|Standard model of particle physics|
The Standard Model of particle physics is a theory of three of the four known fundamental interactions and the elementary particles that take part in these interactions. These particles make up all visible matter in the universe. Every high energy physics experiment carried out since the mid-20th century has eventually yielded findings consistent with the Standard Model. Still, the Standard Model falls short of being a complete theory of fundamental interactions because it does not include gravitation, dark matter, or dark energy. It is not quite a complete description of leptons either, because it does not describe nonzero neutrino masses, although simple natural extensions do.
The standard model is a gauge theory of the strong (SU(3)) and electroweak (SU(2)×U(1)) interactions with the gauge group (sometimes called the Standard Model symmetry group) SU(3)×SU(2)×U(1). It does not take into account gravitation.
The first step towards the Standard Model was Sheldon Glashow's discovery, in 1960, of a way to combine the electromagnetic and weak interactions. In 1967, Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashow's electroweak theory, giving it its modern form.
The Higgs mechanism is believed to give rise to the masses of all the elementary particles, for which the Standard Model accounts. This includes the masses of the W and Z bosons, and the fermions. The Higgs mechanism is also believed to give rise to the masses of quarks and leptons. Quarks are fundamental components, which make up the hadrons, and leptons are elementary particles, with no fundamental components, such as the electron. (See the table above, which depicts the Standard Model).
After the discovery at CERN of neutral weak currents, caused by Z boson exchange, the electroweak theory became widely accepted. Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in Physics for discovering the electroweak theory. The W and Z bosons were discovered experimentally in 1981, and their masses were found to be as the Standard Model predicted.
At present, matter and energy are best understood in terms of the kinematics and interactions of elementary particles. To date, physics has reduced the laws governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. A major goal of physics is to find the "common ground" that would unite all of these theories into one integrated theory of everything, of which all the other known laws would be special cases, and from which the behavior of all matter and energy could be derived (at least in principle).
The Standard Model groups two major extant theories — quantum electroweak and quantum chromodynamics — into an internally consistent theory describing the interactions between all experimentally observed particles. The Standard Model describes each type of particle in terms of a mathematical field, via quantum field theory. For a technical description of these fields and their interactions, see Standard Model (mathematical formulation).
|Charge||First generation||Second generation||Third generation|
|0||Electron neutrino||νe||Muon neutrino||νμ||Tauon neutrino||ντ|
The Standard Model includes 12 elementary particles of spin-1⁄2 known as fermions. According to the spin-statistics theorem, fermions respect the Pauli Exclusion Principle. Each fermion has a corresponding antiparticle.
The fermions of the Standard Model are classified according to how they interact (or equivalently, by what charges they carry). There are six quarks (up, down, charm, strange, top, bottom), and six leptons (electron, electron neutrino, muon, muon neutrino, tauon, tauon neutrino). Pairs from each classification are grouped together to form a generation, with corresponding particles exhibiting similar physical behavior (see table).
The defining property of the quarks is that they carry color charge, and hence, interact via the strong interaction. The infrared confining behavior of the strong force results in quarks being perpetually (or at least since very soon after the start of the big bang) bound to one another, forming color-neutral composite particles (hadrons) containing either a quark and an antiquark (mesons) or three quarks (baryons). The familiar proton and the neutron are the two baryons having the smallest mass. Quarks also carry electric charge and weak isospin. Hence they interact with other fermions both electromagnetically and via the weak nuclear interaction.
The remaining six fermions do not carry color charge and are called leptons. The three neutrinos do not carry electric charge either, so their motion is directly influenced only by the weak nuclear force, which makes them notoriously difficult to detect. However, by virtue of carrying an electric charge, the electron, muon, and tauon all interact electromagnetically.
Each member of a generation has greater mass than the corresponding particles of lower generations. The first generation charged particles do not decay; hence all ordinary (baryonic) matter is made of such particles. Specifically, all atoms consist of electrons orbiting atomic nuclei ultimately constituted of up and down quarks. Second and third generations charged particles, on the other hand, decay with very short half lives, and are observed only in very high-energy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter.
Interactions in physics are the ways that particles influence other particles. At a macro level, electromagnetism allows particles to interact with one another via electric and magnetic fields, and gravitation allows particles with mass to attract one another in accordance with Einstein's General Relativity. 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.
The interactions between all the particles described by the Standard Model are summarized by the diagram at the top of this section.
