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Standard Model

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Theory of forces and subatomic particles
This article is about a non-mathematical general overview of the Standard Model of particle physics. For a mathematical description, seeMathematical formulation of the Standard Model. For other uses, seeStandard model (disambiguation).

Standard Model ofparticle physics
Elementary particles of the Standard Model

TheStandard Model ofparticle physics is thetheory describing three of the four knownfundamental forces (electromagnetic,weak andstrong interactions – excludinggravity) in theuniverse and classifying all knownelementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide,[1] with the current formulation being finalized in the mid-1970s uponexperimental confirmation of the existence ofquarks. Since then, proof of thetop quark (1995), thetau neutrino (2000), and theHiggs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties ofweak neutral currents and theW and Z bosons with great accuracy.

Although the Standard Model is believed to be theoretically self-consistent[note 1] and has demonstrated some success in providingexperimental predictions, it leaves somephysical phenomena unexplained and so falls short of being acomplete theory of fundamental interactions.[3] For example, it does not fully explainwhy there is more matter than anti-matter, incorporate the fulltheory of gravitation[4] as described bygeneral relativity, or account for theuniverse's accelerating expansion as possibly described bydark energy. The model does not contain any viabledark matter particle that possesses all of the required properties deduced from observationalcosmology. It also does not incorporateneutrino oscillations and their non-zero masses.

The development of the Standard Model was driven bytheoretical andexperimental particle physicists alike. The Standard Model is a paradigm of aquantum field theory for theorists, exhibiting a wide range of phenomena, includingspontaneous symmetry breaking,anomalies, and non-perturbative behavior. It is used as a basis for building more exotic models that incorporatehypothetical particles,extra dimensions, and elaborate symmetries (such assupersymmetry) to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations.

Historical background

[edit]
See also:History of quantum field theory,History of subatomic physics,Julian Schwinger, andJohn Clive Ward

In 1928,Paul Dirac introduced theDirac equation, which implied the existence ofantimatter.

In 1954,Yang Chen-Ning andRobert Mills extended the concept ofgauge theory forabelian groups, e.g.quantum electrodynamics, tononabelian groups to provide an explanation forstrong interactions.[5] In 1957,Chien-Shiung Wu demonstratedparity was not conserved in theweak interaction.[6]

In 1961,Sheldon Glashow combined theelectromagnetic andweak interactions.[7] In 1964,Murray Gell-Mann andGeorge Zweig introduced quarks and that same yearOscar W. Greenberg implicitly introduced color charge of quarks.[8] In 1967Steven Weinberg[9] andAbdus Salam[10] incorporated theHiggs mechanism[11][12][13] into Glashow'selectroweak interaction, giving it its modern form.

In 1970, Sheldon Glashow, John Iliopoulos, and Luciano Maiani introduced theGIM mechanism, predicting thecharm quark.[14] In 1973 Gross and Wilczek and Politzer independently discovered that non-Abelian gauge theories, like the color theory of the strong force, haveasymptotic freedom.[14] In 1976, Martin Perl discovered thetau lepton at theSLAC.[15][16] In 1977, a team led by Leon Lederman at Fermilab discovered the bottom quark.[17]

The Higgs mechanism is believed to give rise to themasses of all theelementary particles in the Standard Model. This includes the masses of theW and Z bosons, and the masses of thefermions, i.e. thequarks andleptons.

After theneutral weak currents caused byZ boson exchangewere discovered atCERN in 1973,[18][19][20][21] the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979Nobel Prize in Physics for discovering it. The W± and Z0bosons were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted.[22]

The theory of thestrong interaction (i.e.quantum chromodynamics, QCD), to which many contributed, acquired its modern form in 1973–74 whenasymptotic freedom was proposed[23][24] (a development that made QCD the main focus of theoretical research)[25] and experiments confirmed that thehadrons were composed of fractionally charged quarks.[26][27]

The term "Standard Model" was introduced byAbraham Pais andSam Treiman in 1975,[28] with reference to the electroweak theory with four quarks.[29]Steven Weinberg has since claimed priority, explaining that he chose the term StandardModel out of a sense of modesty[30][31][32][better source needed] and used it in 1973 during a talk in Aix-en-Provence in France.[33]

Particle content

[edit]

The Standard Model includes members of several classes of elementary particles, which in turn can be distinguished by other characteristics, such ascolor charge.

