Standard Model

• 1. Introduction

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  On the 4th of July 2012, two experiments at CERN's Large Hadron Collider, ATLAS and CMS, reported the same thing on the same day. Each had found a new particle weighing about 125 GeV, roughly 133 proton masses. Both teams used careful language. The particle was consistent with the Higgs boson. Eight months later, on the 13th of March 2013, it was confirmed to be the very particle physicists had hunted for decades. That hunt was the final test of the Standard Model of particle physics, a theory that describes three of the four known fundamental forces and sorts every known elementary particle into place. It explains electromagnetism, the weak interaction, and the strong interaction. It leaves out gravity entirely. How does a single theory account for everything from the electron in an atom to the binding of an atomic nucleus, yet stay silent on the force that holds you to the floor? And why, after confirming its last predicted particle, do physicists still call it incomplete?

• 2. Built In Stages

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  In 1928, Paul Dirac introduced the Dirac equation, and its mathematics implied that antimatter must exist. That insight opened decades of construction by scientists across the world. In 1954, Yang Chen-Ning and Robert Mills extended gauge theory from abelian groups, such as quantum electrodynamics, to nonabelian groups, reaching toward an account of the strong interaction. In 1957, Chien-Shiung Wu demonstrated that parity is not conserved in the weak interaction, overturning an assumption about symmetry.

  In 1961, Sheldon Glashow combined the electromagnetic and weak interactions into one framework. Three years later, in 1964, Murray Gell-Mann and George Zweig introduced quarks, and that same year Oscar W. Greenberg implicitly introduced the color charge that quarks carry. In 1967, Steven Weinberg and Abdus Salam folded the Higgs mechanism into Glashow's electroweak interaction, giving the theory its modern shape.

  In 1970, Glashow, John Iliopoulos, and Luciano Maiani introduced the GIM mechanism, which predicted the charm quark before anyone saw it. In 1973, Gross and Wilczek and, independently, Politzer discovered that non-Abelian gauge theories like the color theory of the strong force have asymptotic freedom. In 1976, Martin Perl discovered the tau lepton at SLAC. In 1977, a team led by Leon Lederman at Fermilab discovered the bottom quark. The current formulation was finalized in the mid-1970s, once experiments confirmed that quarks were real.

• 3. Naming The Theory

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  The term "Standard Model" was introduced by Abraham Pais and Sam Treiman in 1975, referring to the electroweak theory with four quarks. Steven Weinberg has since claimed priority on the phrase. He explained that he chose the words out of a sense of modesty, and that he had used them in 1973 during a talk in Aix-en-Provence in France. The name stuck, and it now covers a theory whose pieces were assembled by many hands over half a century.

• 4. The Twelve Fermions

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  The Standard Model includes twelve elementary particles known as fermions, and they obey the Pauli exclusion principle, so two identical fermions cannot occupy the same quantum state in the same atom. Each fermion has an antiparticle with the same properties but opposite charges. Fermions split into two groups by how they interact: quarks and leptons. Within each group, particles pair off into three generations, and every member of a generation is heavier than its counterpart in the generations before it.

  First-generation particles do not decay, so they make up all ordinary baryonic matter. Every atom is electrons orbiting a nucleus built ultimately from up and down quarks. Second- and third-generation charged particles decay with very short half-lives and appear only in high-energy environments.

  There are six quarks: up, down, charm, strange, top, and bottom. Quarks carry color charge, so they feel the strong interaction. Color confinement binds them so tightly that they form color-neutral composites called hadrons, and a quark can never exist alone. A hadron holds either a quark-antiquark pair, called a meson, or three quarks, called a baryon. The lightest baryons are the nucleons, the proton and the neutron.

  The six leptons are the electron, electron neutrino, muon, muon neutrino, tau, and tau neutrino. Leptons carry no color charge and ignore the strong force. The charged leptons carry an electric charge of -1 e, while the three neutrinos carry zero. Neutrinos respond only to the weak interaction and gravity, which is why they pervade the universe yet rarely touch baryonic matter.

• 5. The Force Carriers

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  The Standard Model includes four kinds of gauge bosons of spin 1, and they act as force carriers that mediate the fundamental interactions. Because they carry integer spin, bosons escape the Pauli exclusion principle, so there is no theoretical limit on how densely they can pack into a region of space.

  Photons mediate the electromagnetic force between electrically charged particles. The photon is massless and is described by quantum electrodynamics. Electromagnetism is the only long-range force in the model, and it shapes atomic electron shells, chemical bonds, electric circuits, and electronics.

