Standard Model - Wikipedia &Oldid=492552000

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Standard Model 1

Standard Model

The Standard Model of elementary particles, with the gauge bosons in the

rightmost column.

The Standard Model of particle physics is

a theory concerning the electromagnetic,

weak, and strong nuclear interactions, which

mediate the dynamics of the known

subatomic particles. Developed throughout

the mid to late 20th century, the current

formulation was finalized in the mid 1970s

upon experimental confirmation of the

existence of quarks. Since then, discoveries

of the bottom quark (1977), the top quark

(1995) and the tau neutrino (2000) have

given further credence to the Standard

Model. Because of its success in explaining

a wide variety of experimental results, the

Standard Model is sometimes regarded as a

"theory of almost everything".

The Standard Model falls short of being a

complete theory of fundamental interactions

because it does not incorporate the physics

of dark energy nor of the full theory of

gravitation as described by general

relativity. The theory does not contain any

viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It

also does not correctly account for neutrino oscillations (and their non-zero masses). Although the Standard Model is

believed to be theoretically self-consistent, it has several apparently unnatural properties giving rise to puzzles like

the strong CP problem and the hierarchy problem.

Nevertheless, the Standard Model is important to theoretical and experimental particle physicists alike. For theorists,

the Standard Model is a paradigmatic example of a quantum field theory, which exhibits a wide range of physics

including spontaneous symmetry breaking, anomalies, non-perturbative behavior, etc. It is used as a basis for

building more exotic models that incorporate hypothetical particles, extra dimensions, and elaborate symmetries

(such as supersymmetry) in an attempt to explain experimental results at variance with the Standard Model, such as

the existence of dark matter and neutrino oscillations. In turn, experimenters have incorporated the Standard Modelinto simulators to help search for new physics beyond the Standard Model.

Recently, the Standard Model has found applications in fields besides particle physics, such as astrophysics,

cosmology, and nuclear physics.

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Standard Model 2

Historical background

The first step towards the Standard Model was Sheldon Glashow's discovery in 1960 of a way to combine the

electromagnetic and weak interactions.[1]

In 1967 Steven Weinberg[2]

and Abdus Salam[3]

incorporated the Higgs

mechanism[4][5][6]

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 in the Standard Model.

This includes the masses of the W and Z bosons, and the masses of the fermions, i.e. the quarks and leptons.

After the neutral weak currents caused by Z boson exchange were discovered at CERN in 1973,[7][8][9][10]

the

electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in

Physics for discovering it. The W and Z bosons were discovered experimentally in 1981, and their masses were

found to be as the Standard Model predicted.

The theory of the strong interaction, to which many contributed, acquired its modern form around 197374, when

experiments confirmed that the hadrons were composed of fractionally charged quarks.

Overview

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).[11]

The Standard Model groups two major extant theoriesquantum electroweak and quantum chromodynamicsinto

an internally consistent theory that describes the interactions between all known particles in terms of quantum field

theory. For a technical description of the fields and their interactions, see Standard Model (mathematical

formulation).

Particle content

Fermions

Organization of Fermions

Charge First generation Second generation Third generation

Quarks +2/3 Up u Charm c Top t

1/3 Down d Strange s Bottom b

Leptons 1 Electron e Muon

Tau

0 Electron neutrino e

Muon neutrino

Tau neutrino

The Standard Model includes 12 elementary particles of spin 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, tau, tau 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. Aphenomenon called color confinement results in quarks being perpetually (or at least since very soon after the start of
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Standard Model 3

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 interaction.

The remaining six fermions do not carry colour 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 themnotoriously difficult to detect. However, by virtue of carrying an electric charge, the electron, muon, and tau 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.

Gauge bosons

Summary of interactions between particles described by the Standard Model.

In the Standard Model, gauge bosons

are defined as force carriers that

mediate the strong, weak, and

electromagnetic fundamental

interactions.

Interactions in physics are the ways

that particles influence other particles.

At a macroscopic level,

electromagnetism allows particles tointeract with one another via electric

and magnetic fields, and gravitation

allows particles with mass to attract

one another in accordance with

Einstein's theory of general relativity.