All particles can be summarized as follows:

Elementary particles
ElementaryfermionsHalf-integerspinObey theFermi–Dirac statisticsElementarybosonsInteger spinObey theBose–Einstein statistics
Quarks and antiquarksSpin =⁠1/2⁠Havecolor chargeParticipate instrong interactionsandelectroweak interactionsLeptons and antileptonsSpin =⁠1/2⁠No color chargeElectroweak interactionsGauge bosonsSpin = 1Force carriersScalar bosonsSpin = 0
Three generations
  1. Electron (e−
    ), [†]
    Electron neutrino (ν
    e    )
  2. Muon (μ−
    ),
    Muon neutrino (ν
    μ    )
  3. Tau (τ−
    ),
    Tau neutrino (ν
    τ    )
One kind

Higgs boson (H0
)

Notes:
[†] An anti-electron (e+
) is conventionally called a "positron".

Fermions

[edit]

The Standard Model includes 12elementary particles ofspin⁠1/2⁠, known asfermions.[34] Fermions respect thePauli exclusion principle, meaning that twoidentical fermions cannot simultaneously occupy the same quantum state in the same atom.[35] Each fermion has a correspondingantiparticle, which are particles that have corresponding properties with the exception ofoppositecharges.[36] Fermions are classified based on how they interact, which is determined by the charges they carry, into two groups:quarks andleptons. Within each group, pairs of particles that exhibit similar physical behaviors are then grouped intogenerations (see the table). Each member of a generation has a greater mass than the corresponding particle of generations prior. Thus, there are three generations of quarks and leptons.[37] As first-generation particles do not decay, they comprise all of ordinary (baryonic) matter. Specifically, all atoms consist of electrons orbiting around theatomic nucleus, ultimately constituted of up and down quarks. On the other hand, second- and third-generation charged particles decay with very shorthalf-lives and can only be observed in high-energy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter.

There are six quarks:up,down,charm,strange,top, andbottom.[34][37] Quarks carrycolor charge, and hence interact via thestrong interaction. Thecolor confinement phenomenon results in quarks being strongly bound together such that they form color-neutral composite particles calledhadrons; quarks cannot individually exist and must always bind with other quarks. Hadrons can contain either a quark-antiquark pair (mesons) or three quarks (baryons).[38] The lightest baryons are thenucleons: theproton andneutron. Quarks also carryelectric charge andweak isospin, and thus interact with other fermions throughelectromagnetism andweak interaction. The six leptons consist of theelectron,electron neutrino,muon,muon neutrino,tau, andtau neutrino. The leptons do not carry color charge, and do not respond to strong interaction. The charged leptons carry anelectric charge of −1 e, while the threeneutrinos carry zero electric charge. Thus, the neutrinos' motions are influenced by only theweak interaction andgravity, making them difficult to observe.

Gauge bosons

[edit]
Interactions in the Standard Model. All Feynman diagrams in the model are built from combinations of these vertices.q is any quark,g is a gluon,X is any charged particle, γ is a photon,f is any fermion,m is any particle with mass (with the possible exception of the neutrinos),mB is any boson with mass. In diagrams with multiple particle labels separated by '/', one particle label is chosen. In diagrams with particle labels separated by '|', the labels must be chosen in the same order. For example, in the four boson electroweak case the valid diagrams are WWWW, WWZZ, WWγγ, WWZγ. The conjugate of each listed vertex (reversing the direction of arrows) is also allowed.[39]

The Standard Model includes 4 kinds ofgauge bosons ofspin 1,[34] with bosons being quantum particles containing an integer spin. The gauge bosons are defined asforce carriers, as they are responsible for mediating thefundamental interactions. The Standard Model explains the four fundamental forces as arising from the interactions, with fermionsexchangingvirtual force carrier particles, thus mediating the forces. At a macroscopic scale, this manifests as aforce.[40] As a result, they do not follow the Pauli exclusion principle that constrains fermions; bosons do not have a theoretical limit on theirspatial density. The types of gauge bosons are described below.

