The
Contents 1 Historical background
2 Overview
3
3.1 Fermions 3.2 Gauge bosons 3.3 Higgs boson 4 Theoretical aspects 4.1 Construction of the
4.1.1
5 Fundamental forces 6 Tests and predictions 7 Challenges 8 See also 9 Notes and references 10 References 11 Further reading 12 External links Historical background[edit]
See also:
Elementary particles Elementary fermions
Elementary bosons
Quarks and antiquarksSpin = 1/2Have color chargeParticipate in strong interactions Leptons and antileptonsSpin = 1/2No color chargeElectroweak interactions Gauge bosonsSpin ≠ 0Force carriers Scalar bosonsSpin = 0 Generations Up (u), Down (d) Charm (c), Strange (s) Top (t), Bottom (b) Generations
Four kinds (four fundamental interactions)
Notes: 1. The antielectron (e+) is traditionally called positron. 2. The known force carrier bosons all have spin = 1 and are therefore vector bosons. The hypothetical graviton has spin = 2 and is a tensor boson; whether it is a gauge boson as well, is unknown. Fermions[edit] Summary of interactions between particles described by the Standard Model The
The above interactions form the basis of the standard model. Feynman
diagrams in the standard model are built from these vertices.
Modifications involving
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
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 theory of general relativity. The Standard
Model explains such forces as resulting from matter particles
exchanging other particles, generally referred to as force mediating
particles. 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
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-handed particles and right-handed antiparticles. 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. red–antigreen).[nb 1] Because the gluons have 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.
Higgs boson[edit]
Main article: Higgs boson
The Higgs particle is a massive scalar elementary particle theorized
by
Parameters of the Standard Model Symbol Description Renormalization scheme (point) Value me
511 keV mμ
105.7 MeV mτ Tau mass 1.78 GeV mu
1.9 MeV md
4.4 MeV ms
87 MeV mc
1.32 GeV mb
4.24 GeV mt
θ12 CKM 12-mixing angle 13.1° θ23 CKM 23-mixing angle 2.4° θ13 CKM 13-mixing angle 0.2° δ
CKM
0.995 g1 or g' U(1) gauge coupling μ MS = mZ 0.357 g2 or g
0.652 g3 or gs SU(3) gauge coupling μ MS = mZ 1.221 θQCD QCD vacuum angle ~0 v Higgs vacuum expectation value 246 GeV mH Higgs mass 6992200416256758830♠125.09±0.24 GeV 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
L QCD = ∑ ψ ψ ¯ i ( i γ μ ( ∂ μ δ i j − i g s G μ a T i j a ) − m ψ δ i j ) ψ j − 1 4 G μ ν a G a μ ν , displaystyle mathcal L _ text QCD =sum _ psi overline psi _ i left(igamma ^ mu (partial _ mu delta _ ij -ig_ s G_ mu ^ a T_ ij ^ a )-m_ psi delta _ ij right)psi _ j - frac 1 4 G_ mu nu ^ a G_ a ^ mu nu , where ψ i is the Dirac spinor of the quark field, where i = r, g, b represents color, γμ are the Dirac matrices, Ga μ is the 8-component ( a = 1 , 2 , … , 8 displaystyle a=1,2,dots ,8 ) SU(3) gauge field, Ta ij are the 3 × 3 Gell-Mann matrices, generators of the SU(3) color group, Ga μν are the field strength tensors for the gluons, gs is the strong coupling constant.
