elementary particle

any of several entities, such as electrons, neutrons, or protons, that are less complex than atoms and are regarded as the constituents of all matter

Elementary particle

A particle that is not a compound of other particles. At one time the elementary particles of matter were the atoms of the chemical elements, but the atoms are now known to be compounds of the electron, proton, and neutron. In turn, the proton and neutron, and likewise all the other hadrons (strongly interacting particles), are now known to be compounds of quarks. It is convenient, however, to continue to call hadrons elementary particles to distinguish them from their compounds (atomic nuclei, for instance); this usage is also justified by the fact that quarks are not strictly particles, because, as far as is known, they cannot be isolated. The term fundamental particle can be used to denote particles that are truly fundamental constituents of matter and are not compounds in any sense. See Electron, Hadron, Neutron, Proton, Quarks

The known fundamental particles (see table) fall into two categories: the gauge bosons, comprising the photon, gluon, and weak bosons; and the fermions, comprising the quarks and leptons. The graviton, the quantum of the gravitational field, has been omitted from table since it plays no role in high-energy particle physics: it is firmly predicted by theory, but the prospect of direct observation is exceedingly remote. Of the gauge bosons, the photon has been known since the beginning of quantum mechanics. The heavy gauge bosons W ^± and Z ⁰ were observed in 1983; their properties had been deduced from the weak interactions, for which they are responsible. The lightest (and stable) lepton, the electron (e), is the first known fundamental particle. The next found was the muon (μ, originally called the mu meson). The fundamental fermions are grouped into three families. Gluons and quarks are never seen as free particles; this phenomenon is known as confinement. Particles that are composed of quarks and gluons are called hadrons; essentially, mesons are composed of a quark-antiquark pair q, and baryons are three quarks qqq, bound together by the exchange of gluons. See Baryon, Gluons, Graviton, Intermediate vector boson, Lepton, Meson, Photon

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Particles with the properties of the quarks of the quark model (charges ±23e or ±13e and masses less than 300 MeV) have never been observed. Direct evidence both for quarks and for their confinement is given by the phenomenon of hadronic jets. For example, in high-energy deep-inelastic electron-proton scattering, in which the electron loses a sizable fraction of its energy, the observed cross section shows that the charge of the proton is carried by pointlike (radius less than 10^-1 femtometer) particles of small mass. However, no such particles are seen in the final state of this process, or indeed of any other high-energy collision. What is seen is a narrow shower of hadrons. The interpretation is that the electron scatters off one of the quarks in the proton and gives it a large energy and momentum, the quark responding as though it were a free particle of mass much less than 100 MeV, consistent with the masses of the u and d quarks (see table). Later, through the production of quark-antiquark pairs, the energy and momentum of the struck quark is divided among a number of hadrons, mostly pions, a process called hadronization or fragmentation of the quark, which is to be distinguished from the decay of a free particle. The resulting shower of hadrons, whose total momentum vector is roughly that of the original quark, is called a hadronic jet (like a jet of water which breaks up into a spray of droplets). Such jets are also seen in other high-energy reactions, such as e⁺e^- annihilation into hadrons, and also in pp collisions; they are the closest available phenomenon to the actual observation of a quark as a free particle.

To each kind of particle there corresponds an antiparticle, or conjugate particle, which has the same mass and spin, belongs to the conjugate representation (multiplet) of internal symmetry, and has opposite values of charge, I₃, strangeness, and so forth (quantum numbers which are conserved additively). The product of the space parities of a particle and its antiparticle is +1 if the particle is a boson, -1 if a fermion. For instance, the electron e and its antiparticle, the positron e^-, have the same masses and spins, and opposite charges and lepton number, and an S-wave state of e and e^- has parity -1. Particles for which the antiparticle is the same as the particle are called self-conjugate; examples are the photon γ and the neutral pion &pgr;⁰. The equality of masses implies the equality of lifetimes of particle and antiparticle. Thus the positron is stable; however, in the presence of ordinary matter it soon annihilates with an electron, and thus is not a component of ordinary matter. See Antimatter, Positron

The interactions of particles are responsible for their scattering and transformations (decays and reactions). Because of interactions, an isolated particle may decay into other particles. Two particles passing near each other may transform, perhaps into the same particles but with changed momenta (elastic scattering) or into other particles (inelastic scattering). The rates or cross sections of these transformations, and so also the interactions responsible for them, fall into three groups: strong (typical decay rates of 10²¹–10²³ s^-1), electromagnetic (10¹⁶–10¹⁹ s^-1), and weak (<10¹⁵ s^-1). Strong interactions occur only between hadrons. Electromagnetic interactions result from the coupling of charge to the electromagnetic field. Weak interactions are usually unobservable in competition with strong or electromagnetic interactions. They are observable only when they do something which those much stronger interactions cannot do (forbidden by the selection rules); for instance, by changing flavors they can make a particle decay which would otherwise be stable, and by making parity-violating transition amplitudes they can produce an otherwise absent asymmetry in the angular distribution of a reaction. See Selection rules (physics)

