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Elementary

Contributed by: Frank E. Close

Publication year: 2015

Key Concepts

• Elementary —including , , and —were conventionally considered to

be fundamental particles of , although some of these are now known to be compounds of other

particles.

• Other elementary particles include (which result from the decay of unstable neutrons),

(fundamental constituents of protons and neutrons), and other , and taus (types of

), and (a type of ).

• Fundamental that act on elementary particles are , the electromagnetic , the strong

force, and the weak force, all of which act through the exchange of gauge bosons.

• of elementary particles may cause scattering and transformations (decays and reactions) of

particles.

• Characteristics of elementary particles include , , , , , and bottomness.

• The explains the mass of elementary particles as being due to their interactions with the

Higgs field, as manifested by Higgs bosons.

A label usually applied to protons, neutrons, electrons, and related subatomic particles that were previously considered to be fundamental, although some of these are now known to be compounds of other particles.

Our identification of the elementary particles has evolved with our understanding of matter. The idea that everything is made from a few basic elements originated in ancient Greece. In the nineteenth century, the elementary pieces of matter were believed to be the of the chemical elements, but in the first half of the twentieth century, atoms were found to be made up of electrons, protons, and neutrons. These became known as elementary particles, that is, particles that are not compounds of other particles. Today, however, many such particles (including the and ) are known to be compounds of quarks. All of these are conventionally, if illogically, known as elementary particles. See also: ; NEUTRON ; PROTON . AccessScience from McGraw-Hill Education Page 2 of 21 www.accessscience.com

Historical overview

The electrical attraction of opposite electric charges is what grips negatively charged electrons around the positively charged ; it is the protons that give a nucleus its charge. The amount of positive charge on a proton is equal in magnitude but opposite in sign to that on an electron. This is crucial for the fact that matter in bulk is electrically neutral, with the result that gravity controls the motion of planets and our attraction to the Earth’s surface. However, why these two particles carry such precisely counterbalanced electric charges is a mystery. See also: COULOMB’S LAW ; ; GRAVITATION .

2 A proton is some 1836 times as massive as an electron, their being, respectively, 938.3 and 0.511 MeV ∕ c, , 2 where c is the speed of . A neutron has a mass of 939.6 MeV ∕ c , and is very similar to a proton. In the immediate aftermath of its discovery in 1932, the neutron was thought to be a version of a proton with no electric charge; however, today their relationship is understood to be more profound.

An electron or a proton is stable, at least on time scales longer than the age of the . When neutrons are in the nuclei of atoms such as iron, they too may survive unchanged for billions of years. However, an isolated neutron is unstable, with a mean life of 886 s. Neutrons can also be unstable when large numbers of them are packed into a nucleus with protons; this leads to natural radioactivity of many elements. Such neutrons undergo beta decay, a result of the weak force, which converts a neutron into a proton and emits an electron and a . See also: BETA PARTICLES ; RADIOACTIVITY .

Neutrinos have no electric charge and masses that are too small to measure with present techniques. The 2 neutrino emitted in the neutron beta decay has a mass that is less than 2 eV ∕ c , , that is, less than 1 ∕ 100,000 the mass of the electron. See also: NEUTRINO .

In the 1930s, the known elementary particles were the four just named and the ( γ ), the quantum particle of electromagnetic radiation. The electron and the neutrino are known as leptons and are still recognized as elementary in the sense that they are not composed of more fundamental constituents, whereas the proton and the neutron are built from quarks. Two varieties, or flavors, of are required to make protons and neutrons. 2 They are the (denoted u ), with an electric charge that is a fraction + ∕3 of a proton’s charge, and the 1 ( d ), whose fractional charge is − ∕3 . The combination uud is sufficient to make a proton, and ddu makes a neutron. See also: ; PHOTON ; QUARKS .

The up and down quarks, together with the electron and the neutrino, form a basic family of what is known as the standard model of fundamental particles. These particles are , defined by having an intrinsic angular ,1 momentum or spin of ∕, 2 in units of Planck’s quantum. The photon is a , with an integer spin of 1. The exchange of photons between electrically charged particles transmits the electromagnetic force. See also:

ANGULAR MOMENTUM ; ; QUANTUM STATISTICS ; SPIN () ; STANDARD MODEL . AccessScience from McGraw-Hill Education Page 3 of 21 www.accessscience.com

This simple picture began to break down around 1950 with the discoveries of new forms of particles, first in cosmic rays and then in experiments at high-energy accelerators. With modern hindsight, it is possible to classify the discoveries into two classes: leptons and . See also: COSMIC RAYS ; PARTICLE

ACCELERATOR .

The is a lepton with the same spin and electric charge as an electron, but some 207 times more massive at 2 105.7 MeV ∕ c , . Today, six members of the lepton family are known: three that are electrically charged—the 2 electron ( e ), muon ( μ), and ( τ) [mass 1777 MeV ∕ c , ]—and three varieties of neutrino known as the ν ν ν electron-neutrino ( ,e ), the ( ,μ ), and the ( ,τ ) [ Table 1 ]. The masses of the neutrinos have not yet been directly measured, but it is known from neutrino oscillations that at least two neutrinos have nonzero masses. All of these are fundamental particles. Leptons are unaffected by the strong (nuclear) force but feel the weak force and, if electrically charged (the electron, muon, and tau), the electromagnetic force. See also:

STRONG NUCLEAR INTERACTIONS ; WEAK NUCLEAR INTERACTIONS .

Particles that feel the strong force are known as hadrons. The cosmic rays revealed the existence of unstable hadrons, some of which became known as strange particles, such as the K and the lambda ( Λ).

Experiments at particle accelerators enabled such particles to be produced when the kinetic energy of particles colliding with atomic nuclei was converted into ephemeral particles, which were revealed by their trails in bubble chambers (or nowadays by electronic detectors). Among these were short-lived heavier versions of the −23 proton and the neutron, known as resonances, whose lifetimes of the order of 10, s are similar to the time it takes a beam of light to traverse a proton. All of these hadrons are composed of quarks. See also: HADRON ;

PARTICLE DETECTOR .