The Higgs particle is a hypothetical massive scalar elementary particle theorized by Robert Brout, Francois Englert, Peter Higgs, Gerald Guralnik, C. R. Hagen, and Tom Kibble in 1964 (see Overview and differences of 1964 PRL symmetry breaking papers) and is a key building block in the Standard Model. It has no intrinsic spin, and for that reason is classified as a boson (like the force mediating particles, which have integer spin). Because an exceptionally large amount of energy and beam luminosity are theoretically required to observe a Higgs boson in high energy colliders, it is the only fundamental particle predicted by the Standard Model that has yet to be observed.
The Higgs boson plays a unique role in the Standard Model, by explaining why the other elementary particles, the photon and gluon excepted, are massive. In particular, the Higgs boson would explain why the photon has no mass, while the W and Z bosons are very heavy. Elementary particle masses, and the differences between electromagnetism (mediated by the photon) and the weak force (mediated by the W and Z bosons), are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. In electroweak theory, the Higgs boson generates the masses of the leptons (electron, muon, and tauon) and quarks.
As yet, no experiment has directly detected the existence of the Higgs boson. It is hoped that the Large Hadron Collider at CERN will confirm the existence of this particle. It is also possible that the Higgs boson may already have been produced but overlooked.
The standard model has the following fields:
By CPT symmetry, there is a set of right-handed fermions with the opposite quantum numbers.
This describes one generation of leptons and quarks, and there are three generations, so there are three copies of each field. Note that there are twice as many left-handed lepton field components as left-handed antilepton field components in each generation, but an equal number of left-handed quark and antiquark fields.
This field acquires a vacuum expectation value, leaving a combination of the weak isospin, I3, and weak hypercharge unbroken. This is the electromagnetic gauge group, and the photon remains massless. The standard formula for the electric charge (which defines the normalization of the weak hypercharge, Y, which would otherwise be somewhat arbitrary) is:[nb 2]
The Lagrangian for the spin 1 and spin 1⁄2 fields is the most general renormalizable gauge field Lagrangian with no fine tunings:
where the traces are over the SU(2) and SU(3) indices hidden in W and G respectively. The two-index objects are the field strengths derived from W and G the vector fields. There are also two extra hidden parameters: the theta angles for SU(2) and SU(3).
The spin 1⁄2 particles can have no mass terms because there is no right/left helicity pair with the same SU(2) and SU(3) representation and the same weak hypercharge. This means that if the gauge charges were conserved in the vacuum, none of the spin 1⁄2 particles could ever swap helicity, and they would all be massless.
For a neutral fermion, for example a hypothetical right-handed lepton N (or Nα in relativistic two-spinor notation), with no SU(3), SU(2) representation and zero charge, it is possible to add the term:
This term gives the neutral fermion a Majorana mass. Since the generic value for M will be of order 1, such a particle would generically be unacceptably heavy. The interactions are completely determined by the theory – the leptons introduce no extra parameters.
The Lagrangian for the Higgs includes the most general renormalizable self interaction:
The parameter v2 has dimensions of mass squared, and it gives the location where the classical Lagrangian is at a minimum. In order for the Higgs mechanism to work, v2 must be a positive number. v has units of mass, and it is the only parameter in the standard model which is not dimensionless. It is also much smaller than the Planck scale; it is approximately equal to the Higgs mass, and sets the scale for the mass of everything else. This is the only real fine-tuning to a small nonzero value in the standard model, and it is called the Hierarchy problem.
It is traditional to choose the SU(2) gauge so that the Higgs doublet in the vacuum has expectation value (v,0).
The rest of the interactions are the most general spin-0 spin-1⁄2 Yukawa interactions, and there are many of these. These constitute most of the free parameters in the model. The Yukawa couplings generate the masses and mixings once the Higgs gets its vacuum expectation value.
The terms L*HR generate a mass term for each of the three generations of leptons. There are 9 of these terms, but by relabeling L and R, the matrix can be diagonalized. Since only the upper component of H is nonzero, the upper SU(2) component of L mixes with R to make the electron, the muon, and the tauon, leaving over a lower massless component, the neutrino.
The terms QHU generate up masses, while QHD generate down masses. But since there is more than one right-handed singlet in each generation, it is not possible to diagonalize both with a good basis for the fields, and there is an extra CKM matrix.
|me||Electron mass||511 keV|
|mμ||Muon mass||106 MeV|
|mτ||Tauon mass||1.78 GeV|
|mu||Up quark mass||μMS = 2 GeV||1.9 MeV|
|md||Down quark mass||μMS = 2 GeV||4.4 MeV|
|ms||Strange quark mass||μMS = 2 GeV||87 MeV|
|mc||Charm quark mass||μMS = mc||1.32 GeV|
|mb||Bottom quark mass||μMS = mb||4.24 GeV|
|mt||Top quark mass||On-shell scheme||172.7 GeV|
|θ12||CKM 12-mixing angle||13.1°|
|θ23||CKM 23-mixing angle||2.4°|
|θ13||CKM 13-mixing angle||0.2°|
|δ||CKM CP-violating Phase||0.995|
|g1||U(1) gauge coupling||μMS = mZ||0.357|
|g2||SU(2) gauge coupling||μMS = mZ||0.652|
|g3||SU(3) gauge coupling||μMS = mZ||1.221|
|θQCD||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.