Most particles are unstable and decay into smaller-mass particles. The only particles which appear to be stable are the massless particles (graviton, photon), the neutrinos (possibly massless), the electron, the proton, and the ground states of stable nuclei, atoms, and molecules. It is speculated that some or all of the neutrinos may be massive and unstable and that the proton (and therefore all nuclei) may be unstable. The present view is that the only massive particles which are strictly stable are the electron and the lightest neutrino(s). The electron is the lightest charged particle; its decay would be into neutral particles and could not conserve charge. Likewise, the lightest neutrino is the lightest fermion; its decay would be into bosons and could not conserve angular momentum. See Neutrino

The unstable elementary particles must be studied within a short time of their creation, which occurs in the collision of a fast (high-energy) particle with another particle. Such fast particles exist in nature, namely the cosmic rays, but their flux is small; thus most elementary particle research is based on high-energy particle accelerators. See Nuclear reaction, Particle accelerator, Particle detector

Hadrons can be divided into the quasistable (or hadronically stable) and the unstable. The quasistable hadrons are simply those that are too light to decay into other hadrons by way of the strong interactions, such decays being restricted by the requirement that isobaric spin I and flavors be conserved.

The unstable hadrons are also called particle resonances. Their lifetimes, of the order of 10^-23 s, are much too short to be observed directly. Instead they appear, through the uncertainty principle, as spreads in the masses of the particles—that is, in their widths—just as in the case of nuclear resonances. See Uncertainty principle

A characteristic of the hadrons is that they are grouped into i-spin multiplets (for example, n, p; &pgr;^-, &pgr;⁰, &pgr;⁺); the masses of the particles in each multiplet differ by only a few megaelectronvolts (MeV). The i-spin multiplets of hadrons themselves form groups (called supermultiplets) which were recognized in 1961 as multiplets (representations) of the group SU₃ (now referred to as SU₃^flavor to distinguish this physical symmetry from SU₃^color). For instance, the lightest mesons (&eegr;, K, &pgr;) and baryons (&Lgr;, N, &Xgr;, &Sgr;) are each a set of eight particles having i-spins I = (0, 12, 12, 1) and hypercharges Y = (0,1, - 1,0) respectively; this pattern is that of the octet, {8}, representation of the group SU₃. Again, the lowest-mass J^P = &frac;32⁺ baryons (Δ, &Sgr;*, &Xgr;*, &OHgr;), ten particles with I = (&frac;32, 1, 12, 0) and Y = (1, 0, -1, -2), form a decuplet, {10}, representation of SU₃. The spread of the masses in these groups is about a hundred times greater than in the i-spin multiplets, a few hundred MeV compared to a few MeV. According to the quark model, this SU₃ symmetry and the pattern of charges in the SU₃ multiplets result simply from the existence of a third kind (flavor) of quark, the s (strange) quark, with charge the same as the d quark, namely 13, together with the flavor independence of the glue force; that is, all three quarks u, d, and s have the same interaction with the glue field. The resulting flavor SU₃ symmetry is broken by the relatively large mass of the s, approximately 150 MeV. The three quarks make up the fundamental triplet, {3}, representation of SU₃.

Hadrons are known which contain yet more massive quarks, the c and the b (see the table). The resulting symmetry is badly broken, and the supermultiplets hardly recognizable.

It appears that the “glue” field which binds quarks together to make hadrons is a Yang-Mills (that is, a non-abelian) gauge field of an SU₃ symmetry group, SU₃^color. This is an exact symmetry of nature. The quanta of the field are called gluons, and its quantum theory is called quantum chromodynamics (QCD). The gluon field resembles the electromagnetic field, but has an internal symmetry index (octet index) which runs over eight values; that is, there are really eight fields, corresponding to the eight parameters needed to specify an SU₃ transformation. Just as the electromagnetic field is coupled to (that is, photons are emitted and absorbed by) the density and current of a conserved quantity, charge, the gluon field is coupled to color. The coupling of the gluon to a particle is fixed by the color of the particle (that is, what member of what color multiplet) and just one universal coupling constant g, analogous to the electronic unit of charge e. (The analogy breaks down in quantum theory, as discussed below; the quantity g is no longer constant but it is still universal.)

Since the long-range forces observed between hadrons are no different than those between other particles, hadrons must be colorless, that is, color singlet combinations of quarks, their colored constituents. The two simplest combinations of quarks which can be colorless are ₁q₂ and q₁q₂q₃; these are found in nature as the basic structure of mesons and baryons, respectively. The exchange of gluons between any of the quarks in these colorless combinations gives rise to an attractive force, which binds them together.