2 There are six flavors of quark. The up ( u ), charm ( c ), and top ( t ) have electric charge + ∕3 ; the down ( d ), strange 1 ( s ), and bottom ( b ) have charge − ∕3 ( Table 1 ). As individual quarks cannot appear in isolation, a direct measure of their mass is not possible, but approximate scales of mass have been determined. When they are trapped inside hadrons, the up and down quarks have energies of around 300 MeV; most of this is due to their motion, 2 2 their masses being at most 6 MeV ∕ c , . The is some 100 MeV ∕ c , more massive, the 2 2 2 mass is around 1.3 GeV ∕ c , (1300 MeV ∕ c , ), the mass is around 4.5 GeV ∕ c , , and the 2 mass is around 175 GeV ∕ c , . The reason behind these values, or even their qualitative pattern, is not understood.

Strange hadrons contain one or more strange quarks. Hadrons containing charm or bottom quarks are known as charm and bottom hadrons (including a special category known as charmonium and bottomonium). Top quarks are so heavy that no hadrons containing them have been identified. It is even possible that top hadrons cannot → ν form, as the top quark is so unstable that it decays (in a form of beta decay, t be ,e ) before it can grip to other quarks to make observable hadrons. AccessScience from McGraw-Hill Education Page 4 of 21 www.accessscience.com

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Fundamental particles and interactions

The fundamental forces that act on the particles are gravity, the electromagnetic force, and the strong and weak forces. These forces act through the exchange of particles known as gauge bosons ( Table 1 ). For the electromagnetic, strong, and weak forces, these have been identified, respectively, as the photon, , and weak bosons; the , the quantum of the gravitational force, is firmly predicted by theory, but the prospect of direct observation is exceedingly remote. The gravitational force between individual particles is so feeble that it can be ignored for all practical purposes. See also: FUNDAMENTAL INTERACTIONS ; ; GRAVITON .

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 be transformed, perhaps into the same particles but with changed momenta (elastic scattering) or perhaps AccessScience from McGraw-Hill Education Page 5 of 21 www.accessscience.com

into other particles (inelastic scattering). The rates or cross sections of these transformations, and so also the 21 23 −1 interactions responsible for them, fall into three groups: strong (typical decay rates of 10, –10, s, ), 16 19 −1 15 −1 electromagnetic (10, –10, s, ), and weak ( < 10, s, ).

The photon, gluon, and weak bosons have spin 1. The photon and gluon have no mass, whereas weak bosons are + − 2 massive. The weak bosons may be electrically charged (the W, and W, ), with masses of 80.4 GeV ∕ c, , or neutral 0 2 (the Z , ), with mass of 91.2 GeV ∕ c , . The fundamental couplings are known as gauge couplings ( Table 1 ), in which a is absorbed or emitted by a fundamental particle ( or gauge boson). See also: GAUGE

THEORY ; INTERMEDIATE .

A massless photon with little or no energy can be emitted and absorbed by electrons in atoms or within the normal laws of energy and momentum conservation. However, when a neutron undergoes beta decay, − it converts to a proton by emitting a “virtual” W , , violating energy conservation by some 80 GeV. The

Heisenberg uncertainty principle of quantum mechanics states that such a violation can occur, but only for a − limited time, within which time the W , converts into an electron and a neutrino, which are the real end products of beta decay. The energy violation of 80 GeV is so extreme that the ensuing time scale, and in − consequence the distance through which the W , can travel, is exceedingly short. This limits the effects of the forces associated with W exchange, leading it to appear “weak.” See also: ENERGY ; UNCERTAINTY PRINCIPLE .

0 Data show that the fundamental couplings of a photon or of a W or Z , to a lepton or quark are similar in magnitude, so that the electromagnetic and weak forces are now regarded as being two manifestations of a single electroweak force. The apparent difference in their strengths is because the weak bosons are massive, whereas the photon is massless. These differences in masses, and the consequent differences in the effective forces, are examples of breaking. The source of this broken symmetry is a spinless particle known as the . It is the between the Higgs boson and the fundamental fermions and bosons that gives them 2 their masses. The mass of the Higgs boson is around 126 GeV ∕ c, . See also: ; HIGGS BOSON ;

SYMMETRY BREAKING .

Stability

Most particles are unstable and decay into particles with lower masses. Massless particles, such as the photon, are stable. Neutrinos, which were long thought to be massless and stable, are now known to have small masses; the lightest neutrino is the lightest fermion and is stable, as its decay would be into bosons, which could not conserve angular momentum. The present view is that the only massive particles that are strictly stable are the electron and the lightest neutrino or neutrinos. The electron is the lightest charged particle; its decay would be into neutral particles and could not conserve charge. The proton may be stable, although there is no fundamental 30 reason why it need be; for all practical purposes, it is stable with a half-life exceeding 10, years. AccessScience from McGraw-Hill Education Page 6 of 21 www.accessscience.com

Unstable elementary particles must be studied within a short time after their creation, which occurs during the collision of a fast (high-energy) particle with another particle. Such high-energy particles occur naturally in the cosmic rays, but their flux is small; thus, most research is based on high-energy particle accelerators.

Hadrons can be divided into the quasistable and the unstable. The quasistable hadrons ( Fig. 1 ) are those that are too light to decay into other hadrons by way of the strong interactions, such decays being restricted by the requirement that flavors be conserved. The quasistable hadrons that decay through weak interactions have long ,10  ,2 ,−23 mean lives—more than 10 times the characteristic time of strong interactions, ∕ ( m, π c ) = 0.5 × 10 s, where π  π π,0 η ,0 m, π is the mass of the meson or , and is Planck’s constant divided by 2 . Three hadrons, , , and Σ , can ,5  , 2 decay by way of the electromagnetic interaction. These three have mean lives of the order of 10 × ∕ ( m, π c ).