The global Poincaré symmetry is postulated for all relativistic quantum field theories. It consists of the familiar translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity. The local SU(3)×SU(2)×U(1) gauge symmetry is an internal 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 different representations of the various symmetry groups of the Standard Model (see table). Upon writing the most general Lagrangian, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment. The parameters are summarized in the table at right.
The electroweak sector is a Yang–Mills gauge theory with the symmetry group U(1)×SU(2)L,
where Bμ is the U(1) gauge field; YW is the weak hypercharge — the generator of the U(1) group; is the three-component SU(2) gauge field; are the Pauli matrices — infinitesimal generators of the SU(2) group. The subscript L indicates that they only act on left fermions; g′ and g are coupling constants.
where the indexes + and 0 indicate the electric charge (Q) of the components. The weak isospin (YW) of both components is 1.
Before symmetry breaking, the Higgs Lagrangian is:
which can also be written as:
From the theoretical point of view, the Standard Model exhibits four additional global symmetries, not postulated at the outset of its construction, collectively denoted accidental symmetries, which are continuous U(1) global symmetries. The transformations leaving the Lagrangian invariant are:
The first transformation rule is shorthand meaning that all quark fields for all generations must be rotated by an identical phase simultaneously. The fields ML, TL and (μR)c, (τR)c are the 2nd (muon) and 3rd (tauon) generation analogs of EL and (eR)c fields.
By Noether's theorem, each symmetry above has an associated conservation law: the conservation of baryon number, electron number, muon number, and tauon number. Each quark is assigned a baryon number of 1/3, while each antiquark is assigned a baryon number of -1/3. Conservation of baryon number implies that the number of quarks minus the number of antiquarks is a constant. Within experimental limits, no violation of this conservation law has been found.
Similarly, each electron and its associated neutrino is assigned an electron number of +1, while the antielectron and the associated antineutrino carry −1 electron number. Similarly, the muons and their neutrinos are assigned a muon number of +1 and the tau leptons are assigned a tau lepton number of +1. The Standard Model predicts that each of these three numbers should be conserved separately in a manner similar to the way baryon number is conserved. These numbers are collectively known as lepton family numbers (LF). Symmetry works differently for quarks than for leptons, mainly because the Standard Model predicts that neutrinos are massless. However, it was recently found that neutrinos have small masses and oscillate between flavors, signaling that the conservation of lepton family number is violated.
In addition to the accidental (but exact) symmetries described above, the Standard Model exhibits several approximate symmetries. These are the "SU(2) custodial symmetry" and the "SU(2) or SU(3) quark flavor symmetry."
|Symmetry||Lie Group||Symmetry Type||Conservation Law|
|Poincaré||Translations×SO(3,1)||Global symmetry||Energy, Momentum, Angular momentum|
|Gauge||SU(3)×SU(2)×U(1)||Local symmetry||Color charge, Weak isospin, Electric charge, Weak hypercharge|
|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|
|Tauon phase||U(1)||Accidental Global symmetry||Tauon number|
|Left-handed quark||(, , )|
|Left-handed up antiquark||(, , )|
|Left-handed down antiquark||(, , )|
|Left-handed lepton||(, , )|
|Left-handed antielectron||(, , )|
|Hypercharge gauge field||(, , )|
|Isospin gauge field||(, , )|
|Gluon field||(, , )|
|Higgs field||(, , )|
|Electron neutrino||< 2 eV ****|
|Antielectron neutrino||< 2 eV ****|
|Up quark||~ 3 MeV ***|
|Up antiquark||~ 3 MeV ***|
|Down quark||~ 6 MeV ***|
|Down antiquark||~ 6 MeV ***|
|Muon neutrino||< 2 eV ****|
|Antimuon neutrino||< 2 eV ****|
|Charm quark||~ 1.337 GeV|
|Charm antiquark||~ 1.3 GeV|
|Strange quark||~ 100 MeV|
|Strange antiquark||~ 100 MeV|
|Tauon neutrino||< 2 eV ****|
|Antitauon neutrino||< 2 eV ****|
|Top quark||171 GeV|
|Top antiquark||171 GeV|
|Bottom quark||~ 4.2 GeV|
|Bottom antiquark||~ 4.2 GeV|
The Standard Model (SM) predicted the existence of the W and Z bosons, gluon, and the top and charm quarks before these particles were observed. Their predicted properties were experimentally confirmed with good precision. To give an idea of the success of the SM, the following table compares the measured masses of the W and Z bosons with the masses predicted by the SM:
|Quantity||Measured (GeV)||SM prediction (GeV)|
|Mass of W boson||80.398 ± 0.025||80.390 ± 0.018|
|Mass of Z boson||91.1876 ± 0.0021||91.1874 ± 0.0021|
There is some experimental evidence consistent with neutrinos having mass, which the Standard Model does not allow. To accommodate such findings, the Standard Model can be modified by adding a non-renormalizable interaction of lepton fields with the square of the Higgs field. This is natural in certain grand unified theories, and if new physics appears at about 1016 GeV, the neutrino masses are of the right order of magnitude.
