spin 0 for the Higgs). Bosons can pile on top of each other in unlimited numbers, which is why a laser beam can stack 10²⁰ photons into the same mode and why your kitchen lamp does not blow up from quantum overcrowding. The third piece is “gauge.” A gauge boson is the particle you exchange to make a force. Two electrons feel each other through the exchange of photons; two quarks feel each other through the exchange of gluons; a neutron decays by tossing a W boson at one of its own quarks. Gauge bosons are how forces get carried from one particle to another.

The matter half of the table is sliced into two species, quarks and leptons. Quarks come in six flavors: up, down, charm, strange, top, bottom. They carry fractional electric charge (+2/3 or −1/3 in units of the proton charge e), they carry a second kind of charge called color (red, green, or blue, see the next chapter), and they never appear in isolation. Every quark in nature is bound inside a hadron. Leptons come in six flavors too: the electron, the muon, and the tau, plus three neutrinos that pair with them. Leptons carry integer electric charge (−1 for the charged ones, 0 for the neutrinos), carry no color, and do appear in isolation. An electron is a quark only in the sense that an apple is an orange: both are fermions, both are spin 1/2, and there the resemblance stops.

The most surprising design choice in the whole table is that the six quarks and six leptons are arranged into three nearly identical generations. The first generation contains the up quark, the down quark, the electron, and the electron neutrino. These four particles, plus the photon and the gluons, are enough to build every atom, every molecule, every cell, every human being, every star. The second generation (charm, strange, muon, muon neutrino) is a near-clone of the first, identical in every quantum number except mass, which is roughly a hundred to a thousand times larger. The third generation (top, bottom, tau, tau neutrino) is another clone, again with the same quantum numbers, again heavier still. The universe runs on the first generation. The other two are visible only at energies high enough to make them, and they decay back into the first generation within microseconds. As the Columbia experimentalist Isidor Rabi once said when the muon was discovered, “Who ordered that?” Sixty years later, nobody knows.

The force half of the table is shorter. There are four entries. The photon, written γ (gamma), is the carrier of the electromagnetic force. It has no electric charge, no mass, and spin 1, and it is the particle every visible photon (every glint of sunlight, every X-ray, every radio wave) is made of. The W boson comes in two flavors, W⁺ and W⁻, each with electric charge ±e and a mass of about 80 GeV (eighty times the mass of a proton). The Z boson is electrically neutral and weighs about 91 GeV. Together the W and Z carry the weak force, the force responsible for radioactive beta decay and for the fusion reactions that power the Sun. The strong force is carried by eight gluons, all massless, all electrically neutral, but each carrying a color-anti-color charge of its own. The gluons hold quarks inside protons and protons inside nuclei.

A short table of the visible numbers makes the pattern concrete. Charge is quantized in units of e (the proton charge), spin is quantized in units of ℏ, mass spans roughly twelve orders of magnitude from the lightest neutrino to the top quark.

Two patterns leap out of the table as soon as you read it carefully. The first is charge quantization. Every electric charge in the universe is an integer multiple of e/3, with the constraint that anything appearing in isolation is an integer multiple of e. Quarks carry +2/3 or −1/3, but they are always confined inside hadrons in combinations that sum to whole-number charges. (A proton is uud: 2/3 + 2/3 − 1/3 = +1. A neutron is udd: 2/3 − 1/3 − 1/3 = 0.) The proton’s charge is exactly equal in magnitude to the electron’s charge, to a precision of better than one part in 10²¹ in the best experimental tests. There is no clean reason in the Standard Model why this should be exactly true, and the fact that it is exactly true is one of the strongest hints that a deeper theory lies beneath the table.

The second pattern is spin quantization. Every fermion in the table has spin exactly 1/2. Every gauge boson has spin exactly 1. The Higgs has spin exactly 0. There are no spin 3/2 particles in the Standard Model, no spin 2 ones either (although the hypothetical graviton, if it exists as a quantum of gravity, would be spin 2). The whole spectrum sits on three rungs of a small spin ladder, and the rungs are not arbitrary; they are determined by the representation theory of the Lorentz group, the same mathematics that Wigner worked out in 1939 when he classified the elementary particles of any relativistic quantum theory.

Σ_doublets ( Y_L ) = 0

1 · (−1) + 3 · (+1/3) = 0

The unification of electromagnetism and the weak force, the work for which Glashow, Salam, and Weinberg shared the 1979 Nobel, has the most dramatic experimental consequence of any single result in the table. In the 1950s the weak force and the electromagnetic force looked nothing alike: one was carried by a massless photon and reached across the universe; the other was so short-ranged and feeble that no one had any idea how it propagated. By 1968 Glashow’s old algebraic skeleton, dressed in the Higgs mechanism by Salam and Weinberg, had become a single mathematical object called the electroweak gauge group, SU(2) × U(1). At energies high enough that the Higgs field stops mattering (above roughly 250 GeV), the photon and the W and Z bosons behave like four members of a single family. Below that energy scale (which means in every laboratory and every star), the Higgs field shifts and the four bosons split. Three of them (W⁺, W⁻, Z) eat a piece of the Higgs and become heavy; one of them (the photon) does not, and stays massless. The four forces we see at low energy are the broken pieces of one force we would see at high energy.

That picture made one extraordinary prediction. If the Z exists, the weak force must have a “neutral current” component, a piece of itself that flips no quantum numbers at all. Beta decay (in which a neutron emits an electron and an antineutrino) flips charges around; that is a charged current. A neutral current would be a weak interaction in which the participants exchange a Z and walk away unchanged in every way except their direction. In 1973 the Gargamelle bubble chamber at CERN saw the first neutral-current event: a muon neutrino had bounced off an electron without changing anything but the electron’s trajectory. The prediction was right. Ten years later, in 1983, Carlo Rubbia’s UA1 experiment at CERN actually produced W and Z bosons in proton-antiproton collisions and measured their masses, finding 80.4 and 91.2 GeV almost exactly where the theory said they would be. The Higgs, the last piece, took another twenty-nine years; CERN’s Large Hadron Collider announced its discovery on July 4, 2012, with mass 125.1 GeV.

To see how brutal the mass spread is across the table, look at one column only. The three charged leptons (electron, muon, tau) carry identical quantum numbers in every respect except mass.

What the table does not tell you is, in a way, what the table is. The Standard Model is not a list of particles. It is a quantum field theory, written down as a single Lagrangian about half a page long, whose equations of motion produce the entire table as a list of stable excitations. The fermions are the quantized vibrations of fermion fields; the gauge bosons are the quantized vibrations of gauge fields; the Higgs is the quantized vibration of one extra scalar field. The structure that picks out three generations, the precise pattern of charges, and the existence of confinement all comes from one specification: the gauge group SU(3) × SU(2) × U(1), with one Higgs doublet, and three copies of the matter content. The seventeen tiles on the poster are the seventeen particles you get when you ask “what are the lowest-energy excitations of this Lagrangian?” There is no separate list of particles to memorize. There is only the Lagrangian, and the poster is its receipt.

That same Lagrangian has stood up to every direct experimental test ever thrown at it. The Z mass and the W mass were predicted before they were measured. The branching ratios for top-quark decay were calculated before any top quark had been produced. The Higgs boson’s couplings to W, Z, top, bottom, and tau were predicted from the symmetry structure before the boson itself was discovered, and the 2012 measurement at the LHC has been consistent with every one of those predictions to within experimental uncertainty. There is no result in the Standard Model that has, to date, been contradicted by experiment in a reproducible way. The poster, in other words, is correct. The next two chapters will start to ask what the poster does not contain, and where its successor might live.