The important practical distinctions in the experimental study of interactions are among (1) the stable massive particles (electrons and nuclei), which can be used as target particles as well as in beams; (2) the particles with ,−8 γ ν μ,± π,± ,± mean lives greater than 10 s ( , , , , K, L , K ), which can be used only in beams; (3) the quasistable ,−10 ,0 , − ,± ,− hadrons with mean lives of the order of 10 s ( Ξ , Λ, Σ , K, S , Ω ), which have only a small but usable chance of interacting in matter before decaying; and (4) the remaining hadrons, which have a vanishingly small chance of reinteracting except when produced within a nucleus.

 ,2 The unstable hadrons are also called particle resonances. Their lifetimes, of the order of ∕ ( m, π c ), 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 ( Fig. 2 ). See also: RESONANCE

(QUANTUM MECHANICS) .

The first unstable hadron observed was the Δ(1232) in pion- scattering. Flavorless vector mesons can be formed as resonances in collisions between electrons and . This technique has led to the discovery of charmonium and bottomonium spectroscopies: quasiatomic systems made from a charm or bottom quark and its corresponding antiquark.

Antiparticles

To each kind of particle there corresponds an , or conjugate particle, which has the same mass and spin but has opposite values of charge, strangeness, charm, or bottomness (quantum numbers that are conserved additively). are denoted by putting a bar over the symbol of the corresponding particle: , antiquark , and so forth. Thus a , such as the proton, made of three quarks implies that an antibaryon is made of three antiquarks, . All and antibaryons have half-integer values of spin and are fermions. Mesons are examples of hadrons that have integer spins and are made of an equal number of quarks and antiquarks. The simplest example of such a meson is thus , and scores of examples are known. It is theoretically possible to form mesons made of , known as or molecules, or even made entirely from gluons, with no quarks, known AccessScience from McGraw-Hill Education Page 7 of 21 www.accessscience.com

WIDTH:CFig. 1 Decay modes of quasistable baryons made from u , d , or s quarks.

, 2 as . There is some evidence that mesons with no spin, f, 0 and a, 0 , having masses 980 MeV ∕ c , are , 2 examples of , and that heavier examples of spinless mesons f, 0 with masses of 1500 and 1710 MeV ∕ c may be quantum mixtures of and a . See also: ; BARYON ; MESON . AccessScience from McGraw-Hill Education Page 8 of 21 www.accessscience.com

WIDTH:CFig. 2 Observation of the η meson ( m = 550 MeV) and the ω meson ( m = 783 MeV) as resonances in the reaction π,+ p → π,+ p π,+ π,− π,0 . Effective mass is the total relativistic energy of three of the emerging in their center-of-mass coordinate system. Peaks in the data indicate that collisions can create a short-lived particle of corresponding mass, which decays into three pions.

Nomenclature

Hadrons with the same spin, of similar mass, and distinguished by their electric charges are distinguished by + 0 writing charge as a superscript, for example, the pi meson ( π) and sigma hyperon Σ have π, and Σ, . (But p and n + 0 are usually written instead of N , and N , .)

With the discovery of large numbers of unstable hadrons, it has become impossible to name each with a different letter; instead, letters are used to denote classes of hadrons. First, hadrons with a common value of spin (denoted

J ), whose quantum wave functions behave the same under space and charge , P and C , and whose masses are similar, form families with the same , I . In recognition of these patterns, a naming scheme has been π , P C ,−+ developed ( Table 2 ). For instance, ,2 is used for any meson with the properties I = 1 and J = 2 , and a AccessScience from McGraw-Hill Education Page 9 of 21 www.accessscience.com

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π particular hadron is distinguished by giving its approximate mass, in MeV [for instance, ,2 (1670)]. If the hadron is the lightest one of its class, the mass can be omitted from its name; it is always omitted if the hadron is hadronically stable. The mass can be replaced by a specification of the quark state of the hadron if this is known; for instance, ψ(2 S ) instead of ψ(3686). The scheme is described in full in The Review of Particle Physics , which is published biennially and updated more frequently on the World Wide Web. See also: I-SPIN ; PARITY (QUANTUM

MECHANICS) ; SYMMETRY LAWS (PHYSICS) .

Since hadrons have an extended structure, they can have rotationally excited states, as do molecules and deformed nuclei. Such states form a sequence of hadrons with increasing spins ( J, 0 , J, 0 + 1, . . . ) and masses, but with the same values of other quantum numbers (except for space and charge parity, P and C , which alternate in sign). For historical reasons, such sequences of hadrons are called Regge trajectories.

Quantum chromodynamics

In addition to their electric charges and flavors, quarks carry a property called color, which is the source of the force between quarks. As photons couple to electric charge and mediate the electromagnetic force, so massless gluons transmit the color force. The quantum theory of the color force is called

(QCD). See also: COLOR (QUANTUM MECHANICS) .

The gluon field is coupled to color. The coupling of the gluon to a particle is fixed by the color of the particle and just one universal g , analogous to the electronic unit of charge e . There are three varieties of color for quarks and three of opposite sign for antiquarks. The rules of attraction and repulsion for electrostatics have an analogy in chromostatics: like colors repel, and unlike colors attract. The latter property has two manifestations. One is directly analogous to electrostatics, in that a quark with a given color attracts an antiquark carrying the opposite sign of . The other possibility is attraction between quarks, each carrying a different color, and in a quantum state that is antisymmetric under interchange of the two particles.

Just as electric charges of opposite sign lead to neutral atoms, so do the color charges of quarks and antiquarks combine to form overall colorless hadrons. Such states are known as color singlets in the language of the AccessScience from McGraw-Hill Education Page 10 of 21 www.accessscience.com

mathematical theory underpinning QCD. As hadrons are colorless, the long-range forces observed between them are no different from those between other particles. The two simplest combinations of quarks that can be colorless are and q, 1 q, 2 q, 3 ; these are found in 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 that binds them together.