  • Electromagnetism:Photons mediate the electromagnetic force, responsible for interactions between electrically charged particles. The photon is massless and is described by the theory ofquantum electrodynamics (QED).
  • Strong interaction:Gluons mediate the strong interactions, which binds quarks to each other by influencing thecolor charge, with the interactions being described in the theory ofquantum chromodynamics (QCD). They have no mass, and there are eight distinct gluons, with each being denoted through a color-anticolor charge combination (e.g. red–antigreen).[note 2] As gluons have an effective color charge, they can also interact amongst themselves.
  • Weak interaction: TheW+
    ,W−
    , andZ     gauge bosons mediate the weak interactions between all fermions, being responsible forradioactivity. They contain mass, with theZ having more mass than theW±
    . The weak interactions involving theW±
     act only onleft-handed particles andright-handed antiparticles respectively. TheW±
     carries an electric charge of +1 and −1 and couples to the electromagnetic interaction. The electrically neutralZ boson interacts with both left-handed particles and right-handed antiparticles. These three gauge bosons along with the photons are grouped together, as collectively mediating theelectroweak interaction.
  • Gravitation: It is currently unexplained in the Standard Model, as the hypothetical mediating particlegraviton has been proposed, but not observed.[42] This is due to the incompatibility of quantum mechanics andEinstein's theory of general relativity, regarded as being the best explanation for gravity. In general relativity, gravity is explained as being the geometric curving of spacetime.[43]

TheFeynman diagram calculations, which are a graphical representation of theperturbation theory approximation, invoke "force mediating particles", and when applied to analyzehigh-energy scattering experiments are in reasonable agreement with the data. However, perturbation theory (and with it the concept of a "force-mediating particle") fails in other situations. These include low-energy quantum chromodynamics,bound states, andsolitons. The interactions between all the particles described by the Standard Model are summarized by the diagrams on the right of this section.

Higgs boson

[edit]
Main article:Higgs boson

The Higgs particle is a massivescalar elementary particle theorized byPeter Higgs (and others) in 1964, when he showed that Goldstone's 1962 theorem (generic continuous symmetry, which is spontaneously broken) provides a third polarisation of a massive vector field. Hence, Goldstone's original scalar doublet, the massive spin-zero particle, wasproposed as the Higgs boson, and is a key building block in the Standard Model.[44] It has no intrinsicspin, and for that reason is classified as aboson with spin-0.[34]

The Higgs boson plays a unique role in the Standard Model, by explaining why the other elementary particles, except thephoton andgluon, are massive. In particular, the Higgs boson explains why the photon has no mass, while theW and Z bosons are very heavy. Elementary-particle masses and the differences betweenelectromagnetism (mediated by the photon) and theweak force (mediated by the W and Z bosons) are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. Inelectroweak theory, the Higgs boson generates the masses of the leptons (electron, muon, and tau) and quarks. As the Higgs boson is massive, it must interact with itself.

Because the Higgs boson is a very massive particle and also decays almost immediately when created, only a very high-energyparticle accelerator can observe and record it. Experiments to confirm and determine the nature of the Higgs boson using theLarge Hadron Collider (LHC) atCERN began in early 2010 and were performed atFermilab'sTevatron until its closure in late 2011. Mathematical consistency of the Standard Model requires that any mechanism capable of generating the masses of elementary particles must become visible[clarification needed] at energies above1.4 TeV;[45] therefore, the LHC (designed to collide two7 TeV proton beams) was built to answer the question of whether the Higgs boson actually exists.[46]

On 4 July 2012, two of the experiments at the LHC (ATLAS andCMS) both reported independently that they had found a new particle with a mass of about125 GeV/c2 (about 133 proton masses, on the order of10−25 kg), which is "consistent with the Higgs boson".[47][48] On 13 March 2013, it was confirmed to be the searched-for Higgs boson.[49][50]