The Standard Model explains such

forces as resulting from matter

particles exchanging other particles, known as force mediating particles (strictly speaking, this is only so if

interpreting literally what is actually an approximation method known as perturbation theory). When a force

mediating particle is exchanged, at a macroscopic 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. The Feynman
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Standard Model 4

The above interactions form the basis of the standard model.

Feynman diagrams in the standard model are built from these

vertices. Modifications involving Higgs boson interactions and

neutrino oscillations are commonly added. The charge of theW bosons are dictated by the fermions they interact with.

diagram calculations, which are a graphical representation of

the perturbation theory approximation, invoke "force

mediating particles", and when applied to analyze

high-energy scattering experiments are in reasonable

agreement with the data. However, perturbation theory (and

with it the concept of a "force-mediating particle") fails inother situations. These include low-energy quantum

chromodynamics, bound states, and solitons.

The gauge bosons of the Standard Model all have spin (as do

matter particles). The value of the spin is 1, making them

bosons. As a result, they do not follow the Pauli exclusion

principle that constrains fermions: thus bosons (e.g. photons)

do not have a theoretical limit on their spatial density

(number per volume). The different types of gauge bosons

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

exclusively act on left-handedparticles and right-handedantiparticles only. Furthermore, the W

carries an

electric charge of +1 and 1 and couples to the electromagnetic interaction. The electrically neutral Z boson

interacts with both left-handed particles and antiparticles. These three gauge bosons along with the photons are

grouped together, as collectively mediating the electroweak interaction.

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 anticolor charge (e.g.

redantigreen).[12]

Because the gluon has an effective color charge, they can also 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 by the diagrams on the

right of this section.
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Standard Model 5

Higgs boson

The Higgs particle is a hypothetical massive scalar elementary particle theorized by Robert Brout, Franois Englert,

Peter Higgs, Gerald Guralnik, C. R. Hagen, and Tom Kibble in 1964 (see 1964 PRL symmetry breaking papers) and

is a key building block in the Standard Model.[13][14][15][16]

It has no intrinsic spin, and for that reason is classified as

a boson (like the gauge bosons, 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 onlyfundamental 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,

except the photon and gluon, 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 tau) and quarks.

As yet, no experiment has conclusively detected the existence of the Higgs boson. It is hoped that the Large Hadron

Collider at CERN will confirm the existence of this particle. As of August 2011, a significant portion of the possible

masses for the Higgs have been excluded at 95% confidence level: CMS has excluded the mass ranges 145-216

GeV, 226-288 GeV and 310-400 GeV,[17]

while the ATLAS experiment has excluded 146-232 GeV, 256-282 GeV

and 296-466 GeV.[18]

Note that these exclusions apply only to the Standard Model Higgs, and that more complex

Higgs sectors which are possible in Beyond the Standard Model scenarios may be significantly more difficult to

characterize. CERN director general Rolf Heuer has predicted that by the end of 2012 either the Standard Model

Higgs boson will be observed, or excluded in all mass ranges, implying that the Standard Model is not the whole

story.[19]

On December 13, 2011 CERN announced that both ATLAS and CMS experiments had detected 'hints' of the Higgs

boson in at approximately 124GeV. These results were not sufficiently strong to announce that the Higgs boson had

been found (ATLAS showed a 2.3 sigma level of certainty for an excess at 126GeV, while CMS showed a 1.9 sigmalevel excess at 124GeV) but the fact that two separate experiments show excesses in the same energy range has led

to much excitement in the particle physics world.[20]

Field content

The Standard Model has the following fields:

Spin 1

1. A U(1) gauge fieldB

with coupling g (weak U(1), or weak hypercharge)

2. An SU(2) gauge field W

with coupling g (weak SU(2), or weak isospin)

3. An SU(3) gauge field G

with coupling gs

(strong SU(3), or color charge)

Spin1

2

The spin particles are in representations of the gauge groups. For the U(1) group, we list the value of the weak

hypercharge instead. The left-handed fermionic fields are:

1. An SU(3) triplet, SU(2) doublet, with U(1) weak hypercharge (left-handed quarks)

2. An SU(3) triplet, SU(2) singlet, with U(1) weak hypercharge (left-handed down-type antiquark)

3. An SU(3) singlet, SU(2) doublet with U(1) weak hypercharge 1 (left-handed lepton)

4. An SU(3) triplet, SU(2) singlet, with U(1) weak hypercharge (left-handed up-type antiquark)

5.5. An SU(3) singlet, SU(2) singlet with U(1) weak hypercharge 2 (left-handed antilepton)

By CPT symmetry, there is a set of right-handed fermions with the opposite quantum numbers.
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Standard Model 6

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.