Not just quarks and antiquarks but also gluons carry color, and therefore gluons can mutually attract and repel one another. This situation is very different from electromagnetism, where the photon does not carry charge. The consequence of this self-coupling is that the interaction between two colored particles through the gluon field, 2 2 which at short distances is an inverse-square Coulomb force, proportional to g , ∕ r , (where r is the distance between the particles), becomes stronger than this inverse-square force at larger r . This property is interpreted by saying that the coupling strength g is effectively larger at larger r ; this coupling strength defines the so-called running coupling constant g ( r ). Computer simulations of the QCD theory imply that this coupling becomes −15 infinitely strong at distances of the order of 10, m, leading to confinement of the constituent quarks within colorless hadrons, in accord with experiments. The mutual interaction among gluons is predicted to lead to colorless hadrons made from gluons, without the need for quarks. As mentioned earlier, such hadrons are known as glueballs.

This situation is very different from that in (QED). There the long-range force is 2 precisely of the inverse-square form at large distances, with a coefficient equal to the product of the charges, e , . 2 In dimensionless form, this is e , ∕ c 1 ∕ 137, the dimensionless parameter α of QED. In QED, vacuum polarization shields a charge—just as in any polarizable medium—resulting in an increase in the apparent charge as one gets closer, penetrating the cloud of shielding charge; in QCD, vacuum polarization—the effect of the gluon self-coupling—is antishielding, resulting in an apparent decrease in the color strength as one gets closer. This short-distance property of QCD is known as asymptotic freedom. See also: FINE STRUCTURE (SPECTRAL LINES) ;

FUNDAMENTAL CONSTANTS ; QUANTUM ELECTRODYNAMICS .

At small r , or equivalently at large momentum transfer, the running coupling becomes small, and consequently perturbation theory becomes reliable. Calculations in perturbative QCD, such as the gluonic radiative corrections to the cross section for hadrons, are in good agreement with experiment. This is an important reason for the present view that QCD is the correct theory of the hadron glue. The ability to make precise computations in QCD for hadron interactions involving large transfers of momentum underpins much of the experimental planning at facilities such as the (LHC) at CERN. See also: QUANTUM CHROMODYNAMICS ; PERTURBATION

(QUANTUM MECHANICS) .

Quarkonium

According to the so-called na¨ ıve , hadrons are bound states of nonrelativistic (slowly moving) quarks, analogous to nuclei as bound states of . The interactions between the quarks are taken qualitatively from AccessScience from McGraw-Hill Education Page 11 of 21 www.accessscience.com

WIDTH:CFig. 3 Level schemes and transitions of ( a ) charmonium and ( b ) bottomonium. Observed radiative transitions are indicated by wavy lines, observed states and other observed transitions by solid lines, and uncertain states and transitions by broken lines. The notation γ,∗ refers to decay processes involving intermediate virtual photons, including decays to e ,+ e ,− and μ,+ μ,− . ( After Particle Data Group, Review of particle properties, Phys. Lett., 179B:1–350, 1986 )

QCD, namely, a confining central potential and (exactly analogous to electromagnetic interactions) spin-spin 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. See also: ATOMIC STRUCTURE AND SPECTRA .

As mentioned earlier, mesons with the composition and are called charmonium and bottomonium. These names

are based on the model of , the atomic of a and an electron; the generic name

for flavorless mesons, is ( Fig. 3 ). The mesons are classified by their intrinsic angular momentum or

spin, J , and the behavior of their quantum wavefunctions under parity P and charge conjugation C . See also:

POSITRONIUM .

,− ,+ ,− ,+ → γ,∗ → 𝐪̄ ,−− Some states of quarkonium are cleanly observable as resonances in e e collisions: e e ( q ) , 1 , ∗ P C −− where γ, is a virtual photon that materializes into a state of a quark and antiquark with J , = 1, (the quantum

numbers of a photon). This vector quarkonium meson is made at rest in the center-of-mass frame of the colliding e − + , and e, and is unaccompanied by other hadrons. Quarkonium states of other quantum numbers can be observed −− as decay products of excited 1, mesons. Charmonium has been produced also by the annihilation of

on protons, and observed in the decay products of bottom mesons ( B ), as in the process B → K + J ∕ ψ(3097).

Since both heavy quarkonium and positronium are systems of a fermion bound to its antifermion by a central

force, they are qualitatively very similar (quantitatively, their masses and excitation energies are in the ratios of 4 7 ∼10, and 10, , respectively). However, the potential between the quarks is not ∼1 ∕ r (coulombic), which gives a AccessScience from McGraw-Hill Education Page 12 of 21 www.accessscience.com

different ordering in the energy levels for quarkonium and positronium. The pattern observed for quarkonium shows that the quark-antiquark potential is consistent with r (linear potential), which agrees with the prediction of QCD, as calculated by the lattice Monte Carlo method. Information on the spin-spin and spin-orbit parts of the interaction also comes from the quarkonium energy levels. See also: MONTE CARLO METHOD .

Just as positronium decays by annihilation of its constituents into photons, quarkonium can decay by annihilation of its q and into gluons, which then fragment into hadrons. This mechanism results in a strong C dependence of η ψ decay rates; for example, the ,c (2981) decays ∼350 times faster than the J ∕ (3097). Vector quarkonium also has 𝐪̄ ,−− → γ,∗ → the decays ( q ), 1 , where x is any charged fundamental fermion that is lighter than the quark q ; this decay mode accounts for about 28% of the decays of the J ∕ ψ and 17% of the decays of the upsilon ( Υ) meson.

See also: J ∕ PSI PARTICLE ; UPSILON PARTICLES .

Weak decays of quarkonium, in which one of the heavy quarks is transformed to a lighter quark, are negligibly −8 slow; for example, the chance that a J ∕ ψ meson decays this way is ∼10, .

Excited states of quarkonium have decay modes in which the heavy quarks neither annihilate nor transform. If the heavy quarks remain bound, this is a deexcitation, a decay into a lower state of the quarkonium with emission γ η χ χ χ of one or more hadrons or a (radiative decay). Radiative decays are the main source of the ,c , ,0 , ,1 , and ,2 mesons.

