Standard Model

From Wikipedia, the free encyclopedia

(Redirected from Standard model) For other uses, see Standard model (disambiguation).

Quantum field theory

Feynman diagram

History of...

Background
Gauge theory Field theory Poincaré symmetry Quantum mechanics Spontaneous symmetry breaking

Symmetries
Crossing symmetry Charge conjugation Parity Time reversal

Tools
Anomaly Effective field theory Expectation value Faddeev-Popov ghosts Feynman diagram LSZ reduction formula Partition function Propagator Quantization Renormalization Vacuum state Wick's theorem Wightman axioms

Equations
Dirac equation Klein–Gordon equation Proca equations Wheeler-deWitt equation

Standard model
Electroweak interaction Higgs mechanism Quantum chromodynamics Quantum electrodynamics Yang-Mills theory

Incomplete theories
Quantum gravity String theory Supersymmetry Theory of everything

Scientists

Adler • Bethe • Bogoliubov • Callan • Coleman • DeWitt • Dyson • Fermi • Feynman • Fierz • Fröhlich • Gell–Mann • Goldstone • Gross • 't Hooft • Jackiw • Klein • Landau • Lee • Lehman • Majorana • Nambu • Parisi • Polyakov • Salam • Schwinger • Skyrme • Stueckelberg •Symanzik • Tomonaga • Veltman • Weinberg • Weisskopf • Wilson • Witten • Yang • Yukawa • Zimmermann • Zinn–Justin

This box: view • talk • edit

The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions among the elementary particles that make up all matter. It groups the electroweak theory and quantum chromodynamics into a structure denoted by the gauge group SU(3)×SU(2)×U(1). It is a relativistic quantum field theory which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions.

The Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, and also because of the recent observation of neutrino oscillations.

1 Historical background
2 Overview
3 Particle Content
4 Theoretical Aspects
5 Tests and predictions
6 Challenges to the standard model
7 See also
8 Notes
9 References
10 External links

Historical background

The formulation of the unification of the electromagnetic and weak interactions in the Standard Model is due to Steven Weinberg, Abdus Salam and, subsequently, Sheldon Glashow. The unification model was initially proposed by Steven Weinberg in 1967, and completed integrating it with the proposals by P. Higgs, G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, and F. Englert and R. Brout of spontaneous symmetry breaking which gives origin to the masses of all particles described in the model.

After the discovery, made at CERN of the existence of neutral weak currents, mediated by the Z boson, foreseen in the Standard Model, Glashow, Salam, and Weinberg received the Nobel Prize in Physics in 1979.

Overview

In physics, the dynamics of both matter and energy in nature is presently best understood in terms of the kinematics and interactions of fundamental particles. To date, science has managed to reduce the laws which seem to govern the behavior and interaction of all types of matter and energy we are aware of, to a small core of fundamental laws and theories. A major goal of physics is to find the 'common ground' that would unite all of these into one integrated model of everything, in which all the other laws we know of would be special cases, and from which the behavior of all matter and energy can be derived (at least in principle). "Details can be worked out if the situation is simple enough for us to make an approximation, which is almost never, but often we can understand more or less what is happening." (Feynman's lectures on Physics, Vol 1. 2–7)

The standard model is a grouping of two major theories — quantum electroweak and quantum chromodynamics — which provides an internally consistent theory describing interactions between all experimentally observed particles. Technically, quantum field theory provides the mathematical framework for the standard model. The standard model describes each type of particle in terms of a mathematical field. For a technical description of the fields and their interactions, see standard model (mathematical formulation).

Particle Content

v • d • e Particles in physics

Elementary particles	Fermions: Quarks: u · d · c · s · t · b • Leptons: e− · e+ · μ− · μ+ · τ− · τ+ · νe · νμ · ντ · νe · νμ · ντ Bosons: Gauge bosons: γ · g · W± · Z Other: Ghosts

Composite particles	Hadrons: Baryons/Hyperons/Nucleons: p+ · n0 · Δ · Λ · Σ · Ξ · Ω • Mesons/Quarkonia: π · K · ρ · J/ψ · Υ Other: Atomic nuclei • Atoms • Exotic atoms: Positronium · Muonium · Onia • Molecules

Hypothetical elementary particles	Superpartners: Axino · Chargino · Gaugino · Gluino · Gravitino · Higgsino · Neutralino · Sfermion Other: Axion · Dilaton · Graviton · H0 · J · Tachyon · X · Y · W' · Z' · Sterile neutrino

Hypothetical composite particles	Exotic hadrons: Exotic baryons: Dibaryon · Pentaquark • Exotic mesons: Glueball · Tetraquark Other: Mesonic molecule · Pomeron

Quasiparticles	Davydov soliton · Exciton · Magnon · Phonon · Plasmon · Polariton · Polaron · Roton

Lists	List of particles · List of quasiparticles · List of baryons · List of mesons · Timeline of particle discoveries

The particles of the standard model are organized into three classes according to their spin: fermions (spin-½ particles of matter), gauge bosons (spin-1 force-mediating particles), and the (spin-0) Higgs boson.