Spin 0

1.1. An SU(2) doublet H with U(1) hyper-charge +1 (Higgs field)

Note that , summed over the two SU(2) components, is invariant under both SU(2) and under U(1), and so it

can appear as a renormalizable term in the Lagrangian, as can its square.

This field acquires a vacuum expectation value, leaving a combination of the weak isospin, , 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, , which would

otherwise be somewhat arbitrary) is:[21]

Lagrangian

The Lagrangian for the spin 1 and spin1

2fields is the most general renormalizable gauge field Lagrangian with no

fine tunings:

Spin 1:

where the traces are over the SU(2) and SU(3) indices hidden in Wand G respectively. The two-index objects are the

field strengths derived from Wand G the vector fields. There are also two extra hidden parameters: the theta angles

for SU(2) and SU(3).

The spin-12

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 spin1

2particles could ever swap helicity, and they would all be massless.

For a neutral fermion, for example a hypothetical right-handed lepton N(or N

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 forMwill 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.

Higgs mechanism

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).
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Standard Model 7

Masses and CKM matrix

The rest of the interactions are the most general spin-0 spin-1

2Yukawa 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 termsL*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 ofH is nonzero, the upper

SU(2) component ofL mixes with R to make the electron, the muon, and the tau, leaving over a lower massless

component, the neutrino. Note: Neutrino oscillations show neutrinos have mass.[22]

See also:

PontecorvoMakiNakagawaSakata matrix.

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.

Theoretical aspects

Construction of the Standard Model Lagrangian

Parameters of the Standard Model

Symbol Description Renormalization

scheme (point)

Value

me

Electron mass 511 keV

m

Muon mass 105.7 MeV

m

Tau mass 1.78 GeV

mu Up quark mass MS = 2 GeV 1.9 MeV

md

Down quark mass MS

= 2 GeV 4.4 MeV

ms

Strange quark mass MS

= 2 GeV 87 MeV

mc

Charm quark mass MS

= mc

1.32 GeV

mb

Bottom quark mass MS

= mb

4.24 GeV

mt

Top quark mass On-shell scheme 172.7 GeV

12

CKM 12-mixing angle 13.1

23


13


CKM CP-violating Phase 0.995

g1

or g' U(1) gauge coupling MS

= mZ

0.357

g2

or g SU(2) gauge coupling MS

= mZ

0.652

g3

or gs

SU(3) gauge coupling MS

= mZ

1.221

QCD

QCD vacuum angle ~0

Higgs quadratic coupling Unknown

Higgs self-coupling strength Unknown

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
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Standard Model 8

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 Poincar 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 theStandard 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.

Quantum chromodynamics sector

The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, with SU(3)

symmetry, generated by Ta. 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 by

is the SU(3) gauge field containing the gluons, are the Dirac matrices, D and U are the Dirac spinors

associated with up- and down-type quarks, and gs

is the strong coupling constant.

Electroweak sector

The electroweak sector is a YangMills gauge theory with the symmetry group U(1)SU(2)L,

where B

is the U(1) gauge field; YW

is the weak hyperchargethe generator of the U(1) group; is the

three-component SU(2) gauge field; are the Pauli matricesinfinitesimal generators of the SU(2) group. The

subscript L indicates that they only act on left fermions; g and g are coupling constants.

Higgs sector

In the Standard Model, the Higgs field is a complex spinor of the group SU(2)L:

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:
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Standard Model 9

Additional symmetries of the Standard Model

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 , and , are the 2nd (muon) and 3rd (tau)

generation analogs of and fields.

By Noether's theorem, each symmetry above has an associated conservation law: the conservation of baryon number,

electron number, muon number, and tau number. Each quark is assigned a baryon number of , while each

antiquark is assigned a baryon number of . 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 anti-electron and

the associated anti-neutrino carry a 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 (incorrectly)

that neutrinos are massless. However, in 2002 it was discovered that neutrinos have mass (now established to be not

greater than 0.28 electron volts), and as neutrinos oscillate between flavors (muon neutrinos have been observedchanging to tau neutrinos) the discovery of neutrino mass indicates that the conservation of lepton family number is

violated.[23]

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."