Gluons are not colorless, and therefore they are coupled to themselves. This situation is very different from electromagnetism, where the photon does not carry charge. The consequence of this self-coupling of massless particles is a severe infrared (small momentum transfer or large distance) divergence of perturbation theory. In particular, the interaction between two colored particles through the gluon field, which in lowest order is an inverse-square Coulomb force, proportional to g²/r² (where r is the distance between the particles), becomes stronger than this inverse-square force at larger r. A way of describing this is to say that the coupling constant g is effectively larger at larger r; this defines the so-called running coupling constant g(r). According to the first-order radiative correction, g(r) becomes infinite at a certain distance, the so-called scale parameter r_c.

A specific form for the gluonic force between two colored particles, at large r, namely that it falls to a nonzero constant value λ, of the order of ℏcr_c^-2 (where ℏ is Planck's constant divided by 2&pgr;, and c is the speed of light), is suggested by a model, the superconductor analogy. This force is confining.

The conjecture is that the vacuum is like a superconductor with respect to color, with the interchange, however, of electric and magnetic quantities. That is, the vacuum acts like a color magnetic superconductor which confines color flux into bundles which have a diameter of order r_c and an energy per unit length equal to λ of order ℏcr_c^-2. The color flux bundles run between colored particles; they can also form closed loops. These flux bundles are often idealized as having vanishing diameter and are then called strings. This idealization is obviously good only if the flux bundles are long compared to r_c, and if their local radius of curvature is always much larger than r_c.

According to the so-called naive quark model, hadrons are bound states of nonrelativistic (slowly moving) quarks, analogous to nuclei as bound states of nucleons. The interactions between the quarks are taken qualitatively from QCD, namely a confining central potential and (exactly analogous to electrodynamic interactions) spin-spin (hyperfine) and spin-orbit potentials; quantitatively, these potentials are adjusted to make the energy levels of the model system fit the observed hadron masses. This model should be valid for hadrons composed of heavy quarks but not for hadrons containing light quarks (u, d, s), but in fact it succeeds in giving a good description of many properties of all hadrons. One reason is that many of these properties follow from so-called angular physics, that is, symmetry-based physical principles that transcend the specific model. A meson is a bound state of a quark and an antiquark, q₁q₂. A baryon is a bound state of three quarks, q₁q₂q₃.

The known heavy quarks are the c (charm), b (bottom), and t (top) quarks, whose masses are larger than the natural energy scale of QCD, ≈1 GeV. But because the width of the t is also larger than 1 GeV, the t quark decays before the QCD force acts on it, and thus before any well-defined hadron forms. So in the present context “heavy quarks” mean only c and b. A hadron which contains a single heavy quark resembles an atom; the heavy quark sits nearly at rest at the center, and is a static source of the color field, just as the atomic nucleus is a static source of the electric field. Just as an atom is changed very little (except in mass) if its nucleus is replaced by another of the same charge (an isotope), a heavy-quark hadron is changed very little (except in mass) if its heavy quark is replaced by another of the same color. This is called heavy-quark symmetry. So, for example, the D, D*, B, and B* mesons are similar, except in mass. This plays an important role in the quantitative analysis of their weak decays.

If a hadron contains two heavy quarks, then in a not too highly excited state the heavy quarks move slowly, compared to the speed of light c, and so the effect of the exchange of gluons between the quarks can be approximated (up to radiative corrections) by a potential energy which depends only on the positions of the quarks (local static potential); further, the wave function of the system satisfies the ordinary nonrelativistic Schrödinger equation. Consequently, the properties of hadrons composed of heavy quarks are rather easily calculated.

Mesons with the composition c and b are called charmonium and bottomonium, respectively. These names are based on the model of positronium, ee^-; the generic name for flavorless mesons, q, is quarkonium. Since both heavy quarkonium and positronium are systems of a fermion bound to its antifermion by a central force, they are qualitatively very similar.

The electroweak theory, starting from the observation that both the electromagnetic and weak interactions result from the exchange of vector (spin-1) bosons, has unified these interactions into a spontaneously broken gauge theory. Similarly, the observation that the strong (hadronic) interactions are also due to the exchange of vector bosons (gluons) suggests that all these vector bosons (the photon, the three weak bosons, and the eight gluons) are quanta of the components of the gauge field of a large symmetry group, SU₅ or larger. Such theories are called grand unification theories (GUTs). The large symmetry group of the grand unification theory must be spontaneously broken, making all the gauge bosons massive except the gluon octet and the photon, leaving SU₃ × U₁ (color × electromagnetism) as the apparent gauge symmetry of the world. See Grand unification theories

In these theories, the leptons and quarks occur together in multiplets of the large symmetry group. These multiplets are called families (or generations). The known fundamental fermions do seem to fall into three families (see table). Each family consists of a weak i-spin doublet of leptons (neutrino [charge 0] and charged lepton [charge +e]), and a color triplet of weak i-spin doublets of quarks (up-type [charge 23e] and down-type [charge -13e]).