Theoretical aspects

[edit]
Main article:Mathematical formulation of the Standard Model

Construction of the Standard Model Lagrangian

[edit]
Parameters of the Standard Model
#SymbolDescriptionRenormalization
scheme (point)		Value
1meElectron mass0.511 MeV
2mμMuon mass105.7 MeV
3mτTau mass1.78 GeV
4muUp quark massμMS = 2 GeV1.9 MeV
5mdDown quark massμMS = 2 GeV4.4 MeV
6msStrange quark massμMS = 2 GeV87 MeV
7mcCharm quark massμMS =mc1.32 GeV
8mbBottom quark massμMS =mb4.24 GeV
9mtTop quark massOn shell scheme173.5 GeV
10θ12CKM 12-mixing angle13.1°
11θ23CKM 23-mixing angle2.4°
12θ13CKM 13-mixing angle0.2°
13δCKM CP violation Phase0.995
14g1 org'U(1) gauge couplingμMS =mZ0.357
15g2 orgSU(2) gauge couplingμMS =mZ0.652
16g3 orgsSU(3) gauge couplingμMS =mZ1.221
17θQCDQCD vacuum angle~0
18vHiggs vacuum expectation value246 GeV
19mHHiggs mass125.09±0.24 GeV

Technically,quantum field theory provides the mathematical framework for the Standard Model, in which aLagrangian controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamicalfield that pervadesspace-time.[51]The construction of the Standard Model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most generalrenormalizable Lagrangian from its particle (field) content that observes these symmetries.

TheglobalPoincaré symmetry is postulated for all relativistic quantum field theories. It consists of the familiartranslational symmetry,rotational symmetry and the inertial reference frame invariance central to the theory ofspecial relativity. Thelocal SU(3) × SU(2) × U(1)gauge symmetry is aninternal symmetry that essentially defines the Standard Model. Roughly, the three factors of the gauge symmetry give rise to the three fundamental interactions. The fields fall into differentrepresentations of the various symmetry groups of the Standard Model (see table). Upon writing the most general Lagrangian, one finds that the dynamics depends on 19 parameters, whose numerical values are established by experiment. The parameters are summarized in the table (made visible by clicking "show") above.

Quantum chromodynamics sector

[edit]
Main article:Quantum chromodynamics

The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, which is aYang–Mills gauge theory with SU(3) symmetry, generated byTa=λa/2{\displaystyle T^{a}=\lambda ^{a}/2}. Since leptons do not interact with gluons, they are not affected by this sector. The Dirac Lagrangian of the quarks coupled to the gluon fields is given byLQCD=ψ¯iγμDμψ−14GμνaGaμν,{\displaystyle {\mathcal {L}}_{\text{QCD}}={\overline {\psi }}i\gamma ^{\mu }D_{\mu }\psi -{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu },}whereψ{\displaystyle \psi } is a three component column vector ofDirac spinors, each element of which refers to a quark field with a specificcolor charge (i.e. red, blue, and green) and summation overflavor (i.e. up, down, strange, etc.) is implied.

The gauge covariant derivative of QCD is defined byDμ≡∂μ−igs12λaGμa{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig_{\text{s}}{\frac {1}{2}}\lambda ^{a}G_{\mu }^{a}}, where

The QCD Lagrangian is invariant under local SU(3) gauge transformations; i.e., transformations of the formψ→ψ′=Uψ{\displaystyle \psi \rightarrow \psi '=U\psi }, whereU=e−igsλaϕa(x){\displaystyle U=e^{-ig_{\text{s}}\lambda ^{a}\phi ^{a}(x)}} is 3 × 3 unitary matrix with determinant 1, making it a member of the group SU(3), andϕa(x){\displaystyle \phi ^{a}(x)} is an arbitrary function of spacetime.