Currently, there is one elementary particle predicted by the Standard Model that has yet to be observed: the Higgs boson. A major reason for building the Large Hadron Collider is that the high energies of which it is capable are expected to make the Higgs observable. However, as of August 2008, there is only indirect empirical evidence for the existence of the Higgs boson, so that its discovery cannot be claimed. Moreover, there are serious theoretical reasons for supposing that elementary scalar Higgs particles cannot exist (see Quantum triviality).
A fair amount of theoretical and experimental research has attempted to extend the Standard Model into a Unified Field Theory or a Theory of everything, a complete theory explaining all physical phenomena including constants. Inadequacies of the Standard Model that motivate such research include:
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The Standard Model of physics is a theory of the elementary particles, which are either fermions or bosons. It also explains three of the four basic forces of nature. The Model uses the parts of physics called quantum mechanics and special relativity, and the ideas of physical field and symmetry breaking. Some of the mathematics of the Standard Model is group theory, and also as equations that have biggest and smallest points, called Lagrangians and Hamiltonians. (See principle of least action.) s.1 GeV/c2 = 1.783x10-27 kg. 1 MeV/c2 = 1.783x10-30 kg.]]
Fermions are particles that join together to make up all "matter" we see. Examples of groups of fermions are the proton and the neutron. Fermions have properties, such as charge and mass, which can be seen in everyday life. They also have other properties, such as spin, weak charge, hypercharge, and colour charge, whose effects do not usually appear in everyday life. These properties are given numbers called quantum numbers.
An important fact about fermions is that they follow a rule called the Pauli exclusion principle. This rule says that no two fermions can be in the same "place" at the same time, because no two fermions in an atom can have the same quantum numbers at the same time. Fermions also obey a theory called Fermi-Dirac statistics. The word "fermion" honors the physicist Enrico Fermi.
There are 12 different types of fermions. Each type is called a "flavor." Their names are:
Quarks are grouped into three pairs. Each pair is called a "generation." The first quark in each pair has charge 2/3, and the second quark has charge -1/3. The three kinds of neutrino have a charge of 0. The electron, muon, and tau have charge -1. s in a proton.]]
Matter is made of atoms, and atoms are made of electrons, protons, and neutrons. Protons and neutrons are made of up and down quarks. You can find one lepton by itself, but you can never find quarks alone. This is because quarks are held together by the color force.
Bosons are the second type of elementary particle in the Standard Model. All bosons have an integer spin (1, 2, 3, etc..) so many of them can be in the same place at the same time. The are two types of bosons, gauge bosons and the Higgs boson. Gauge bosons are what make the fundamental forces of nature possible. (We are not yet sure if gravity works through a gauge boson.) Every force that acts on fermions happens because gauge bosons are moving between the fermions, carrying the force. Bosons follow a theory called Bose-Einstein statistics. The word "boson" honors the Indian physicist Satyendra Nath Bose.
The Standard Model says that there are:
These particles have all been seen either in nature or in the laboratory. The Standard Model also predicts that there is a Higgs boson. The Standard Model says that fermions have mass (they are not just pure energy) because Higgs bosons travel back and forth between them. The Higgs boson is the only elementary particle in the Standard Model that physicists have not yet found.
There are four basic forces of nature. These forces affect fermions, and are carried by bosons traveling between those fermions. The Standard Model explains three of these four forces.
The strong and weak forces are only seen inside the nucleus of an atom, and they only work over very tiny distances: distances that are about as far as a proton is wide. The electromagnetic force and gravity work over any distance, but the strength of these forces goes down as the affected objects get farther apart. The force goes down with the square of the distance between the affected objects: for example, if two objects become 2 times as far away from each other, the force of gravity between them becomes 4 times less strong (22=4).