Particles of matter

All fermions in the Standard Model are spin-½, and follow the Pauli Exclusion Principle in accordance with the spin-statistics theorem.

Organization of Fermions
	Generation 1		Generation 2		Generation 3
Quarks	Up	u	Charm	c	Top	t
Quarks	Down	d	Strange	s	Bottom	b
Leptons	Electron Neutrino	νe	Muon Neutrino	νμ	Tau Neutrino	ντ
Leptons	Electron	e−	Muon	μ−	Tau	τ−

Apart from their antiparticle partners, a total of twelve different fermions are known and accounted for. They are classified according to how they interact (or equivalently, what charges they carry): six of them are classified as quarks (up, down, charm, strange, top, bottom), and the other six as leptons (electron, muon, tau, and their corresponding neutrinos).

Pairs from each classification are grouped together to form a generation, with corresponding particles exhibiting similar physical behavior (see table of fermions).

The defining property of the quarks is that they carry color charge, and hence, interact via the strong force. The infrared confining behavior of the strong force results in the quarks being perpetually bound to one another forming color-neutral composite particles (hadrons) of either two quarks (mesons) or three quarks (baryons). The familiar proton and the neutron are examples of the two lightest baryons. Quarks also carry electric charges and weak isospin. Hence they interact with other fermions electromagnetically and via the weak nuclear interactions.

The remaining six fermions that do not carry color charge are defined to be the leptons. The three neutrinos do not carry electric charge either, so their motion is directly influenced only by means of the weak nuclear force. For this reason neutrinos are notoriously difficult to detect in laboratories. However, the electron, muon and the tau lepton carry an electric charge so they interact electromagnetically, too.

Force mediating particles

Summary of interactions between particles described by the Standard Model.

Forces in physics are the ways that particles interact and influence each other. At a macro level, the electromagnetic force allows particles to interact with one another via electric and magnetic fields, and the force of gravitation allows two particles with mass to attract one another in accordance with Newton's Law of Gravitation. The standard model explains such forces as resulting from matter particles exchanging other particles, known as force mediating particles. When a force mediating particle is exchanged, at a macro level the effect is equivalent to a force influencing both of them, and the particle is therefore said to have mediated (i.e., been the agent of) that force. Force mediating particles are believed to be the reason why the forces and interactions between particles observed in the laboratory and in the universe exist.

The known force mediating particles described by the Standard Model also all have spin (as do matter particles), but in their case, the value of the spin is 1, meaning that all force mediating particles are bosons. As a result, they do not follow the Pauli Exclusion Principle. The different types of force mediating particles are described below.

Photons mediate the electromagnetic force between electrically charged particles. The photon is massless and is well-described by the theory of quantum electrodynamics.

The W+, W−, and Z gauge bosons mediate the weak interactions between particles of different flavors (all quarks and leptons). They are massive, with the Z being more massive than the W±. The weak interactions involving the W± act on exclusively left-handed particles and right-handed antiparticles. Furthermore, the W± carry an electric charge of +1 and −1 and couple to the electromagnetic interactions. The electrically neutral Z boson interacts with both left-handed particles and antiparticles. These three gauge bosons along with the photons are grouped together which collectively mediate the electroweak interactions.

The eight gluons mediate the strong interactions between color charged particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combination of color and an anticolor charge (e.g., red–antigreen). Because the gluon has an effective color charge, they can interact among themselves. The gluons and their interactions are described by the theory of quantum chromodynamics.

The interactions between all the particles described by the Standard Model are summarized in the illustration immediately above and to the right.

Force Mediating Particles
Electromagnetic Force		Weak Nuclear Force		Strong Nuclear Force
Photon	γ	W+, W−, and Z Gauge Bosons	W+, W−, Z	Gluons	g

The Higgs boson

Main article: Higgs boson

The Higgs particle is a hypothetical massive scalar elementary particle predicted by the Standard Model, and the only fundamental particle predicted by that model which has not been directly observed as yet. This is because it requires an exceptionally large amount of energy and beam luminosity to create and observe at high energy colliders. It has no intrinsic spin, and thus, (like the force mediating particles, which also have integral spin) is also classified as a boson.