Electroweak sector

[edit]
Main article:Electroweak interaction

The electroweak sector is aYang–Mills gauge theory with the symmetry groupU(1) × SU(2)L,LEW=Q¯LjiγμDμQLj+u¯RjiγμDμuRj+d¯RjiγμDμdRj+ℓ¯LjiγμDμℓLj+e¯RjiγμDμeRj−14WaμνWμνa−14BμνBμν,{\displaystyle {\mathcal {L}}_{\text{EW}}={\overline {Q}}_{{\text{L}}j}i\gamma ^{\mu }D_{\mu }Q_{{\text{L}}j}+{\overline {u}}_{{\text{R}}j}i\gamma ^{\mu }D_{\mu }u_{{\text{R}}j}+{\overline {d}}_{{\text{R}}j}i\gamma ^{\mu }D_{\mu }d_{{\text{R}}j}+{\overline {\ell }}_{{\text{L}}j}i\gamma ^{\mu }D_{\mu }\ell _{{\text{L}}j}+{\overline {e}}_{{\text{R}}j}i\gamma ^{\mu }D_{\mu }e_{{\text{R}}j}-{\tfrac {1}{4}}W_{a}^{\mu \nu }W_{\mu \nu }^{a}-{\tfrac {1}{4}}B^{\mu \nu }B_{\mu \nu },}where the subscriptj{\displaystyle j} sums over the three generations of fermions;QL,uR{\displaystyle Q_{\text{L}},u_{\text{R}}}, anddR{\displaystyle d_{\text{R}}} are the left-handed doublet, right-handed singlet up type, and right handed singlet down type quark fields; andℓL{\displaystyle \ell _{\text{L}}} andeR{\displaystyle e_{\text{R}}} are the left-handed doublet and right-handed singlet lepton fields.

The electroweakgauge covariant derivative is defined asDμ≡∂μ−ig′12YWBμ−ig12τ→LW→μ{\displaystyle D_{\mu }\equiv \partial _{\mu }-ig'{\tfrac {1}{2}}Y_{\text{W}}B_{\mu }-ig{\tfrac {1}{2}}{\vec {\tau }}_{\text{L}}{\vec {W}}_{\mu }}, where

Notice that the addition of fermion mass terms into the electroweak Lagrangian is forbidden, since terms of the formmψ¯ψ{\displaystyle m{\overline {\psi }}\psi } do not respectU(1) × SU(2)L gauge invariance. Neither is it possible to add explicit mass terms for the U(1) and SU(2) gauge fields. The Higgs mechanism is responsible for the generation of the gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field.

Higgs sector

[edit]
Main article:Higgs mechanism

In the Standard Model, theHiggs field is an SU(2)L doublet of complexscalar fields with four degrees of freedom:φ=(φ+φ0)=12(φ1+iφ2φ3+iφ4),{\displaystyle \varphi ={\begin{pmatrix}\varphi ^{+}\\\varphi ^{0}\end{pmatrix}}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}\varphi _{1}+i\varphi _{2}\\\varphi _{3}+i\varphi _{4}\end{pmatrix}},}where the superscripts + and 0 indicate the electric chargeQ{\displaystyle Q} of the components. The weak hyperchargeYW{\displaystyle Y_{\text{W}}} of both components is 1. Before symmetry breaking, the Higgs Lagrangian isLH=(Dμφ)†(Dμφ)−V(φ),{\displaystyle {\mathcal {L}}_{\text{H}}=\left(D_{\mu }\varphi \right)^{\dagger }\left(D^{\mu }\varphi \right)-V(\varphi ),}whereDμ{\displaystyle D_{\mu }} is the electroweak gauge covariant derivative defined above andV(φ){\displaystyle V(\varphi )} is the potential of the Higgs field. The square of the covariant derivative leads to three and four point interactions between the electroweak gauge fieldsWμa{\displaystyle W_{\mu }^{a}} andBμ{\displaystyle B_{\mu }} and the scalar fieldφ{\displaystyle \varphi }. The scalar potential is given byV(φ)=−μ2φ†φ+λ(φ†φ)2,{\displaystyle V(\varphi )=-\mu ^{2}\varphi ^{\dagger }\varphi +\lambda \left(\varphi ^{\dagger }\varphi \right)^{2},}whereμ2>0{\displaystyle \mu ^{2}>0}, so thatφ{\displaystyle \varphi } acquires a non-zeroVacuum expectation value, which generates masses for the Electroweak gauge fields (the Higgs mechanism), andλ>0{\displaystyle \lambda >0}, so that the potential is bounded from below. The quartic term describes self-interactions of the scalar fieldφ{\displaystyle \varphi }.