L EW = ∑ ψ ψ ¯ γ μ ( i ∂ μ − g ′ 1 2 Y W B μ − g 1 2 τ → L W → μ ) ψ − 1 4 W a μ ν W μ ν a − 1 4 B μ ν B μ ν , displaystyle mathcal L _ text EW =sum _ psi bar psi gamma ^ mu left(ipartial _ mu -g' tfrac 1 2 Y_ text W B_ mu -g tfrac 1 2 vec tau _ text L vec W _ mu right)psi - tfrac 1 4 W_ a ^ mu nu W_ mu nu ^ a - tfrac 1 4 B^ mu nu B_ mu nu , where Bμ is the U(1) gauge field,
YW is the weak hypercharge – the generator of the U(1) group,
W→μ is the 3-component
W a μ ν displaystyle W^ amu nu ( a = 1 , 2 , 3 displaystyle a=1,2,3 ) and B μ ν displaystyle B^ mu nu are the field strength tensors for the weak isospin and weak hypercharge fields. Notice that the addition of fermion mass terms into the electroweak lagrangian is forbidden, since terms of the form m ψ ¯ ψ displaystyle m overline psi psi do not respect U(1) × SU(2)L gauge invariance. Neither is it
possible to add explicit mass terms for the U(1) and
φ = 1 2 ( φ + φ 0 ) , displaystyle varphi = frac 1 sqrt 2 left( begin array c varphi ^ + \varphi ^ 0 end array right), where the superscripts + 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 L H = φ † ( ∂ μ − i 2 ( g ′ Y W B μ + g τ → W → μ ) ) ( ∂ μ + i 2 ( g ′ Y W B μ + g τ → W → μ ) ) φ − λ 2 4 ( φ † φ − v 2 ) 2 , displaystyle mathcal L _ text H =varphi ^ dagger left(partial ^ mu - frac i 2 left(g'Y_ text W B^ mu +g vec tau vec W ^ mu right)right)left(partial _ mu + frac i 2 left(g'Y_ text W B_ mu +g vec tau vec W _ mu right)right)varphi - frac lambda ^ 2 4 left(varphi ^ dagger varphi -v^ 2 right)^ 2 , which can also be written as L H =
( ∂ μ + i 2 ( g ′ Y W B μ + g τ → W → μ ) ) φ
2 − λ 2 4 ( φ † φ − v 2 ) 2 . displaystyle mathcal L _ text H =leftleft(partial _ mu + frac i 2 left(g'Y_ text W B_ mu +g vec tau vec W _ mu right)right)varphi right^ 2 - frac lambda ^ 2 4 left(varphi ^ dagger varphi -v^ 2 right)^ 2 . Yukawa sector[edit]
The
L Yukawa = U ¯ L G u U R ϕ 0 − D ¯ L G u U R ϕ − + U ¯ L G d D R ϕ + + D ¯ L G d D R ϕ 0 + h c , displaystyle mathcal L _ text Yukawa = overline U _ L G_ u U_ R phi ^ 0 - overline D _ L G_ u U_ R phi ^ - + overline U _ L G_ d D_ R phi ^ + + overline D _ L G_ d D_ R phi ^ 0 +hc, where Gu,d are 3 × 3 matrices of Yukawa couplings, with the ij term giving the coupling of the generations i and j. Fundamental forces[edit] Main article: Fundamental interaction This section needs expansion. You can help by adding to it. (October 2015) The
The four fundamental interactions of nature[32] Property/Interaction Gravitation Weak Electromagnetic Strong (Electroweak) Fundamental Residual Acts on:
Strength at the scale of quarks: 6959100000000000000♠10−41 6996100000000000000♠10−4 1 60 Not applicable to quarks Strength at the scale of protons/neutrons: 6964100000000000000♠10−36 6993100000000000000♠10−7 1 Not applicable to hadrons 20 Tests and predictions[edit]
The
Unsolved problem in physics: What gives rise to the
(more unsolved problems in physics) Self-consistency of the
The model does not explain gravitation, although physical confirmation
of a theoretical particle known as a graviton would account for it to
a degree. Though it addresses strong and electroweak interactions, the
Currently, no proposed
Book:
Fundamental interaction: Quantum electrodynamics
Strong interaction: Color charge, Quantum chromodynamics,
Gauge theory: Nontechnical introduction to gauge theory
Generation
Higgs mechanism: Higgs boson, Higgsless model
J. C. Ward
J. J.
Notes and references[edit] ^ Technically, there are nine such color–anticolor combinations. However, there is one color-symmetric combination that can be constructed out of a linear superposition of the nine combinations, reducing the count to eight. References[edit] ^ R. Oerter (2006). The Theory of Almost Everything: The Standard
Model, the Unsung Triumph of Modern
Further reading[edit] 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
Introductory textbooks I. Aitchison; A. Hey (2003). Gauge Theories in
Advanced textbooks T. P. Cheng; L. F. Li (2006).
Journal articles E. S. Abers; B. W. Lee (1973). "Gauge theories".
External links[edit] "The
v t e Standard Model Background
Fermions Gauge boson Higgs boson Quantum field theory Gauge theory Quantum electrodynamics Strong interaction Color charge
Quantum chromodynamics
Weak interaction
Constituents CKM matrix
Spontaneous symmetry breaking
Higgs mechanism
Beyond the Standard Model Evidence Hierarchy problem
Dark matter
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Elementary Fermions Quarks Up (quark antiquark) Down (quark antiquark) Charm (quark antiquark) Strange (quark antiquark) Top (quark antiquark) Bottom (quark antiquark) Leptons Electron
Positron
Muon
Antimuon
Tau
Antitau
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