User:TriTertButoxy/Sandbox

For the standard model in cryptography, see Standard Model (cryptography).

For the standard model in cosmology, see the article on the big bang.

The standard model of particle physics is a grouping of two theories – quantum electroweak and quantum chromodynamics – which, together, provides an internally consistent theory describing the electromagnetic, weak nuclear, and strong nuclear interactions between all experimentally known elementary particles. It is a quantum field theory based on the internal symmetry group SU(3)$\times$SU(2)$\times$U(1), which is consistent with both quantum mechanics and special relativity. The modern formulation of the standard model appeared in 1973 with the electroweak unification and the discovery of asymptotic freedom in quantum chromodynamics. Upon fixing the 19 free parameters that appear in the theory with observations, almost all experimental tests of the three forces described by the standard model have agreed with its predictions. All particles found in nature are accounted for by the standard model, but, as of yet, it additionally demands the existence of one unobserved particle known as the Higgs Boson, required to dynamically break an internal symmetry of nature.

History

• Unification of Electromagnetism
• Invention of Quantum Mechanics, chemical elements explained, radioactivity heuristically explained
• Development of Relativity
• Relativistic quantum mechanics (Dirac)
• Development of QFT
• Problems with renormalization
• Quantum Electrodynamics
• The Particle Zoo fiasco
• Quark Model
• Disentanglement of Weak and Strong nuclear interactions
• Fermi's theory of weak interactions
• Yang-Mills Theories
• Difficulties of extracting predictions from QCD
• Parton model
• Unification of Electromagnetism and weak nuclear interactions
• Asymptotic Freedom of QCD confirmed
• Discovery of W/Z, top quark
• Discovery of Neutrino Oscillations

Particle Content

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.

Organization of Fermions

	Generation 1		Generation 2		Generation 3
Quarks	Up	$u\,$	Charm	$c\,$	Top	$t\,$
	Down	$d\,$	Strange	$s\,$	Bottom	$b\,$
Leptons	Electron Neutrino	$\nu _{e}\,$	Muon Neutrino	$\nu _{\mu }\,$	Tau Neutrino	$\nu _{\tau }\,$
	Electron	$e\,$	Muon	$\mu \,$	Tau	$\tau \,$

Fermions

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

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.

Gauge Bosons

The standard model explains familiar macroscopic forces in terms of interactions between the fermions by means of exchanging force-mediating particles. In the standard model, the force-mediating particles give rise to the three fundamental forces of nature.

These interactions are a direct consequence of internal (gauge) symmetries exhibited by the standard model. Thus, unlike the fermions which are put into the standard model by hand to match observational data, the existence of the force-mediating particles, are in some sense, theoretically required to exist (see Yang-Mills theory), with spin-1. For this reason, they are also known as gauge bosons.

The gauge bosons in the standard model are listed below.

• Photons mediate the electromagnetic force between electrically charged particles (the quarks and charged leptons). The photon is massless and interactions mediated by them is addressed by quantum electrodynamics.

• The W⁺, W^–, and Z⁰ gauge bosons mediate the weak interactions between particles carrying weak isospin (all quarks and leptons). While the $W^{\pm }$ are exchanged exclusively by left-handed particles (right-handed antiparticles), the Z⁰ bosons are exchanged by both left-handed and right-handed particles and antiparticles. Importantly, the W and Z bosons are massive, making interactions involving these particles short-ranged.

• The gluons mediate the strong interactions between color charged particles (the quarks). Like the photon, gluons are massless. 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	$\gamma$	W+, W-, and Z<br\> Gauge Bosons	$W^{+}$, $W^{-}$, <br\> $Z$	Gluons	$g$

Higgs Boson

Main article: Higgs Boson

The Higgs boson is a massive spin-0 elementary particle; it has no intrinsic spin, and thus is classified as a boson. As of yet, it is the only fundamental particle predicted by the standard model which has not been observed. This is partly because it requires an exceptionally large amount of energy to create and observe under laboratory circumstances. Physicists hope that upon the completion of the Large Hadron Collider, experiments conducted at CERN would bring experimental evidence confirming the existence of the particle.