The Higgs boson plays a unique role in the Standard Model, and a key role in explaining the origins of the mass of other elementary particles, in particular the difference between the massless photon and the very heavy W and Z bosons. Elementary particle masses, and the differences between electromagnetism (caused by the photon) and the weak force (caused by the W and Z bosons), are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. In electroweak theory it generates the masses of the massive leptons (electron, muon and tau); and also of the quarks.

As of September 2008, no experiment has directly detected the existence of the Higgs boson, but there is some indirect evidence for it. It is hoped that upon the completion of the Large Hadron Collider, experiments conducted at CERN would bring experimental evidence confirming the existence of the particle.

Science, a journal of original scientific research, has reported: "...experimenters may have already overlooked a Higgs particle, argues theorist Chien-Peng Yuan of Michigan State University in East Lansing and his colleagues. They considered the simplest possible supersymmetric theory. Ordinarily, theorists assume that the lightest of theory's five Higgses is the one that drags on the W and Z. Those interactions then feed back on Higgs and push its mass above 121 times the mass of the proton, the highest mass searched for at CERN's Large Electron–Positron (LEP) collider, which ran from 1989 to 2000. But it's possible that the lightest Higgs weighs as little as 65 times the mass of a proton and has been missed, Yuan and colleagues argue in a paper to be published in Physical Review Letters`."

Theoretical Aspects

Construction of the Standard Model Lagrangian

$\mu_{\overline{\text{MS}}}=2\text{ GeV}$ $\mu_{\overline{\text{MS}}}=2\text{ GeV}$ $\mu_{\overline{\text{MS}}}=2\text{ GeV}$ $\mu_{\overline{\text{MS}}}=m_c$ $\mu_{\overline{\text{MS}}}=m_b$ $\mu_{\overline{\text{MS}}}=M_\text{Z}$ $\mu_{\overline{\text{MS}}}=M_\text{Z}$ $\mu_{\overline{\text{MS}}}=M_\text{Z}$

Parameters of the Standard Model
Symbol	Description	Renormalization scheme (point)	Value
m_e	Electron mass		511 keV
m_μ	Muon mass		106 MeV
m_τ	Tau lepton mass		1.78 GeV
m_u	Up quark mass	1.9 MeV
m_d	Down quark mass	4.4 MeV
m_s	Strange quark mass	87 MeV
m_c	Charm quark mass	1.32 GeV
m_b	Bottom quark mass	4.24 GeV
m_t	Top quark mass	(on-shell scheme)	172.7 GeV
θ₁₂	CKM 12-mixing angle		0.229
θ₂₃	CKM 23-mixing angle		0.042
θ₁₃	CKM 13-mixing angle		0.004
δ	CKM CP-Violating Phase		0.995
g₁	U(1) gauge coupling	0.357
g₂	SU(2) gauge coupling	0.652
g₃	SU(3) gauge coupling	1.221
θ_QCD	QCD Vacuum Angle		~0
μ	Higgs quadratic coupling		Unknown
λ	Higgs self-coupling strength		Unknown

Technically, quantum field theory provides the mathematical framework for the standard model, in which a Lagrangian controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamical field that pervades space-time. 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 general renormalizable Lagrangian from its particle (field) content that observes these symmetries.

$\times$

Additional Symmetries of the Standard Model

From the theoretical point of view, the standard model exhibits additional global symmetries that were not postulated at the outset of its construction. There are four such symmetries and are collectively called accidental symmetries, all of which are continuous U(1) global symmetries. The transformations leaving the Lagrangian invariant are

$\psi_\text{q}(x)\rightarrow e^{i\alpha/3}\psi_\text{q}$ $E_L\rightarrow e^{i\beta}E_L\text{ and }(e_R)^c\rightarrow e^{i\beta}(e_R)^c$ $M_L\rightarrow e^{i\beta}M_L\text{ and }(\mu_R)^c\rightarrow e^{i\beta}(\mu_R)^c$ $T_L\rightarrow e^{i\beta}T_L\text{ and }(\tau_R)^c\rightarrow e^{i\beta}(\tau_R)^c.$

The first transformation rule is shorthand to mean that all quark fields for all generations must be rotated by an identical phase simultaneously. The fields M_L, T_L and (μ_R)^c, (τ_R)^c are the 2nd (muon) and 3rd (tau) generation analogs of E_L and (e_R)^c fields.

By Noether's theorem, each of these symmetries yields an associated conservation law. They are the conservation of baryon number, electron number, muon number, and tau number. Each quark carries 1/3 of a baryon number, while each antiquark carries -1/3 of a baryon number. The conservation law implies that the total number of quarks minus number of antiquarks stays constant throughout time. Within experimental limits, no violation of this conservation law has been found.