The minimum of the potential is degenerate with an infinite number of equivalentground state solutions, which occurs whenφ†φ=μ22λ{\displaystyle \varphi ^{\dagger }\varphi ={\tfrac {\mu ^{2}}{2\lambda }}}. It is possible to perform agauge transformation onφ{\displaystyle \varphi } such that the ground state is transformed to a basis whereφ1=φ2=φ4=0{\displaystyle \varphi _{1}=\varphi _{2}=\varphi _{4}=0} andφ3=μλ≡v{\displaystyle \varphi _{3}={\tfrac {\mu }{\sqrt {\lambda }}}\equiv v}. This breaks the symmetry of the ground state. The expectation value ofφ{\displaystyle \varphi } now becomes⟨φ⟩=12(0v),{\displaystyle \langle \varphi \rangle ={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0\\v\end{pmatrix}},}wherev{\displaystyle v} has units of mass and sets the scale of electroweak physics. This is the only dimensional parameter of the Standard Model and has a measured value of ~246 GeV/c2.

After symmetry breaking, the masses of the W and Z are given bymW=12gv{\displaystyle m_{\text{W}}={\frac {1}{2}}gv} andmZ=12g2+g′2v{\displaystyle m_{\text{Z}}={\frac {1}{2}}{\sqrt {g^{2}+g'^{2}}}v}, which can be viewed as predictions of the theory. The photon remains massless. The mass of theHiggs boson ismH=2μ2=2λv{\displaystyle m_{\text{H}}={\sqrt {2\mu ^{2}}}={\sqrt {2\lambda }}v}. Sinceμ{\displaystyle \mu } andλ{\displaystyle \lambda } are free parameters, the Higgs's mass could not be predicted beforehand and had to be determined experimentally.

Yukawa sector

[edit]

TheYukawa interaction terms are:LYukawa=(Yu)mn(Q¯L)mφ~(uR)n+(Yd)mn(Q¯L)mφ(dR)n+(Ye)mn(ℓ¯L)mφ(eR)n+h.c.{\displaystyle {\mathcal {L}}_{\text{Yukawa}}=(Y_{\text{u}})_{mn}({\bar {Q}}_{\text{L}})_{m}{\tilde {\varphi }}(u_{\text{R}})_{n}+(Y_{\text{d}})_{mn}({\bar {Q}}_{\text{L}})_{m}\varphi (d_{\text{R}})_{n}+(Y_{\text{e}})_{mn}({\bar {\ell }}_{\text{L}})_{m}{\varphi }(e_{\text{R}})_{n}+\mathrm {h.c.} }whereYu{\displaystyle Y_{\text{u}}},Yd{\displaystyle Y_{\text{d}}}, andYe{\displaystyle Y_{\text{e}}} are3 × 3 matrices of Yukawa couplings, with themn term giving the coupling of the generationsm andn, and h.c. means Hermitian conjugate of preceding terms. The fieldsQL{\displaystyle Q_{\text{L}}} andℓL{\displaystyle \ell _{\text{L}}} are left-handed quark and lepton doublets. Likewise,uR,dR{\displaystyle u_{\text{R}},d_{\text{R}}} andeR{\displaystyle e_{\text{R}}} are right-handed up-type quark, down-type quark, and lepton singlets. Finallyφ{\displaystyle \varphi } is the Higgs doublet andφ~=iτ2φ∗{\displaystyle {\tilde {\varphi }}=i\tau _{2}\varphi ^{*}} is its charge conjugate state.

The Yukawa terms are invariant under the SU(2)L × U(1)Y gauge symmetry of the Standard Model and generate masses for all fermions after spontaneous symmetry breaking.