The Higgs boson plays a key role in explaining the origins of the mass of all other elementary particles. This is theoretically understood to be a result of the spontaneous breakdown of the SU(2)$\times$U(1) internal symmetry induced by the Higgs boson. Without symmetry breaking, every pair of quarks and leptons of each generation would be massless. In addition, the W⁺, W^–, and Z⁰ gauge bosons would also be equally massless.

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

Parameters of the Standard Model

Symbol	Description	Renormalization scheme (point)	Value
$m_{e}$	Electron mass		511 keV
$m_{\mu }$	Muon mass		106 MeV
$m_{\tau }$	Tau lepton mass		1.78 GeV
$m_{u}$	Up quark mass	($\mu _{\overline {\text{MS}}}=2{\text{ GeV}}$)	1.9 MeV
$m_{d}$	Down quark mass	($\mu _{\overline {\text{MS}}}=2{\text{ GeV}}$)	4.4 MeV
$m_{s}$	Strange quark mass	($\mu _{\overline {\text{MS}}}=2{\text{ GeV}}$)	87 MeV
$m_{c}$	Charm quark mass	($\mu _{\overline {\text{MS}}}=m_{c}$)	1.32 MeV
$m_{b}$	Bottom quark mass	($\mu _{\overline {\text{MS}}}=m_{b}$)	4.24 GeV
$m_{t}$	Top quark mass	(on-shell scheme)	172.7 GeV
$\theta _{12}$	CKM 12-mixing angle		0.229
$\theta _{23}$	CKM 23-mixing angle		0.042
$\theta _{13}$	CKM 13-mixing angle		0.004
$\delta$	CKM CP-Violating Phase		0.995
$g_{1}$	U(1) gauge coupling	($\mu _{\overline {\text{MS}}}=M_{\text{Z}}$)	0.357
$g_{2}$	SU(2) gauge coupling	($\mu _{\overline {\text{MS}}}=M_{\text{Z}}$)	0.652
$g_{3}$	SU(3) gauge coupling	($\mu _{\overline {\text{MS}}}=M_{\text{Z}}$)	1.221
$\theta _{\text{QCD}}$	QCD Vacuum Angle		~0
$\mu$	Higgs quadratic coupling		Unknown
$\lambda$	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 type 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 compiling a list of postulated symmetries for 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 familar translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity. The local SU(3)$\times$SU(2)$\times$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). The most general renormalizable Lagrangian that respects the postulated symmetries is

${\mathcal {L}}_{\text{SM}}=\sum {\bar {\psi }}(iD_{\mu }\gamma ^{\mu }-m)\psi$

, 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.

Additional Symmetries of the Standard Model

From the theoretical point of view, the standard model exhibits additional global symmetries that were not posulated 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 symmetires. The transformations leaving the Lagrangian invariant are

$\psi _{\text{q}}(x)\rightarrow e^{i\alpha /3}\psi _{\text{q}}$

$E_{L}\rightarrow e^{i\beta }E_{L}{\text{ and }}(e_{R})^{c}\rightarrow e^{i\beta }(e_{R})^{c}$

$M_{L}\rightarrow e^{i\beta }M_{L}{\text{ and }}(\mu _{R})^{c}\rightarrow e^{i\beta }(\mu _{R})^{c}$

$T_{L}\rightarrow e^{i\beta }T_{L}{\text{ and }}(\tau _{R})^{c}\rightarrow e^{i\beta }(\tau _{R})^{c}$.

Here, $\psi _{\text{q}}$ in the first rule indicates that all quark fields for all generations must be rotated by an identical phase simultaneously. The fields $M_{L}$, $T_{L}$ and $(\mu _{R})^{c}$, $(\tau _{R})^{c}$ are the 2nd and 3rd generation analogs of $E_{L}$ and $(e_{R})^{c}$.

