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This unit takes the story of the basic constituents of matter beyond the fundamental particles that we encountered in unit 1. It focuses on the interactions that hold those particles together or tear them asunder. Many of the forces responsible for those interactions are basically the same even though they manifest themselves in different ways. Today we recognize four fundamental forces: gravity, electromagnetism, and the strong and weak nuclear forces. Detailed studies of those forces suggest that the last three—and possibly all four—were themselves identical when the universe was young, but have since gone their own way. But while physicists target a grand unification theory that combines all four forces, they also seek evidence of the existence of new forces of nature

**angular momentum**

In classical physics, the angular momentum of a system is the momentum associated with its rotational motion. It is defined as the system’s moment of inertia multiplied by its angular velocity. In quantum mechanics, a system’s total angular momentum is the sum of the angular momentum from its rotational motion (called orbital angular momentum) and its spin.

**baryon**

The term “baryon” refers to any particle in the Standard Model that is made of three quarks. Murray Gell-Mann arranged the baryons into a periodic table-like structure according to their baryon number and strangeness (see Unit 1, Fig. 1). Protons and neutrons are the most familiar baryons.

**beta decay**

Beta decay is a type of radioactive decay in which a beta particle (electron or positron) is emitted together with a neutrino. Beta decay experiments provided the first evidence that neutrinos exist, which was unexpected theoretically at the time. Beta decay proceeds via the weak interaction.

**boson**

A boson is a particle with integer, rather than half-integer, spin. In the Standard Model, the force-carrying particles such as photons are bosons. Composite particles can also be bosons. Mesons such as pions are bosons, as are 4He atoms. See: fermion, meson, spin.

**charge conjugation**

Charge conjugation is an operation that changes a particle into its antiparticle.

**chiral symmetry**

A physical theory has chiral symmetry if it treats left-handed and right-handed particles on equal footing. Chiral symmetry is spontaneously broken in QCD.

**color**

In QCD, color is the name given to the charge associated with the strong force. While the electromagnetic force has positive and negative charges that cancel one another out, the strong force has three types of color, red, green, and blue, that are canceled out by anti-red, anti-green, and anti-blue.

**Compton scattering**

Compton scattering is the scattering of photons from electrons. When Arthur Compton first explored this type of scattering experimentally by directing a beam of electrons onto a target crystal, he found that the wavelength of the scattered photons was longer than the wavelength of the photons incident on the target, and that larger scattering angles were associated with longer wavelengths. Compton explained this result by applying conservation of energy and momentum to the photon-electron collisions.

**cross section**

A cross section, or scattering cross section, is a measure of the probability of two particles interacting. It has units of area, and depends on the initial energies and trajectories of the interacting particles as well as the details of the force that causes the particles to interact.

**electromagnetic interaction**

The electromagnetic interaction, or electromagnetic force, is one of the four fundamental forces of nature. Maxwell first understood at the end of the 19th century that the electric and magnetic forces we experience in daily life are different manifestations of the same fundamental interaction. In modern physics, based on quantum field theory, electromagnetic interactions are described by quantum electrodynamics or QED. The force-carrier particle associated with electromagnetic interactions is the photon.

**fermion**

A fermion is a particle with half-integer spin. The quarks and leptons of the Standard Model are fermions with a spin of 1/2. Composite particles can also be fermions. Baryons, such as protons and neutrons, and atoms of the alkali metals are all fermions. See: alkali metal, baryon, boson, lepton, spin.

**field**

In general, a field is a mathematical function that has a value (or set of values) at all points in space. Familiar examples of classical fields are the gravitational field around a massive body and the electric field around a charged particle. These fields can change in time, and display wave-like behavior. In quantum field theory, fields are fundamental objects, and particles correspond to vibrations or ripples in a particular field.