Fundamental interactions

[edit]
Main article:Fundamental interaction

The Standard Model describes three of the four fundamental interactions in nature; only gravity remains unexplained. In the Standard Model, such an interaction is described as an exchange ofbosons between the objects affected, such as aphoton for the electromagnetic force and agluon for the strong interaction. Those particles are calledforce carriers or messengerparticles.[52]

The four fundamental interactions of nature[53]
Property/InteractionGravitationElectroweakStrong
WeakElectromagneticFundamentalResidual
Mediating particlesNot yet observed
(Graviton hypothesised)		W+, W− and Z0γ (photon)Gluonsπ,ρ andωmesons
Affected particlesAll particlesW+, W−: Left-handedfermions; Z0: All fermionsElectrically chargedQuarks,gluonsHadrons
Acts onStress–energy tensorFlavorElectric chargeColor charge
Bound states formedPlanets, stars, galaxies, galaxy groups—Atoms, moleculesHadronsAtomic nuclei
Strength at the scale of quarks
(relative to electromagnetism)		10−41(predicted)10−4160Not applicable
to quarks
Strength at the scale of
protons/neutrons
(relative to electromagnetism)		10−36(predicted)10−71Not applicable
to hadrons		20
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Gravity

[edit]
See also:Quantum gravity andGravity
Fundamental Interactions of the Standard Model including the hypothetical graviton

Despite being perhaps the most familiar fundamental interaction, gravity is not described by the Standard Model, due to contradictions that arise when combining general relativity, the modern theory of gravity, and quantum mechanics.[54][55] However, gravity is so weak at microscopic scales, that it is essentially unmeasurable. Thegraviton is postulated to be the mediating particle, but has not yet been proved to exist.[56]

Electromagnetism

[edit]
See also:Electromagnetism andQuantum electrodynamics

Electromagnetism is the only long-range force in the Standard Model. It is mediated by photons and couples to electric charge.[57] Electromagnetism is responsible for a wide range of phenomena includingatomic electron shell structure,chemical bonds,electric circuits andelectronics. Electromagnetic interactions in the Standard Model are described by quantum electrodynamics.

Weak interaction

[edit]
See also:Weak interaction andElectroweak interaction

The weak interaction is responsible for various forms ofparticle decay, such asbeta decay. It is weak and short-range, due to the fact that the weak mediating particles, W and Z bosons, have mass. W bosons have electric charge and mediate interactions that change the particle type (referred to as flavor) and charge. Interactions mediated by W bosons arecharged current interactions. Z bosons are neutral and mediate neutral current interactions, which do not change particle flavor. Thus Z bosons are similar to the photon, aside from them being massive and interacting with the neutrino. The weak interaction is also the only interaction to violateparity andCP. Parity violation is maximal for charged current interactions, since the W boson interacts exclusively with left-handed fermions and right-handed antifermions.

In the Standard Model, the weak force is understood in terms of the electroweak theory, which states that the weak and electromagnetic interactions become united into a singleelectroweak interaction at high energies.

Strong interaction

[edit]
See also:Strong interaction,Nuclear force, andQuantum chromodynamics

The strong interaction is responsible for hadronic andnuclear binding. It is mediated by gluons, which couple to color charge. Since gluons themselves have color charge, the strong force exhibitsconfinement andasymptotic freedom. Confinement means that only color-neutral particles can exist in isolation, therefore quarks can only exist in hadrons and never in isolation, at low energies. Asymptotic freedom means that the strong force becomes weaker, as the energy scale increases. The strong force overpowers theelectrostatic repulsion of protons and quarks in nuclei and hadrons respectively, at their respective scales.

While quarks are bound in hadrons by the fundamental strong interaction, which is mediated by gluons, nucleons are bound by an emergent phenomenon termed theresidual strong force ornuclear force. This interaction is mediated by mesons, such as thepion. The color charges inside the nucleon cancel out, meaning most of the gluon and quark fields cancel out outside of the nucleon. However, some residue is "leaked", which appears as the exchange of virtual mesons, which result in an effective attractive force between nucleons. The (fundamental) strong interaction is described by quantum chromodynamics, which is a component of the Standard Model.

