The Standard Model of Particle Physics

The Inventory of the Universe

As of the 2012 discovery of the Higgs boson at CERN’s Large Hadron Collider, the Standard Model of particle physics is complete — in the sense that every particle it predicted has been observed. The model describes all known matter and three of the four fundamental forces. It is the output of roughly fifty years of theoretical and experimental particle physics, beginning in the 1960s and consolidated through the 1970s and 1980s.

The particle content: twelve matter particles (fermions) and the force-carrying particles (bosons). The fermions come in two classes — quarks and leptons — each in three generations. The first generation is stable and makes up ordinary matter: up quarks and down quarks (which combine to form protons and neutrons), electrons, and electron neutrinos. The second and third generations are heavier, unstable copies of the first — muons and tau particles are heavier cousins of the electron, with their own associated neutrinos; charm, strange, bottom, and top quarks are heavier cousins of up and down. Why there are three generations and not two, or four, or seventeen, is unknown. The model does not predict it; it observes it.

The forces are mediated by bosons. Electromagnetism is mediated by photons (massless, infinite range). The weak nuclear force — responsible for radioactive beta decay — is mediated by the W and Z bosons (massive, very short range). The strong nuclear force — which holds quarks together inside protons and neutrons, and protons and neutrons together inside nuclei — is mediated by gluons. Each force corresponds to a symmetry group in the mathematical structure of the theory: U(1) for electromagnetism, SU(2) for the weak force, SU(3) for the strong force. The Standard Model is a quantum field theory with gauge symmetry group SU(3) × SU(2) × U(1).

Quantum Field Theory

The conceptual foundation is quantum field theory (QFT), which unifies quantum mechanics with special relativity. In quantum mechanics, the fundamental objects are particles. In QFT, the fundamental objects are fields — entities that permeate all of spacetime — and particles are excitations of these fields. The electron is not a point particle riding through space; it is a localized excitation of the electron field, which exists everywhere.

This sounds abstract but it has concrete implications. Virtual particles — which appear in Feynman diagrams as internal lines representing particles exchanged in interactions — are not real particles flickering in and out of existence. They are mathematical artifacts of the perturbative expansion of QFT calculations. The expansion is a power series in the coupling constant (the strength of the interaction), and higher-order terms in the expansion involve more virtual particle exchanges. The calculations work to extraordinary precision; the virtual particles are a bookkeeping device, not a literal description of what happens.

Renormalization is the most controversial mathematical technique in QFT. When you calculate quantum corrections to the mass or charge of an electron, the integrals that arise diverge — they give infinite answers. Renormalization is a procedure for absorbing these infinities by noting that the parameters in the theory (mass, charge) are not the bare parameters but the physical, measured parameters, which already include all quantum corrections. When the infinities are properly absorbed, the finite remainders agree with experiment with extraordinary precision.

Paul Dirac hated renormalization. He described it as ignoring infinities that are inconvenient — not a sound mathematical procedure. Feynman, who developed the technique into its modern form, called it a “shell game” in his Nobel lecture. The procedure works spectacularly. Whether it is mathematically rigorous is a separate question that mathematical physicists are still working on.

The Higgs Mechanism

The Higgs mechanism resolves a puzzle in the Standard Model’s structure. The electroweak theory — which unifies electromagnetism and the weak force — requires, for mathematical consistency, that the W and Z bosons be massless. They are observed to be very massive. How can a theory that requires massless force carriers describe particles that are clearly not massless?

Peter Higgs and others (independently: Brout, Englert, Guralnik, Hagen, Kibble) proposed in 1964 that the universe is permeated by a field — the Higgs field — that acquires a nonzero value in its lowest-energy state (the vacuum). This spontaneous symmetry breaking gives the W and Z bosons mass when they couple to the non-zero Higgs field. Other particles also acquire mass through their coupling to the Higgs field; the stronger the coupling, the heavier the particle. The electron is light because it couples weakly to the Higgs field; the top quark is heavy (about 173 proton masses) because it couples strongly.