Symmetries of the Standard Model and Associated Conservation Laws

Symmetry Lie Group Symmetry Type Conservation Law

Poincar TranslationsSO(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

Tau phase U(1) Accidental Global symmetry Tau number
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Standard Model 10

Field content of the Standard Model

Field

(1st generation)

Spin Gauge group

Representation

Baryon

Number

Electron

Number

Left-handed quark(3, 2, +

1

3)

Left-handed up antiquark

Left-handed down antiquark

Left-handed lepton ( , , )

Left-handed antielectron ( , , )

Hypercharge gauge field ( , , )

Isospin gauge field ( , , )

Gluon field ( , , )

Higgs field ( , , )

List of Standard Model fermions

This table is based in part on data gathered by the Particle Data Group.[24]

Left-handed fermions in the Standard Model

Generation 1

Fermion(left-handed)

Symbol Electriccharge

Weakisospin

Weakhypercharge

Color

charge[25]

Mass[26]

Electron 511 keV

Positron 511 keV

Electron neutrino< 0.28 eV

[27][28]

Electron antineutrino< 0.28 eV

[27][28]

Up quark~ 3 MeV

[29]

Up antiquark~ 3 MeV

[29]

Down quark~ 6 MeV

[29]

Down antiquark~ 6 MeV

[29]

Generation 2

Fermion

(left-handed)

Symbol Electric

charge

Weak

isospin

Weak

hyperchargeColor

charge[25]

Mass[26]

Muon 106 MeV

Antimuon 106 MeV

Muon neutrino < 0.28 eV[27][28]

Muon antineutrino< 0.28 eV

[27][28]
http://en.wikipedia.org/w/index.php?title=Muon_antineutrinohttp://en.wikipedia.org/w/index.php?title=Muon_neutrinohttp://en.wikipedia.org/w/index.php?title=Antimuonhttp://en.wikipedia.org/w/index.php?title=Muonhttp://en.wikipedia.org/w/index.php?title=Down_antiquarkhttp://en.wikipedia.org/w/index.php?title=Down_quarkhttp://en.wikipedia.org/w/index.php?title=Up_antiquarkhttp://en.wikipedia.org/w/index.php?title=Up_quarkhttp://en.wikipedia.org/w/index.php?title=Electron_antineutrinohttp://en.wikipedia.org/w/index.php?title=Electron_neutrinohttp://en.wikipedia.org/w/index.php?title=Positronhttp://en.wikipedia.org/w/index.php?title=Electronhttp://en.wikipedia.org/w/index.php?title=Masshttp://en.wikipedia.org/w/index.php?title=Color_chargehttp://en.wikipedia.org/w/index.php?title=Color_chargehttp://en.wikipedia.org/w/index.php?title=Weak_hyperchargehttp://en.wikipedia.org/w/index.php?title=Weak_hyperchargehttp://en.wikipedia.org/w/index.php?title=Weak_isospinhttp://en.wikipedia.org/w/index.php?title=Weak_isospinhttp://en.wikipedia.org/w/index.php?title=Electric_chargehttp://en.wikipedia.org/w/index.php?title=Electric_chargehttp://en.wikipedia.org/w/index.php?title=Particle_Data_Grouphttp://en.wikipedia.org/w/index.php?title=Higgs_fieldhttp://en.wikipedia.org/w/index.php?title=Gluonhttp://en.wikipedia.org/w/index.php?title=Gauge_fieldhttp://en.wikipedia.org/w/index.php?title=Isospinhttp://en.wikipedia.org/w/index.php?title=Gauge_fieldhttp://en.wikipedia.org/w/index.php?title=Hyperchargehttp://en.wikipedia.org/w/index.php?title=Antielectronhttp://en.wikipedia.org/w/index.php?title=Down_antiquarkhttp://en.wikipedia.org/w/index.php?title=Up_antiquarkhttp://en.wikipedia.org/w/index.php?title=Weak_hyperchargehttp://en.wikipedia.org/w/index.php?title=Weak_isospinhttp://en.wikipedia.org/w/index.php?title=Color_chargehttp://en.wikipedia.org/w/index.php?title=Quarkhttp://en.wikipedia.org/w/index.php?title=Lepton_numberhttp://en.wikipedia.org/w/index.php?title=Baryon_numberhttp://en.wikipedia.org/w/index.php?title=Gauge_grouphttp://en.wikipedia.org/w/index.php?title=Spin_%28physics%29http://en.wikipedia.org/w/index.php?title=Field_%28physics%29