Tests and predictions

[edit]

The Standard Model predicted the existence of theW and Z bosons,gluon,top quark andcharm quark, and predicted many of their properties before these particles were observed. The predictions were experimentally confirmed with good precision.[58]

The Standard Model also predicted the existence of theHiggs boson, which was found in 2012 at theLarge Hadron Collider, the final fundamental particle predicted by the Standard Model to be experimentally confirmed.[59]

Challenges

[edit]
See also:Physics beyond the Standard Model
Unsolved problem in physics
  • What gives rise to the Standard Model of particle physics?
  • Why do particle masses andcoupling constants have the values that we measure?
  • Why are there threegenerations of particles?
  • Why is there more matter thanantimatter in the universe?
  • Where doesdark matter fit into the model? Does it even consist of one or more new particles?
More unsolved problems in physics

Self-consistency of the Standard Model (currently formulated as a non-abelian gauge theory quantized through path-integrals) has not been mathematically proved. While regularized versions useful for approximate computations (for examplelattice gauge theory) exist, it is not known whether they converge (in the sense of S-matrix elements) in the limit that the regulator is removed. A key question related to the consistency is theYang–Mills existence and mass gap problem.

Experiments indicate thatneutrinos havemass, which the classic Standard Model did not allow.[60] To accommodate this finding, the classic Standard Model can be modified to include neutrino mass, although it is not obvious exactly how this should be done.

If one insists on using only Standard Model particles, this can be achieved by adding a non-renormalizable interaction of leptons with the Higgs boson.[61] On a fundamental level, such an interaction emerges in theseesaw mechanism where heavy right-handed neutrinos are added to the theory.This is natural in theleft-right symmetric extension of the Standard Model[62][63] and in certaingrand unified theories.[64] As long as new physics appears below or around 1014GeV, the neutrino masses can be of the right order of magnitude.

Theoretical and experimental research has attempted to extend the Standard Model into aunified field theory or atheory of everything, a complete theory explaining all physical phenomena including constants. Inadequacies of the Standard Model that motivate such research include:

  • The model does not explaingravitation, although physical confirmation of a theoretical particle known as agraviton would account for it to a degree. Though it addresses strong and electroweak interactions, the Standard Model does not consistently explain the canonical theory of gravitation,general relativity, in terms ofquantum field theory. The reason for this is, among other things, that quantum field theories of gravity generally break down before reaching thePlanck scale. As a consequence, we have no reliable theory for the very early universe.
  • Some physicists consider it to bead hoc and inelegant, requiring 19 numerical constants whose values are unrelated and arbitrary.[65] Although the Standard Model, as it now stands, can explain why neutrinos have masses, the specifics of neutrino mass are still unclear. It is believed that explaining neutrino mass will require an additional 7 or 8 constants, which are also arbitrary parameters.[66]
  • The Higgs mechanism gives rise to thehierarchy problem if some new physics (coupled to the Higgs) is present at high energy scales. In these cases, in order for the weak scale to be much smaller than thePlanck scale, severe fine tuning of the parameters is required; there are, however, other scenarios that includequantum gravity in which such fine tuning can be avoided.[67]
  • The model is inconsistent with the emergingLambda-CDM model of cosmology. Contentions include the absence of an explanation in the Standard Model of particle physics for the observed amount ofcold dark matter (CDM) and its contributions todark energy, which are many orders of magnitude too large. It is also difficult to accommodate the observed predominance of matter over antimatter (matter/antimatterasymmetry). Theisotropy andhomogeneity of the visible universe over large distances seems to require a mechanism like cosmicinflation, which would also constitute an extension of the Standard Model.

Currently, no proposedtheory of everything has been widely accepted or verified.

See also

[edit]

Notes

[edit]
  1. ^There are mathematical issues regarding quantum field theories still under debate (see e.g.Landau pole), but the predictions extracted from the Standard Model by current methods applicable to current experiments are all self-consistent.[2]
  2. ^Although nine color–anticolor combinations mathematically exist, gluons form color octet particles. As one color-symmetric combination is linear and forms a color singlet particles, there are eight possible gluons.[41]

References

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