Highly excited quarkonium states can decay into pairs of mesons. An example is the bottomonium decay → ,− ,+ Υ(10,580) B B . The is the lightest hadron that contains a b quark, and so 2 m, B = 10,559 MeV is the energy threshold for such decays; the Υ(10,580) = Υ(4 S ) decays to B nearly 100% of the time, with a decay rate 1000 times faster than the total decay rate of the next lower vector bottomonium state, Υ(10,355) = Υ(3 S ).

Generally, autoionization decay modes are the fastest decay modes of quarkonium whenever they are kinematically possible. Electron-positron annihilation at an energy of 10,355 MeV has been used as a source of large amounts of B mesons. Comparison of the properties of B and its antiparticle counterpart is used to investigate possible asymmetries between matter and antimatter.

Heavy-quark hadrons

The known heavy quarks are the c (charm), b (bottom), and t (top) quarks, whose masses are larger than the mass of a proton, ∼1 GeV. A hadron that contains a single heavy quark resembles an in which 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 and B mesons are similar, except in mass, which plays an important role in the quantitative analysis of their weak decays. AccessScience from McGraw-Hill Education Page 13 of 21 www.accessscience.com

The only hadrons so far observed that contain more than one heavy quark are mesons containing a conjugate pair: c and b . The creation of hadrons such as c or ccu from ordinary matter, which contains only u and d quarks, requires the creation of two pairs of heavy quarks at nearly the same place and time; this is highly improbable, hence the difficulty in producing such states.

Bottom mesons, such as B made from b or b and their antiparticle counterparts made from u or d , have special interest, as their weak decays are not symmetric between particle and antiparticle. It was hoped that the study of this asymmetry could shed light on the nature of the large-scale asymmetry between matter and antimatter in the universe. To this end, as previously noted, several billion B - (“B-bar”) pairs have been made at customized

“B-factories”: electron-positron colliders tuned to an energy of around 10.5 GeV, where the production rate of these mesons is optimal. Such experiments have taken place at Stanford, California, and the Belle facility at KEK in Tsukuba, Japan. Large numbers of these particles have been produced at the LHC and recorded in the LHCb detector. The data have revealed differences between matter and antimatter made of strange and bottom flavors, but no clear answer has yet emerged as to why antimatter appears to be absent in the universe at large.

Weak interaction

The changes the flavor of particles as in its most familiar manifestation, the beta decay of the neutron, which transmutes into a proton, an electron, and a neutrino. Neutrinos, which have no color or electric charge, and hence do not respond to strong or electromagnetic forces, are ideal probes of the weak interaction.

All experimental results at low energies are consistent with the weak reactions being point four-Fermi interactions, that is, occurring when four fermions are at one point in space-time. This was the essence of Fermi’s original theory of beta decay. As noted earlier, it is now known that such beta decays are the result of the ± + − exchange of a massive charged vector (spin-1) particle, the W , ( W , and W , are antiparticles of one another), which is emitted and absorbed by the so-called weak . From the quark point of view, the so-called charged-current weak interactions are flavor-changing; here, flavor is meant in a broad sense that includes leptons. This particle is part of a renormalized field theory, which is a spontaneously broken (by the

Higgs mechanism). This is the electroweak theory of S. Weinberg, S. Glashow, and A. Salam, which is now + accepted as the standard model of electroweak interactions. It has four gauge fields, whose quanta are the W , − 0 and W , , a massive neutral vector particle Z , , and the photon.

0 The Z , is coupled to all particles with strengths controlled by a single parameter, the Weinberg (or weak) angle 휃 , W , whose value is determined by observation of the neutral-current weak interactions, which result from 0 exchange of the Z , . These were unknown before this theory suggested their existence. The particle that emits a 0 Z , remains unchanged, as is the case with the emission of a photon.

Universality. An important property of the weak interaction is universality. This property was first observed in the μ → ν → fact that the interactions responsible for the beta decays e, e ,μ and n pe, e are nearly equal; that is, the AccessScience from McGraw-Hill Education Page 14 of 21 www.accessscience.com

ν μ ,± μν ν couplings W ,μ and Wud of the W are nearly equal. (Likewise, it is found that the couplings W ,μ and We ,e are equal.) This near-equality points to a deep similarity between leptons and quarks.

This universality is also seen in Wcs and Wtb couplings, which are also almost equal. In addition to these

couplings within a generation, there are feebler couplings between the generations, at least for the quarks. This

was originally found in the existence of two couplings involving the u quark, namely Wud

(strangeness-conserving) and Wus (strangeness-changing), the latter being about one-fourth as large as the ν ν former. This contrasts with the leptons, where the ,e is involved in only one coupling, namely W ,e e (about ν μ equal in strength to Wud ), and W ,e vanishes. Nonetheless, an overall universality still occurs when all the possible transitions are accounted for in the mathematical matrix formalism of N. Cabibbo, M. Kobayashi, and T.

Maskawa (involving the so-called CKM matrix). The numbers in the CKM matrix cannot, in general, be made real.

As a result, the W coupling leads to an asymmetry between quarks and antiquarks, with potential implications for

the large-scale asymmetry observed between matter and antimatter in the universe. However, while the values of

the CKM matrix elements have been experimentally measured, so far there is no theory for them.

ν μ A similar matrix formalism applies to leptons, and it is possible that transitions such as W ,e occur. Such ideas also suggest that transitions between the electron and the muon might occur, albeit very rarely. This is an active

area of research. See also: INTENSITY FRONTIER OF PARTICLE AND ; THREE NEUTRINO FLAVORS AND THEIR

MIXING .