The Higgs boson is the particle associated with excitations of the Higgs field — the quantum of the field, as photons are the quanta of the electromagnetic field. Finding it was essential to confirming that the Higgs mechanism is correct. The search for the Higgs was one of the primary motivations for building the Large Hadron Collider. Its discovery at ~125 GeV in 2012 was a triumph of decades of theoretical and experimental work.

What the Standard Model Cannot Explain

The Standard Model’s incompleteness is as remarkable as its success. It is a theory of extraordinary precision for phenomena in its domain, and it fails to address several things we know must exist.

Gravity. The Standard Model does not include gravity. Gravity is described by general relativity — a classical field theory, not a quantum field theory. All attempts to quantize gravity in the straightforward way produce non-renormalizable infinities. String theory, loop quantum gravity, and other approaches attempt to resolve this, none so far successfully by empirical test. At ordinary energies, gravity is so weak (compared to the other forces) that this gap is irrelevant for particle physics experiments. At the Planck scale — energies around 10¹⁹ GeV, approximately where quantum gravitational effects become significant — the Standard Model breaks down.

Dark matter. Approximately 27% of the energy content of the universe is in the form of dark matter — matter that has gravitational effects but does not interact electromagnetically (it doesn’t absorb or emit light). The evidence is overwhelming: galaxy rotation curves don’t make sense without dark matter, gravitational lensing shows mass distributions that don’t correspond to visible matter, and the cosmic microwave background’s acoustic oscillations require it. The Standard Model contains no candidate particle for dark matter. The most popular candidates — weakly interacting massive particles (WIMPs) — have been searched for extensively and not found.

Matter-antimatter asymmetry. The Big Bang should have produced equal amounts of matter and antimatter. Matter and antimatter annihilate on contact, so a symmetric universe would contain mostly photons and almost no matter. We live in a universe made of matter. Something broke the matter-antimatter symmetry — a violation of CP symmetry (charge conjugation combined with parity) is required. The Standard Model contains CP violation, but not nearly enough to explain the observed asymmetry. Something is missing.

Neutrino masses. In the Standard Model as originally formulated, neutrinos are exactly massless. They have been experimentally shown to oscillate between flavors — electron, muon, tau neutrinos transforming into each other — which requires them to have nonzero (though tiny) masses. The masses can be inserted into the Standard Model, but the mechanism for generating them is not fully understood and the theoretical elegance of the original construction is compromised.

The hierarchy problem. The Higgs mass receives quantum corrections from loop diagrams involving all particles it couples to, including virtual top quarks. These corrections are enormous — they should push the Higgs mass toward the Planck scale, about 10¹⁵ times larger than its observed value. Either there is a mechanism that cancels these corrections to extraordinary precision (fine-tuning) or there is new physics at an intermediate energy scale that cuts off the corrections. Supersymmetry was the most popular theoretical resolution; experiments at the LHC have not found the supersymmetric particles it predicted at the expected energies.

The Theory and Its Successor

The Standard Model is almost certainly an effective field theory — a theory that correctly describes physics at accessible energies but breaks down at higher energies where effects from a more fundamental theory become important. The goal of the next generation of particle physics experiments is to find the energy scale where the Standard Model fails and what replaces it.

The LHC has found the Higgs boson and is now searching for deviations from Standard Model predictions in Higgs couplings, rare particle decays, and direct production of new particles. No significant deviations have been found. This is either because the new physics is at higher energies than the LHC can reach, or because our theoretical expectations about where to look are wrong.

The Standard Model’s completeness is its most unsettling feature. Every particle it predicted has been found. But the phenomena it manifestly cannot address — dark matter, gravity, the matter-antimatter asymmetry — are not small corrections. They concern most of the universe. The most successful theory in the history of science is pointing, as clearly as it can, at its own limits.