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Standard Model 11

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

hyperchargeColor

charge[25]

Mass[26]

Tau 1.78 GeV

Antitau 1.78 GeV

Tau neutrino< 0.28 eV

[27][28]

Tau antineutrino< 0.28 eV

[27][28]

Top quark 171 GeV

Top antiquark 171 GeV

Bottom quark ~ 4.2 GeV

Bottom antiquark ~ 4.2 GeV

Log plot of masses in the Standard Model.

Tests and predictions

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 80.387 0.019 80.390 0.018

Mass of Z boson 91.1876 0.0021 91.1874 0.0021

The SM also makes several predictions about the decay of Z bosons, which have been experimentally confirmed by

the Large Electron-Positron Collider at CERN.
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Standard Model 12

Challenges

Self-consistency of the Standard Model has not been mathematically proven. While computational approximations

(for example using lattice gauge theory) exist, it is not known whether they converge in the limit. A key question

related to the consistency is the YangMills existence and mass gap problem.

There is some experimental evidence consistent with neutrinos having mass, which the Standard Model does not

allow.[1] 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 boson observable. However, as of January 2012, there is only indirect empirical

evidence for the existence of the Higgs boson, so that its discovery cannot be claimed. Moreover, some theoretical

concerns have been raised positing that elementary scalar Higgs particles cannot exist (see Quantum triviality).

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 theStandard Model that motivate such research include:

It does not attempt to explain gravitation, although a theoretical particle known as a graviton would help explain

it, and unlike for the strong and electroweak interactions of the Standard Model, there is no known way of

describing general relativity, the canonical theory of gravitation, consistently in terms of quantum field theory.

The reason for this is, among other things, that quantum field theories of gravity generally break down before

reaching the Planck scale. As a consequence, we have no reliable theory for the very early universe;

Some consider it to be ad-hoc and inelegant, requiring 19 numerical constants whose values are unrelated and

arbitrary. 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;

The Higgs mechanism gives rise to the hierarchy problem if any new physics (such as quantum gravity) is present

at high energy scales. In order for the weak scale to be much smaller than the Planck scale, severe fine tuning of

Standard Model parameters is required;

It should be modified so as to be consistent with the emerging "Standard Model of cosmology." In particular, the

Standard Model cannot explain the observed amount of cold dark matter (CDM) and gives contributions to dark

energy which are far too large. It is also difficult to accommodate the observed predominance of matter over

antimatter (matter/antimatter asymmetry). The isotropy and homogeneity of the visible universe over large

distances seems to require a mechanism like cosmic inflation, which would also constitute an extension of the

Standard Model.

Currently no proposed Theory of everything has been conclusively verified.
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Standard Model 13

Notes and references

Notes

[1] CERN Press Release (http://press. web. cern.ch/press/PressReleases/Releases2010/PR08.10E. html)

References

Further reading

R. Oerter (2006). The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern

Physics. Plume.

B.A. Schumm (2004).Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins

University Press. ISBN 0-8018-7971-X.

Introductory textbooks

I. Aitchison, A. Hey (2003). Gauge Theories in Particle Physics: A Practical Introduction.. Institute of Physics.

ISBN 978-0-585-44550-2.

W. Greiner, B. Mller (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.

G.D. Coughlan, J.E. Dodd, B.M. Gripaios (2006). The Ideas of Particle Physics: An Introduction for Scientists .

Cambridge University Press.

D.J. Griffiths (1987).Introduction to Elementary Particles. John Wiley & Sons. ISBN 0-471-60386-4.

G.L. Kane (1987).Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.

Advanced textbooks

T.P. Cheng, L.F. Li (2006). Gauge theory of elementary particle physics. Oxford University Press.

ISBN 0-19-851961-3. Highlights the gauge theory aspects of the Standard Model.