**flavor**

In particle physics, the flavor of a particle is a set of quantum numbers that uniquely identify the type of particle it is. The quark flavors are up, down, charm, strange, top, and bottom. The lepton flavors are electron, muon, tau, and their corresponding neutrinos. A particle will have a flavor quantum number of +1 in its flavor, and its antiparticle has a quantum number of -1 in the same flavor. For example, an electron has electron flavor +1, and a positron has electron flavor of -1.

**force carrier**

In quantum field theory, vibrations in the field that correspond to a force give rise to particles called force carriers. Particles that interact via a particular force do so by exchanging these force carrier particles. For example, the photon is a vibration of the electromagnetic field and the carrier of the electromagnetic force. Particles such as electrons, which have negative electric charge, repel one another by exchanging virtual photons. The carrier of the strong force is the gluon, and the carrier particles of the weak force are the W and Z bosons. Force carriers are always bosons, and may be either massless or massive.

**gluons**

Gluons are particles in the Standard Model that mediate strong interactions. Because gluons carry color charge, they can participate in the strong interaction in addition to mediating it. The term “gluon” comes directly from the word glue, because gluons bind together into mesons.

**graviton**

The graviton is the postulated force carrier of the gravitational force in quantum theories of gravity that are analogous to the Standard Model. Gravitons have never been detected, nor is there a viable theory of quantum gravity, so gravitons are not on the same experimental or theoretical footing as the other force carrier particles.

**gravity**

Gravity is the least understood of the four fundamental forces of nature. Unlike the strong force, weak force, and electromagnetic force, there is no viable quantum theory of gravity. Nevertheless, physicists have derived some basic properties that a quantum theory of gravity must have, and have named its force-carrier particle the graviton.

**group**

Group is a mathematical term commonly used in particle physics. A group is a mathematical set together with at least one operation that explains how to combine any two elements of the group to form a third element. The set and its operations must satisfy the mathematical properties of identity (there is an element that leaves other group elements unchanged when the two are combined), closure (combining any two group elements yields another element in the group), associativity (it doesn’t matter in what order you perform a series of operations on a list of elements so long as the order of the list doesn’t change), and invertability (every operation can be reversed by combining the result with another element in the group). For example, the set of real numbers is a group with respect to the addition operator. A symmetry group is the set of all transformations that leave a physical system in a state indistinguishable from the starting state.

**hadron**

The term hadron refers to the Standard Model particle made of quarks. Mesons and baryons are classified as hadrons.

**handedness**

Handedness, also called “chirality,” is a directional property that physical systems may exhibit. A system is “right handed” if it twists in the direction in which the fingers of your right hand curl if your thumb is directed along the natural axis defined by the system. Most naturally occurring sugar molecules are right handed. Fundamental particles with spin also exhibit chirality. In this case, the twist is defined by the particle’s spin, and the natural axis by the direction in which the particle is moving. Electrons produced in beta-decay are nearly always left handed.

**Heisenberg uncertainty principle**

The Heisenberg uncertainty principle states that the values of certain pairs of observable quantities cannot be known with arbitrary precision. The most well-known variant states that the uncertainty in a particle’s momentum multiplied by the uncertainty in a particle’s position must be greater than or equal to Planck’s constant divided by 4. This means that if you measure a particle’s position to better than Planck’s constant divided by 4, you know that there is a larger uncertainty in the particle’s momentum. Energy and time are connected by the uncertainty principle in the same way as position and momentum. The uncertainty principle is responsible for numerous physical phenomena, including the size of atoms, the natural linewidth of transitions in atoms, and the amount of time virtual particles can last.

**Higgs mechanism**

The Higgs mechanism, named for Peter Higgs but actually proposed independently by several different groups of physicists in the early 1960s, is a theoretical framework that explains how fundamental particles acquire mass. The Higgs field underwent a phase transition as the universe expanded and cooled, not unlike liquid water freezing into ice. The condensed Higgs field interacts with the different massive particles with different couplings, giving them their unique masses. This suggests that particles that we can measure to have various masses were massless in the early universe. Although the Higgs mechanism is an internally consistent theory that makes successful predictions about the masses of Standard Model particles, it has yet to be experimentally verified. The clearest signature of the Higgs mechanism would be the detection of a Higgs boson, the particle associated with vibrations of the Higgs field.