  Gluons mediate the strong interaction by acting on color charge, as described by quantum chromodynamics. There are eight distinct gluons, each labeled by a color-anticolor combination such as red-antigreen, and they have no mass. Because gluons themselves carry an effective color charge, they interact among themselves, which gives the strong force both confinement and asymptotic freedom.

  The W and Z bosons mediate the weak interaction among all fermions and are responsible for radioactivity. They carry mass, unlike the photon and gluon. The W boson carries an electric charge of +1 or -1, acts only on left-handed particles and right-handed antiparticles, and changes a particle's flavor. The electrically neutral Z boson interacts with both left-handed particles and right-handed antiparticles without changing flavor. The weak interaction is the only one to violate both parity and CP.

  Gravity has no carrier in the model. The hypothetical graviton has been proposed but never observed, because quantum mechanics and Einstein's general relativity remain incompatible. In general relativity, gravity is the geometric curving of spacetime.

• 6. The Mass Giver

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  Peter Higgs, with others, theorized a massive scalar elementary particle in 1964. He showed that Goldstone's 1962 theorem, about a continuous symmetry that is spontaneously broken, supplies a third polarization for a massive vector field. That scalar particle became known as the Higgs boson, and it has no intrinsic spin, which classifies it as a spin-0 boson.

  The Higgs boson explains why every other elementary particle except the photon and gluon has mass. It explains why the photon stays massless while the W and Z bosons grow very heavy. Through electroweak theory, it generates the masses of the leptons, the electron, muon, and tau, and the masses of the quarks. Because the Higgs boson is itself massive, it must interact with itself.

  A Higgs boson is very massive and decays almost immediately once created, so only a very high-energy accelerator can record it. Mathematical consistency required that any mechanism generating elementary masses become visible at energies above a certain scale, which is why the LHC was designed to collide two 7 TeV proton beams. Experiments to confirm it began at the LHC in early 2010 and ran at Fermilab's Tevatron until that machine closed in late 2011.

• 7. Nineteen Numbers

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  Quantum field theory supplies the mathematical frame for the Standard Model, where a Lagrangian governs the dynamics, and each kind of particle is a field that fills space-time. Builders postulate a set of symmetries first, then write the most general renormalizable Lagrangian consistent with them. The global Poincare symmetry, covering translation, rotation, and the inertial-frame invariance of special relativity, holds for all relativistic quantum field theories.

  The local SU(3) x SU(2) x U(1) gauge symmetry is the internal symmetry that essentially defines the model. Its three factors give rise, roughly, to the three fundamental interactions. The SU(3) sector is quantum chromodynamics, a Yang-Mills theory using the 3 x 3 Gell-Mann matrices, and leptons sit outside it because they do not couple to gluons. The electroweak sector carries the U(1) x SU(2) symmetry, using the Pauli matrices that act only on left-chiral fermions.

  Writing the most general Lagrangian leaves the dynamics dependent on 19 parameters, each fixed by experiment. Among the measured values, the electron mass is 0.511 MeV, the top quark mass is 173.5 GeV, and the Higgs mass is listed as 125.09 GeV. The Higgs field is an SU(2) doublet of complex scalar fields with four degrees of freedom, and its vacuum expectation value sets the scale of electroweak physics at about 246 GeV. That value is the only dimensional parameter of the whole theory.

• 8. What It Cannot Explain

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  Self-consistency of the Standard Model, formulated as a non-abelian gauge theory quantized through path-integrals, has never been mathematically proved. Regularized versions such as lattice gauge theory allow approximate computation, but it is unknown whether they converge once the regulator is removed. This ties into the Yang-Mills existence and mass gap problem.

  Experiments show that neutrinos have mass, which the classic Standard Model did not allow. The model can be modified to include neutrino mass, though it is not obvious how. One route adds a non-renormalizable interaction of leptons with the Higgs boson. A deeper route is the seesaw mechanism, which adds heavy right-handed neutrinos and appears naturally in left-right symmetric extensions and certain grand unified theories.

  Some physicists find the theory ad hoc, pointing to its 19 arbitrary constants whose values are unrelated. Explaining neutrino mass in full is expected to demand another 7 or 8 constants, equally arbitrary. The Higgs mechanism brings the hierarchy problem, which forces severe fine tuning if new physics sits at high energy scales.

  The model also clashes with the Lambda-CDM model of cosmology. It offers no source for the observed cold dark matter, no account of the universe's accelerating expansion linked to dark energy, and no clean explanation for why matter outweighs antimatter. The isotropy and homogeneity of the visible universe seem to demand cosmic inflation, itself an extension beyond the model. No proposed theory of everything has yet been widely accepted or verified, which leaves the next chapter of physics unwritten.