J.F. Donoghue, E. Golowich, B.R. Holstein (1994).Dynamics of the Standard Model. Cambridge University

Press. ISBN 978-0-521-47652-2. Highlights dynamical and phenomenological aspects of the Standard Model.

L. O'Raifeartaigh (1988). Group structure of gauge theories. Cambridge University Press. ISBN 0-521-34785-8.

Highlights group-theoretical aspects of the Standard Model.

Journal articles

E.S. Abers, B.W. Lee (1973). "Gauge theories".Physics Reports9: 1141. Bibcode 1973PhR.....9....1A.

doi:10.1016/0370-1573(73)90027-6.

Y. Hayato et al. (1999). "Search for Proton Decay throughp K+

in a Large Water Cherenkov Detector".

Physical Review Letters83 (8): 1529. arXiv:hep-ex/9904020. Bibcode 1999PhRvL..83.1529H.

doi:10.1103/PhysRevLett.83.1529.

S.F. Novaes (2000). "Standard Model: An Introduction". arXiv:hep-ph/0001283 [hep-ph].

D.P. Roy (1999). "Basic Constituents of Matter and their Interactions A Progress Report.".

arXiv:hep-ph/9912523 [hep-ph].

F. Wilczek (2004). "The Universe Is A Strange Place".Nuclear Physics B - Proceedings Supplements134: 3.

arXiv:astro-ph/0401347. Bibcode 2004NuPhS.134....3W. doi:10.1016/j.nuclphysbps.2004.08.001.
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Standard Model 14

External links

" LHC sees hint of lightweight Higgs boson (http://www.newscientist. com/article/

dn21279-lhc-sees-hint-of-lightweight-higgs-boson. html)" "New Scientist".

" Standard Model may be found incomplete, (http://www.newscientist. com/news/news.jsp?id=ns9999404)"

New Scientist.

" Observation of the Top Quark (http://www-cdf.fnal. gov/top_status/top.html)" at Fermilab.

" The Standard Model Lagrangian. (http://cosmicvariance. com/2006/11/23/thanksgiving)" After electroweak

symmetry breaking, with no explicit Higgs boson.

" Standard Model Lagrangian (http://nuclear. ucdavis. edu/~tgutierr/files/stmL1. html)" with explicit Higgs

terms. PDF, PostScript, and LaTeX versions.

" The particle adventure. (http://particleadventure. org/)" Web tutorial.

Nobes, Matthew (2002) "Introduction to the Standard Model of Particle Physics" on Kuro5hin: Part 1, (http://

www.kuro5hin.org/story/2002/5/1/3712/31700) Part 2, (http://www.kuro5hin.org/story/2002/5/14/

19363/8142) Part 3a, (http://www.kuro5hin.org/story/2002/7/15/173318/784) Part 3b. (http://www.

kuro5hin.org/story/2002/8/21/195035/576)
http://www.kuro5hin.org/story/2002/8/21/195035/576http://www.kuro5hin.org/story/2002/8/21/195035/576http://www.kuro5hin.org/story/2002/7/15/173318/784http://www.kuro5hin.org/story/2002/5/14/19363/8142http://www.kuro5hin.org/story/2002/5/14/19363/8142http://www.kuro5hin.org/story/2002/5/1/3712/31700http://www.kuro5hin.org/story/2002/5/1/3712/31700http://en.wikipedia.org/w/index.php?title=Kuro5hinhttp://particleadventure.org/http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.htmlhttp://en.wikipedia.org/w/index.php?title=Higgs_bosonhttp://en.wikipedia.org/w/index.php?title=Symmetry_breakinghttp://cosmicvariance.com/2006/11/23/thanksgivinghttp://en.wikipedia.org/w/index.php?title=Fermilabhttp://www-cdf.fnal.gov/top_status/top.htmlhttp://en.wikipedia.org/w/index.php?title=New_Scientisthttp://www.newscientist.com/news/news.jsp?id=ns9999404http://en.wikipedia.org/w/index.php?title=New_Scientisthttp://www.newscientist.com/article/dn21279-lhc-sees-hint-of-lightweight-higgs-boson.htmlhttp://www.newscientist.com/article/dn21279-lhc-sees-hint-of-lightweight-higgs-boson.html


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Article Sources and Contributors 15

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