Similarly, each electron and its associated neutrino carries +1 electron number, while the antielectron and the associated antineutrino carry -1 electron number, the muons carry +1 muon number and the tau leptons carry +1 tau number. The standard model predicts that each of these three numbers should be conserved separately in a manner similar to the baryon number. These numbers are collectively known as lepton family numbers (LF). The difference in the symmetry structures between the quark and the lepton sectors is due to the masslessness of neutrinos in the standard model. However, it was recently found that neutrinos have small mass, and oscillate between flavors, signaling the violation of these three quantum numbers.

In addition to the accidental (but exact) symmetries described above, the standard model exhibits a set of approximate symmetries. These are the SU(2) Custodial Symmetry and the SU(2) or SU(3) quark flavor symmetry.

$\rtimes$ $\times$

Symmetries of the Standard Model and Associated Conservation Laws
Symmetry	Lie Group	Symmetry Type	Conservation Law
Poincaré	Global symmetry	Energy, Momentum, Angular momentum
Gauge	Local symmetry	Electric charge, Weak isospin, Color charge
Baryon phase	U(1)	Accidental Global symmetry	Baryon number
Electron phase	U(1)	Accidental Global symmetry	Electron number
Muon phase	U(1)	Accidental Global symmetry	Muon number
Tau phase	U(1)	Accidental Global symmetry	Tau-lepton number

$\mathbf{3}$ $\bar\mathbf{3}$ $\bar\mathbf{3}$ $\mathbf{1}$ $\mathbf{1}$ $\bar\mathbf{1}$ $\mathbf{1}$ $\mathbf{8}$ $\mathbf{1}$

Field content of the Standard Model
Field (1st generation)		Spin	Gauge Group Representation	Baryon Number
Left-handed quark	Q_L	1 / 2	1 / 3	0
Right-handed up quark	(u_R)^c	1 / 2	− 1 / 3	0
Right-handed down quark	(d_R)^c	1 / 2	− 1 / 3	0
Left-handed lepton	E_L	1 / 2	0	1
Right-handed electron	(e_R)^c	1 / 2	0	− 1
Hypercharge gauge field	B_μ	1	0	0
Isospin gauge field	W_μ	1	0	0
Gluon field	G_μ	1	0	0
Higgs field	H	0	0	0

List of standard model fermions

This table is based in part on data gathered by the Particle Data Group (QuarksPDF (54.8 KB)).

$e^-\,$ $-1\,$ $-1/2\,$ $-1\,$ $\bold{1}\,$ $e^+\,$ $+1\,$ $0\,$ $+2\,$ $\bold{1}\,$ $\nu_e\,$ $0\,$ $+1/2\,$ $-1\,$ $\bold{1}\,$ $u\,$ $+2/3\,$ $+1/2\,$ $+1/3\,$ $\bold{3}\,$ $\bar{u}\,$ $-2/3\,$ $0\,$ $-4/3\,$ $\bold{\bar{3}}\,$ $d\,$ $-1/3\,$ $-1/2\,$ $+1/3\,$ $\bold{3}\,$ $\bar{d}\,$ $+1/3\,$ $0\,$ $+2/3\,$ $\bold{\bar{3}}\,$ $\mu^-\,$ $-1\,$ $-1/2\,$ $-1\,$ $\bold{1}\,$ $\mu^+\,$ $+1\,$ $0\,$ $+2\,$ $\bold{1}\,$ $\nu_\mu\,$ $0\,$ $+1/2\,$ $-1\,$ $\bold{1}\,$ $c\,$ $+2/3\,$ $+1/2\,$ $+1/3\,$ $\bold{3}\,$ $\bar{c}\,$ $-2/3\,$ $0\,$ $-4/3\,$ $\bold{\bar{3}}\,$ $s\,$ $-1/3\,$ $-1/2\,$ $+1/3\,$ $\bold{3}\,$ $\bar{s}\,$ $+1/3\,$ $0\,$ $+2/3\,$ $\bold{\bar{3}}\,$ $\tau^-\,$ $-1\,$ $-1/2\,$ $-1\,$ $\bold{1}\,$ $\tau^+\,$ $+1\,$ $0\,$ $+2\,$ $\bold{1}\,$ $\nu_\tau\,$ $0\,$ $+1/2\,$ $-1\,$ $\bold{1}\,$ $t\,$ $+2/3\,$ $+1/2\,$ $+1/3\,$ $\bold{3}\,$ $\bar{t}\,$ $-2/3\,$ $0\,$ $-4/3\,$ $\bold{\bar{3}}\,$ $b\,$ $-1/3\,$ $-1/2\,$ $+1/3\,$ $\bold{3}\,$ $\bar{b}\,$ $+1/3\,$ $0\,$ $+2/3\,$ $\bold{\bar{3}}\,$