**jet**

In the terminology of particle physics, a jet is a highly directed spray of particles produced and detected in a collider experiment. A jet appears when a heavy quark is produced and decays into a shower of quarks and gluons flying away from the center of the collision.

**kinetic energy**

Kinetic energy is the energy associated with the motion of a particle or system. In classical physics, the total energy is the sum of potential and kinetic energy.

**Large Hadron Collider (LHC)**

The Large Hadron Collider (LHC) is a particle accelerator operated at CERN on the outskirts of Geneva, Switzerland. The LHC accelerates two counter-propagating beams of protons in the 27 km synchrotron beam tube formerly occupied by Large Electron-Positron Collider (LEP). It is the largest and brightest accelerator in the world, capable of producing proton-proton collisions with a total energy of 14 TeV. Commissioned in 2008–09, the LHC is expected to find the Higgs boson, the last undiscovered particle in the Standard Model, as well as probe physics beyond the Standard Model.

**LEP**

The Large Electron-Positron Collider (LEP) is a particle accelerator that was operated at CERN on the outskirts of Geneva, Switzerland, from 1989 to 2000. LEP accelerated counterpropagating beams of electrons and positrons in a 27 km diameter synchrotron ring. With a total collision energy of 209 GeV, LEP was the most powerful electron-positron collider ever built. Notably, LEP enabled a precision measurement of the mass of W and Z bosons, which provided solid experimental support for the Standard Model. In 2000, LEP was dismantled to make space for the LHC, which was built in its place.

**leptons**

The leptons are a family of fundamental particles in the Standard Model. The lepton family has three generations, shown in Unit 1, Fig. 1: the electron and electron neutrino, the muon and muon neutrino, and the tau and tau neutrino.

**macroscopic**

A macroscopic object, as opposed to a microscopic one, is large enough to be seen with the unaided eye. Often (but not always), classical physics is adequate to describe macroscopic objects, and a quantum mechanical description is unnecessary.

**meson**

The term meson refers to any particle in the Standard Model that is made of one quark and one anti-quark. Murray Gell-Mann arranged the leptons into a periodic-table-like structure according to their electric charge and strangeness (see Unit 1, Fig. 1). Examples of mesons are pions and kaons.

**Nambu-Goldstone theorem**

The Nambu-Goldstone theorem states that the spontaneous breaking of a continuous symmetry generates new, massless particles.

**Newton’s law of universal gravitation**

Newton’s law of universal gravitation states that the gravitational force between two massive particles is proportional to the product of the two masses divided by the square of the distance between them. The law of universal gravitation is sometimes called the “inverse square law.” See: universal gravitational constant.

**nuclear fission**

Nuclear fission is the process by which the nucleus of an atom decays into a lighter nucleus, emitting some form of radiation. Nuclear fission reactions power nuclear reactors, and provide the explosive energy in nuclear weapons.

**nuclear fusion**

Nuclear fusion is the process by which the nucleus of an atom absorbs other particles to form a heavier nucleus. This process releases energy when the nucleus produced in the fusion reaction is not heavier than iron. Nuclear fusion is what powers stars, and is the source of virtually all the elements lighter than iron in the universe.

**parity**

Parity is an operation that turns a particle or system of particles into its mirror image, reversing their direction of travel and physical positions.

**phase**

In physics, the term phase has two distinct meanings. The first is a property of waves. If we think of a wave as having peaks and valleys with a zero-crossing between them, the phase of the wave is defined as the distance between the first zero-crossing and the point in space defined as the origin. Two waves with the same frequency are “in phase” if they have the same phase and therefore line up everywhere. Waves with the same frequency but different phases are “out of phase.” The term phase also refers to states of matter. For example, water can exist in liquid, solid, and gas phases. In each phase, the water molecules interact differently, and the aggregate of many molecules has distinct physical properties. Condensed matter systems can have interesting and exotic phases, such as superfluid, superconducting, and quantum critical phases. Quantum fields such as the Higgs field can also exist in different phases.