+ − 0 Weak bosons. The weak bosons W , , W , ( = ), and Z , , were first observed in 1983 in proton-antiproton collisions. ± 0 The W , , and similarly the Z , , are made by the annihilation of a quark pair in a p p̄ collision, q 𝐪̄ → W → decay

products, where the q and 𝐪̄ are contained in an incident proton p and an antiproton, respectively. The

branching ratios for the decays into quarks ( Table 1 ) have been predicted from theory and confirmed in

experiment. What the weak bosons do not decay into is important information about the nonexistence of

additional fundamental particles (such as quarks or leptons) with masses less than 45 GeV. The decay modes e ,± ν μ,± ν ,+ ,+ ,− μ,+ μ,− ,0 ,e and ,μ of the W , and e e and of the Z , are easy to observe—despite the rarity of the W or Z 6 production (about 1 per 10, p p̄ collisions)—because no other process makes many leptons with momenta as

high as 40 GeV, at a large angle to the incident p and p̄ . Because there are three times as many kinds of quarks as

there are leptons (each flavor of quark comes in three colors), most decays of the W and Z are into pairs of

quarks, which fragment into 40-GeV jets; but these decays are hard to observe because of the background of

similar jets made by the scattering process q 𝐪̄ → q 𝐪̄.

,0 ,+ ,− → ν The Z is made cleanly by e e annihilation, enabling its decay modes to be easily seen. The decays Z ,l , l , ν where ,l is a neutrino, cannot be seen directly, but at least the total branching ratio into these modes can be 0 deduced by observation of the total width of the Z , . With the assumption of universality, this determines the < ν ν number of light (mass 45 GeV) neutrinos to be 3; that is, there are none beyond those presently known: ,e , ,μ , ν and ,τ . By implication, if every neutrino is accompanied by a charged lepton, and if this lepton pair is also AccessScience from McGraw-Hill Education Page 15 of 21 www.accessscience.com

2 1 accompanied by a pair of quarks (charges ∕3 and − ∕3 ), the three generations of leptons and quarks are the totality of such fermions.

Grand unified theory

19 The negative charge of the electron and the positive charge of a proton are equal to better than 1 part in 10, . As

the electron appears to be a fundamental fermion, as do the quarks that make up the proton, this equality is

remarkable and hints at some deeper relation between the leptons, such as the electron, and the quarks. The 1 balance is achieved by a further act of balance: the electric charges of quarks come in fractions that are ∕3 of an integer (in units of a proton), and the strong color forces acting on the quarks cluster them in threes. Therefore,

the three-ness of the color charges conveniently conspires with the third-integer nature of the electric charges,

suggesting some relation between the electric and color charges.

These hints are further solidified when we look at the quantum field theories of the forces. The carriers of the

electromagnetic and color forces are massless spin-1 particles, the photon and the gluon. The weak force is also

carried by spin-1 particles, the W and Z , although here they are massive. Apart from this mass effect that spoils

the symmetry, and the fact that the weak interactions do not respect mirror symmetry (parity), the underlying

quantum theories of the three forces show profound similarities.

Their strengths differ at room temperature because of the different strengths of the interaction between the

spin-1 particles and the fermions, and also because of the fact that the W and Z are massive. However, in

experiments at higher energies, these differences have been observed to die away. Experiments at the LEP

accelerator at CERN showed that when electrons and positrons annihilate at a total energy of 90 GeV, the Z

boson is produced with a strength that is essentially the same as that of the electromagnetic interaction. Studies

of the W boson at these extreme energies show that here, too, the weak interaction has an intrinsic strength that

is united with the electromagnetic and has been obscured at low energies by the large masses of the W and Z , in

contrast to the massless photon. This unification has been further confirmed by experiments involving the

collisions of protons at the LHC. Thus, as noted earlier, it is now accepted that the electromagnetic and weak

forces are two manifestations of a single electroweak force.

The most familiar form of the weak interaction is beta decay, such as that of a neutron into a proton, an electron,

and a neutrino, which is ultimately driven by a down quark transmuting to an up with the emission of a virtual W − , . The coupling of the W to quarks appears to be identical to its interaction with leptons: were the W boson the

only probe of leptons and quarks, they would be indistinguishable. This identity further strengthens the belief

that leptons and quarks are profoundly related.

In theories that postulate such a relationship, the leptons and quarks occur together in multiplets of the large

symmetry group called families (or generations). The known fundamental fermions do seem to fall into three

families ( Table 1 ). Each family consists of a doublet of leptons (neutrino [charge 0] and charged lepton [charge AccessScience from McGraw-Hill Education Page 16 of 21 www.accessscience.com

2 1 − e ]) and a color triplet of doublets of quarks (up-type [charge ∕3 e ] and down-type [charge − ∕3 e ]). (As 0 previously noted, from the total width of the Z , , it is deduced that there are no more families whose neutrino has mass < 45 GeV.) However, there is no known connection between the leptons and the quarks of each family; ν for example, it is only because ( ,e , e ) is the lightest lepton doublet and ( u , d ) is the lightest quark doublet that they are regarded as members of the same family.

The main difference between them is that quarks carry color and respond to the strong force, whereas leptons do not. Here, though, there are further hints of unity at high energies. The strength of the color forces in QCD weakens with increasing energy; the strength of the analogous electroweak interaction, according to the quantum theory, increases. Extrapolating to higher energies, the theories imply that these forces all have a similar 15 intrinsic strength at 10, GeV, known as the grand unification energy. In grand unification theories, this energy is ,± ,0 the mass m,lq of hypothetical superheavy “ gauge bosons,” analogous to the of the electroweak subtheory. At momentum transfers larger than this, the mass of the leptoquark bosons is irrelevant and the large symmetry is unbroken; for smaller momentum transfers, as at low energies, the symmetry is broken and the three forces appear different, the more so the lower the momentum transfer.

The couplings of the leptoquark gauge bosons turn leptons into quarks, or vice versa (this is the reason for the name leptoquark), or quarks into antiquarks. There are many theoretical ideas concerning the mathematical structure of the true unified theory. Different approaches that agree with known phenomena have widely different implications for the properties of new particles that are implied by the theory. Nonetheless, there are certain common features, such as that the exchange of a leptoquark boson can therefore result in the + 0 transformation qqq → lqq , for example, p → e , π, . This baryon- and lepton-number-violating interaction is a much weaker interaction than the analogous ordinary weak interaction because leptoquark bosons are much heavier than weak bosons. The implication that protons are unstable, albeit with a half-life that exceeds the age of the universe by many orders of magnitude, is a rather general consequence of attempts to build an empirically successful unified theory. Studies of large samples of matter in the hope of finding evidence for a single have been made, but no definitive evidence for proton decay has yet been found. See also: GRAND

UNIFICATION THEORIES .