**Left-handed fermions in the Standard Model**
Generation 1
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge *	Mass **
Electron	511 keV
Positron	511 keV
Electron-neutrino	< 2 eV ****
Up quark	~ 3 MeV ***
Up antiquark	~ 3 MeV ***
Down quark	~ 6 MeV ***
Down antiquark	~ 6 MeV ***

Generation 2
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge *	Mass **
Muon	106 MeV
Antimuon	106 MeV
Muon-neutrino	< 2 eV ****
Charm quark	~ 1.337 GeV
Charm antiquark	~ 1.3 GeV
Strange quark	~ 100 MeV
Strange antiquark	~ 100 MeV

Generation 3
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge *	Mass **
Tau lepton	1.78 GeV
Anti-tau lepton	1.78 GeV
Tau-neutrino	< 2 eV ****
Top quark	171 GeV
Top antiquark	171 GeV
Bottom quark	~ 4.2 GeV
Bottom antiquark	~ 4.2 GeV
Notes: * These are not ordinary abelian charges, which can be added together, but are labels of group representations of Lie groups. Mass is really a coupling between a left-handed fermion and a right-handed fermion. For example, the mass of an electron is really a coupling between a left-handed electron and a right-handed electron, which is the antiparticle of a left-handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left-handed electron antineutrino. *** The masses of baryons and hadrons and various cross-sections are the experimentally measured quantities. Since quarks can't be isolated because of QCD confinement, the quantity here is supposed to be the mass of the quark at the renormalization scale of the QCD scale. ****** The Standard Model assumes that neutrinos are massless. However, several contemporary experiments prove that neutrinos oscillate between their flavour states, which could not happen if all were massless. It is straightforward to extend the model to fit these data but there are many possibilities, so the mass eigenstates are still open. See Neutrino#Mass.

Log plot of masses in the Standard Model.

Tests and predictions

This section needs additional citations for verification.
Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (April 2008)

The Standard Model predicted the existence of W and Z bosons, the gluon, the top quark and the charm quark before these particles had been observed. Their predicted properties were experimentally confirmed with good precision.

The Large Electron-Positron Collider at CERN tested various predictions about the decay of Z bosons, and found them confirmed.

To get an idea of the success of the Standard Model a comparison between the measured and the predicted values of some quantities are shown in the following table:

Quantity	Measured (GeV)	SM prediction (GeV)
Mass of W boson	80.398±0.025	80.3900±0.0180
Mass of Z boson	91.1876±0.0021	91.1874±0.0021

Challenges to the standard model

Unsolved problems in physics: Parameters in the Standard Model: What gives rise to the Standard Model of particle physics? Why do its particle masses and coupling constants possess the values we have measured? Does the Higgs boson predicted by the model really exist? Why are there three generations of particles in the Standard Model?

The Standard Model of particle physics has been empirically determined through experiments over the past fifty years. Currently the Standard Model predicts that there is one more particle to be discovered, the Higgs boson. One of the reasons for building the Large Hadron Collider is that the increase in energy is expected to make the Higgs observable. However, as of August 2008, there are only indirect experimental indications for the existence of the Higgs boson and it can not be claimed to be found.

There has been a great deal of both theoretical and experimental research exploring whether the Standard Model could be extended into a complete theory of everything. This area of research is often described by the term 'Beyond the Standard Model'. There are several motivations for this research. First, the Standard Model does not attempt to explain gravity, and it is unknown how to combine quantum field theory which is used for the Standard Model with general relativity which is the best physical model of gravity. This means that there is not a good theoretical model for phenomena such as the early universe.

Another avenue of research is related to the fact that the standard model seems very ad-hoc and inelegant. For example, the theory contains many seemingly unrelated parameters of the theory — 21 in all (18 parameters in the core theory, plus G, c and h; there are believed to be an additional 7 or 8 parameters required for the neutrino masses, although neutrino masses are outside the standard model and the details are unclear). Research also focuses on the Hierarchy problem (why the weak scale and Planck scale are so disparate), and attempts to reconcile the emerging Standard Model of Cosmology with the Standard Model of particle physics. Many questions relate to the initial conditions that led to the presently observed Universe. Examples include: Why is there a matter/antimatter asymmetry? Why is the Universe isotropic and homogeneous at large distances?