**Planck’s constant**

Planck’s constant, denoted by the symbol h, has the value 6.626 x 10-34 m2 kg/s. It sets the characteristic scale of quantum mechanics. For example, energy is quantized in units of h multiplied by a particle’s characteristic frequency, and spin is quantized in units of h/2. The quantity h/2 appears so frequently in quantum mechanics that it has its own symbol: .

**potential energy**

Potential energy is energy stored within a physical system. A mass held above the surface of the Earth has gravitational potential energy, two atoms bound in a molecule have chemical potential energy, and two electric charges separated by some distance have electric potential energy. Potential energy can be converted into other forms of energy. If you release the mass, its gravitational potential energy will be converted into kinetic energy as the mass accelerates downward. In the process, the gravitational force will do work on the mass. The force is proportional to the rate at which the potential energy changes. It is common practice to write physical theories in terms of potential energy, and derive forces and interactions from the potential.

**quantized**

Any quantum system in which a physical property can take on only discrete values is said to be quantized. For instance, the energy of a confined particle is quantized. This is in contrast to a situation in which the energy can vary continuously, which is the case for a free particle.

**quantum electrodynamics**

Quantum electrodynamics, or QED, is the quantum field theory that describes the electromagnetic force. In QED, electromagnetically charged particles interact by exchanging virtual photons, where photons are the force carried of the electromagnetic force. QED is one of the most stringently tested theories in physics, with theory matching experiment to a part in 1012.

**quantum field theory (QFT)**

Quantum field theory, or QFT, is a generalization of quantum mechanics capable of describing relativistic particles. It is currently the standard mathematical formalism used in particle physics, as well as certain areas of condensed matter and atomic physics. In QFT, fields rather than particles are the fundamental objects. Particles correspond to vibrations of these fields. This formulation puts particles and forces on equal footing, as both are described by fields. An interaction between two particles, which are vibrations in the field that correspond to that type of particle, proceeds through the exchange of the particle that corresponds to a vibration in the field associated with the force. For example, electrons are vibrations of the electron field, and photons are vibrations of the electromagnetic field. When two electrons repel, they exchange photons.

**relativistic**

A relativistic particle is traveling close enough to the speed of light that classical physics does not provide a good description of its motion, and the effects described by Einstein’s theories of special and general relativity must be taken into account.

**relativistic limit**

In general, the energy of an individual particle is related to the sum of its mass energy and its kinetic energy by Einstein’s equation E2 = p2c2 + m2c4, where p is the particle’s momentum, m is its mass, and c is the speed of light. When a particle is moving very close to the speed of light, the first term (p2c2) is much larger than the second (m2c4), and for all practical purposes the second term can be ignored. This approximation—ignoring the mass contribution to the energy of a particle—is called the “relativistic limit.”

**Rutherford scattering**

The term Rutherford scattering comes from Ernest Rutherford’s experiments that led to the discovery of the atomic nucleus. Rutherford directed a beam of alpha particles (which are equivalent to helium nuclei) at a gold foil and observed that most of the alpha particles passed through the foil with minimal deflection, but that occasionally one bounced back as if it had struck something solid.

**spacetime**

In classical physics, space and time are considered separate things. Space is three-dimensional, and can be divided into a three-dimensional grid of cubes that describes the Euclidean geometry familiar from high-school math class. Time is one-dimensional in classical physics. Einstein’s theory of special relativity combines the three dimensions of space and one dimension of time into a four-dimensional grid called “spacetime.” Spacetime may be flat, in which case Euclidean geometry describes the three space dimensions, or curved. In Einstein’s theory of general relativity, the distribution of matter and energy in the universe determines the curvature of spacetime.