Accelerators

For a century, beams of particles have been used to reveal the inner structure of atoms. These beams have progressed from naturally occurring alpha and beta particles, courtesy of natural radioactivity, through cosmic rays, to intense beams of electrons, protons, and other particles at modern accelerators. By smashing the primary beams into a target, some of the energy can be converted into new particles, which can themselves be accumulated and made into secondary beams. Thus, beams of pions, , muons, and neutrinos have been made, as well as antiparticles such as positrons and antiprotons. There are even beams of heavy ions—atoms stripped of their electrons—that enable violent collisions between heavy nuclei to be investigated. AccessScience from McGraw-Hill Education Page 17 of 21 www.accessscience.com

There has also been a renewed interest in cosmic rays, where nature provides particles at energies far beyond anything that we can contemplate achieving on Earth. The problem is that such rays come at random and are much less intense than beams made at accelerators.

The basic principle is that electrically charged particles are accelerated by electric forces. If enough electric force is applied to an electron, say, it will be accelerated along a straight path, as in the linear accelerator at Stanford in

California, which can accelerate electrons to energies of 50 GeV over a distance of 3 km (2 mi).

Under the influence of a magnetic field, the path of a charged particle will curve. By using electric fields to speed them and magnetic fields to bend their trajectory, particles can be guided around circles over and over again.

This is the basic idea behind huge rings, such as the 27-km (17-mi) LEP circular accelerator at CERN, which operated from 1989 to 2000, and could accelerate electrons and positrons to 100 GeV each.

Originally, the beams were directed at static targets. In a linear accelerator aimed at a static target, the debris of the collision is propelled forward, just as a stationary car is shunted forward when another car crashes into its rear. When a beam hits a stationary target, the hard-won energy of the beam particles is transferred largely into energy of motion—into moving particles in the target—and is effectively wasted. This problem is overcome if particles can be brought to collide head-on, so that their energy can be spent on the interaction between them.

In such a collision, the debris flies off in all directions, and the energy is redistributed with it—none of it is wasted in setting stationary lumps in motion. Thus, there has been an increasing strategy of making counterrotating beams of particles and antiparticles, such as electrons and positrons or protons and antiprotons, and colliding them head-on.

A major application has been to enable collisions between particles and antiparticles, principally protons and antiprotons or electrons and positrons. A limit to the energy attainable at a circular accelerator of electrons or positrons is that these high-energy particles radiate away energy when they travel on a circular path. This

“synchrotron radiation” is greater the tighter the radius of the orbit and the higher the energy of the particle.

Protons and antiprotons also emit synchrotron radiation, but with a mass nearly 2000 times that of an electron, they can reach much higher energies before the amount of energy lost becomes significant, and they also pack a bigger punch. Hence they are the prime choice when the aim is to reach out to previously unexplored higher energies, as at the LHC. See also: SYNCHROTRON RADIATION .

At CERN, the 27-km ring of magnets that accelerated electrons and positrons to 100 GeV has been replaced by the superconducting magnets of the LHC. In 2012, this machine guided counterrotating beams of protons up to energies of 4000 GeV (4 TeV). From 2015, it is planned to make head-on collisions at a total energy of 13 TeV.

See also: LARGE HADRON COLLIDER (LHC) ; LARGE HADRON COLLIDER: FIRST YEAR .

In order to carry out fine-detail studies of new particles discovered at the LHC, such as the Higgs particle, there are plans to produce large numbers of these particles under more controlled conditions. To do so, the plan is to generate electron-positron collisions at the optimum energy. As this energy is expected to be several hundred AccessScience from McGraw-Hill Education Page 18 of 21 www.accessscience.com

GeV, two linear accelerators will be required—one for the electrons and the other for the positrons—which are aligned so as to produce head-on collisions of the beams.

Supersymmetry

1 The fundamental particles of matter, the leptons and quarks, are all fermions with spin ∕2 . The forces that act on them are mediated by the photon, the gluon, and the W and Z bosons, all with spin 1. Grand unification is based on this common feature of bosons as force carriers acting on the basic fermions. (SUSY) theory implies that there is a further symmetry between the forces and the matter particles, such that the known fermions are partnered by new bosons, and the known bosons by new fermions, with novel forces being transmitted by these fermions. It is hypothesized that this partnering may lead to a more complete unification between particles and forces.

In SUSY, the families of bosons that twin the known quarks and leptons are known as superquarks and superleptons, more commonly referred to as squarks and sleptons. If SUSY were an exact symmetry, each variety of lepton or quark would have the same mass as its squark or slepton sibling. However, the selectron empirically must have a mass greater than 100 GeV, which implies that it must be hundreds of thousands of times more massive than the electron. Similar remarks follow for all the sleptons and squarks, implying that SUSY is a very badly broken symmetry.

An analogous statement applies to the of the known bosons. The naming convention here is to add

-ino (pronounced “eeno”) to denote the superfermion partner of a standard boson. Thus the , , wino, and zino are predicted. The hypothetical graviton, or carrier of gravity, is predicted to have a partner, the . Here, too, the SUSY is badly broken, and these “inos” must have masses far greater than those of their conventional counterparts.

Although SUSY must be badly broken in the sense that the masses of the particles and the sparticles differ greatly, the basic ideas are appealing mathematically and merge as a fundamental symmetry of space and time, as encoded in Einstein’s theory of relativity and the quantum theory. The resulting pattern of sparticles solves technical problems in the quantum theories of the forces at high energies and the response of the particles to those forces, in particular preventing nonsensical predictions such as that certain processes occur with infinite probability. Quantum effects caused by SUSY particles emerging fleetingly as virtual particles in accordance with the uncertainty principle can affect measurable quantities in present experiments. From such data, it is predicted that the lightest sparticles may occur with masses of a few hundred GeV and as such may be observable in experiments at the LHC. There is also the tantalizing possibility that the lightest sparticles, such as the photino or gluino, are electrically neutral and are metastable. As such, they could form large-scale clusters through their mutual gravitational attraction and form a substantial part of the of the universe. See also: DARK

MATTER ; NATURAL SUPERSYMMETRY ; QUANTUM THEORY ; SUPERSYMMETRY ; WEAKLY INTERACTING MASSIVE PARTICLE (WIMP) . AccessScience from McGraw-Hill Education Page 19 of 21 www.accessscience.com

Mass

The masses of the elementary particles have been discussed previously. Here, a description will be given of how these masses affect physical phenomena, and some of the enigmas associated with mass will be summarized.