**spontaneous symmetry breaking**

Spontaneous symmetry breaking is said to occur when the theory that describes a system contains a symmetry that is not manifest in the ground state. A simple everyday example is a pencil balanced on its tip. The pencil, which is symmetric about its long axis and equally likely to fall in any direction, is in an unstable equilibrium. If anything (spontaneously) disturbs the pencil, it will fall over in a particular direction and the symmetry will no longer be manifest.

**strong interaction**

The strong interaction, or strong nuclear force, is one of the four fundamental forces of nature. It acts on quarks, binding them together into mesons. Unlike the other forces, the strong force between two particles remains constant as the distance between them grows, but actually gets weaker when the particles get close enough together. This unique feature ensures that single quarks are not found in nature. True to its name, the strong force is a few orders of magnitude stronger than the electromagnetic and weak interactions, and many orders of magnitude stronger than gravity.

**superpartner**

In the theory of supersymmetry, every Standard Model particle has a corresponding “sparticle” partner with a spin that differs by 1/2. Superpartner is the general term for these partner particles. The superpartner of a boson is always a fermion, and the superpartner of a fermion is always a boson. The superpartners have the same mass, charge, and other internal properties as their Standard Model counterparts. See: supersymmetry.

**supersymmetry**

Supersymmetry, or SUSY, is a proposed extension to the Standard Model that arose in the context of the search for a viable theory of quantum gravity. SUSY requires that every particle have a corresponding superpartner with a spin that differs by 1/2. While no superpartner particles have yet been detected, SUSY is favored by many theorists because it is required by string theory and addresses other outstanding problems in physics. For example, the lightest superpartner particle could comprise a significant portion of the dark matter.

**symmetry transformation**

A symmetry transformation is a transformation of a physical system that leaves it in an indistinguishable state from its starting state. For example, rotating a square by 90 degrees is a symmetry transformation because the square looks exactly the same afterward.

**virtual particle**

A virtual particle is a particle that appears spontaneously and exists only for the amount of time allowed by the Heisenberg uncertainty principle. According to the uncertainty principle, the product of the uncertainty of a measured energy and the uncertainty in the measurement time must be greater than Planck’s constant divided by 4. This means that a particle with a certain energy can spontaneously appear out of the vacuum and live for an amount of time inversely proportional to its energy. The force carriers exchanged in an interaction are virtual particles. Virtual particles cannot be observed directly, but their consequences can be calculated using Feynman diagrams and are verified experimentally.

**weak interaction**

The weak interaction, or weak force, is one of the four fundamental forces of nature. It is called “weak” because it is significantly weaker than both the strong force and the electromagnetic force; however, it is still much stronger than gravity. The weak changes one flavor of quark into another, and is responsible for radioactive decay.

David E. Kaplan is a professor in the Department of Physics and Astronomy at Johns Hopkins University. His primary research interests are in theoretical particle physics with a particular focus on electroweak superconductivity and potentially related physics, such as supersymmetry, new fundamental forces, extra dimensions, and dark matter. He is also exploring connections between particle physics and cosmology.

Ayana Arce is an assistant professor at Duke University and a former Chamberlain Postdoctoral Fellow at Lawrence Berkeley National Laboratory. She concentrates on experimental techniques to identify and measure the properties of heavy unstable elementary particles such as the top quark in order to search for unexpected interactions. She is currently involved in the ATLAS experiment at the Large Hadron Collider (LHC).

Srini Rajagopalan, a high energy physicist from Brookhaven National Laboratory (BNL) in New York, is currently working on the ATLAS experiment at the LHC, CERN. After earning his Ph.D. from Northwestern University and a post-doctoral appointment at State University of New York at Stony Brook—both at the D0 experiment at Fermilab, Srini joined the BNL staff and started working on ATLAS. He has now been with ATLAS for over 14 years and has worked in a number of projects. He currently oversees the work on its trigger system with responsibility for capturing and recording any new physics that sheds further light in our understanding of the origins of the universe and the matter and forces that shape it.