The mass of matter in bulk is almost entirely due to the nucleons, protons, and neutrons, which form the nuclei of atoms. The mass of the proton is caused by the confining effects of QCD, whereby the quarks and gluons that −15 make up the proton are entrapped within a sphere of radius approximately 10, m. Heisenberg’s uncertainty principle implies that when spatially constrained to such a distance, the constituents gain momentum and energy 2 of hundreds of MeV. The equation E = mc , then implies that this energy acts as an inertia or mass, leading to the 2 938-MeV ∕ c , mass of the proton.

2 The individual up and down quarks within the nucleons carry masses of only a few MeV ∕ c , . Since they are permanently confined within hadrons, a direct measure of their masses is not possible, but these masses can be determined indirectly to be in the range of 1.5–3 MeV for the up quarks and 4–6 MeV for the down quarks. It is the greater mass of the down quark that gives the neutron its slightly larger mass relative to the proton.

2 The strange quark is approximately 100 MeV ∕ c , more massive than the up and down quarks, which gives the extra mass to strange hadrons relative to their nonstrange counterparts. Charm, bottom, and top quarks have 2 larger masses, approximately 1.3, 4.5, and 175 GeV ∕ c , , respectively. The fundamental leptons also have a spread of masses. The neutrinos have masses that are too small to determine and were long thought to be massless; however, the phenomenon of neutrino oscillations shows that at least two of the three have nonzero masses, of 2 the order of a few eV ∕ c , at most, and possibly only a fraction of this. The electron, muon, and tau leptons have 2 masses of about 0.5, 106, and 1777 MeV ∕ c , , respectively. The reason for these patterns in the masses is not understood.

The symmetry properties of unified theories would be realized if all the fundamental particles were massless. In the case of the photon, gluon, and graviton, this is the case empirically, but the W and Z bosons have masses of 2 80.4 and 91.2 GeV ∕ c , , respectively. As described earlier, it is their large masses that enfeeble the weak forces transmitted by W and Z relative to the electromagnetic force transmitted by the massless photon.

15 Relative to the grand unification energy of 10, GeV, all of these masses are negligible, and it is theorized that the true unified symmetries of nature would be exact but for the effect of masses. The nature and origin of these masses is thus a fundamental problem of great interest, and the phenomenon is known as electroweak symmetry breaking. The standard model explains the mass of fundamental particles as being due to a new field called the

Higgs field, after , who in 1964 was one of the first to recognize this theoretical possibility. Mass is then the effect of the interaction between the fundamental particles and the Higgs field. Photons do not interact with the Higgs field and therefore remain massless; the W and Z bosons do interact and thereby gain their large masses. The quarks and leptons also gain masses by such interactions. AccessScience from McGraw-Hill Education Page 20 of 21 www.accessscience.com

The Higgs field is manifested in quantum theory by the appearance of particles known as Higgs bosons. In Higgs’s original formulation, the boson has spin 0. However, if supersymmetry is realized in nature, there should be a family of such particles, including the fermion super-Higgs or “.” The LHC established that the Higgs 2 boson exists with a mass of about 126 GeV ∕ c , and spin 0. It is unstable and has been detected in a variety of decay modes, including to pairs of photons or tau leptons, to four leptons (via the intermediary role of virtual W pairs or Z pairs), and to jets of particles containing bottom or charm quarks. Its properties are consistent with those expected for the Higgs field as the origin of electroweak symmetry breaking. See also: HIGGS BOSON

DETECTION AT THE LHC .

Frank E. Close

Keywords antiparticles; fundamental interactions; fundamental particles; grand unified theory; heavy-quark hadrons; particle accelerator; quantum chromodynamics; quarkonium; supersymmetry; weak interaction

Test Your Understanding

1. Compare and contrast leptons and hadrons, and give examples of each type of particle.

2. Compare and contrast photons, gluons, and weak bosons.

3. What is an antiparticle? How do scientists know that antiparticles exist?

4. Critical Thinking: What combination of up and down quarks make up protons and neutrons?

5. Critical Thinking: Which elementary particles have the strongest interactions with the Higgs field, and

why?

Bibliography

F. Close, The New Cosmic Onion , Taylor and Francis, Boca Raton, FL, 2007

F. Close, Particle Physics: A Very Short Introduction , Oxford University Press, Oxford, UK, 2004, corrected reprint, 2012

B. Greene, The Elegant Universe , 2d ed., W. W. Norton, New York, 2003

K. A. Olive et al. (Particle Data Group), The review of particle physics, Chin. Phys. C , 38:090001 (1677 pp.), 2014

DOI: http://doi.org/10.1088/1674-1137/38/9/090001

S. Weinberg, Dreams of a Final Theory , Vintage, New York, 1993 AccessScience from McGraw-Hill Education Page 21 of 21 www.accessscience.com

Additional Readings

S. Braibant, G. Giacomelli, and M. Spurio, Particles and Fundamental Interactions , Springer, Dordrecht,

Netherlands, 2012

R. N. Cahn and G. Goldhaber, The Experimental Foundations of Particle Physics , 2d ed., Cambridge University

Press, Cambridge, UK, 2009

Y. Nagashima, Elementary Particle Physics , 2 vols., Wiley-VCH, Weinheim, Germany, 2010, 2013

CERN Public Pages

Fermilab: Science for “Inquiring Minds”

Particle Data Group: The Particle Adventure

Particle Data Group: The Review of Particle Physics