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 neutrinos being massless according to 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 symmetires. 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
Poincaré	Translations$\rtimes$SO(3,1)	Global symmetry	Energy, Momentum, Angular Momentum
Gauge	SU(3)$\times$SU(2)$\times$U(1)	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

Field content of the Standard Model

Field (1st generation)		Spin	Gauge Group Representation	Baryon Number	Electron Number
Left-handed quark	$Q_{\text{L}}$	$1/2$	($\mathbf {3}$, $\mathbf {2}$, $+1/6$)	$1/3$	$0$
Right-handed up quark	$(u_{\text{R}})^{c}$	$1/2$	(${\bar {\mathbf {3} }}$, $\mathbf {1}$, $-2/3$)	$-1/3$	$0$
Right-handed down quark	$(d_{\text{R}})^{c}$	$1/2$	(${\bar {\mathbf {3} }}$, $\mathbf {1}$, $+1/3$)	$-1/3$	$0$
Left-handed lepton	$E_{\text{L}}$	$1/2$	($\mathbf {1}$, $\mathbf {2}$, $-1$)	$0$	$1$
Right-handed electron	$(e_{\text{R}})^{c}$	$1/2$	($\mathbf {1}$, $\mathbf {1}$, $+1$)	$0$	$-1$
Hypercharge gauge field	$B_{\mu }$	$1$	(${\bar {\mathbf {1} }}$, $\mathbf {1}$, $0$)	$0$	$0$
Isospin gauge field	$W_{\mu }$	$1$	($\mathbf {1}$, $\mathbf {3}$, $0$)	$0$	$0$
Gluon field	$G_{\mu }$	$1$	($\mathbf {8}$, $\mathbf {1}$, $0$)	$0$	$0$
Higgs field	$H$	$0$	($\mathbf {1}$, $\mathbf {2}$, $+1/2$)	$0$	$0$

Experimental Tests and Predictions

Prediction of Particles

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

Experimental Deviations from the Standard Model

Theoretical Issues Concerning the Standard Model

Although the standard model is an internally consistent theory, there are a few philosophical issues that the standard model raises which suggests hidden physics that has yet to be discovered.

See also

• The theoretical formulation of the standard model
• Weak interactions, Fermi theory of beta decay and electroweak theory
• Strong interactions, flavour, quark model and quantum chromodynamics
• For open questions, see quark matter, CP violation and neutrino masses
• Beyond the standard model
• Quantum chromodynamics
• QCD vacuum

References

Introductory textbooks

• Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 0-471-60386-4.
• D.A. Bromley (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.
• Gordon L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.

Advanced textbooks

• Cheng, Ta Pei; Li, Ling Fong. Gauge theory of elementary particle physics. Oxford University Press. ISBN 0-19-851961-3.{{cite book}}: CS1 maint: multiple names: authors list (link)

  — introduction to all aspects of gauge theories and the Standard Model.

• Donoghue, J. F.; Golowich, E.; Holstein, B. R. Dynamics of the Standard Model. Cambridge University Press. ISBN 0-521-47625-6.{{cite book}}: CS1 maint: multiple names: authors list (link)

  — highlights dynamical and phenomenological aspects of the Standard Model.

• O'Raifeartaigh, L. Group structure of gauge theories. Cambridge University Press. ISBN 0-521-34785-8.

  — highlights group-theoretical aspects of the Standard Model.

Journal articles

• S.F. Novaes, Standard Model: An Introduction, hep-ph/0001283
• D.P. Roy, Basic Constituents of Matter and their Interactions — A Progress Report, hep-ph/9912523
• Y. Hayato et al., Search for Proton Decay through p → νK⁺ in a Large Water Cherenkov Detector. Phys. Rev. Lett. 83, 1529 (1999).
• Ernest S. Abers and Benjamin W. Lee, Gauge theories. Physics Reports (Elsevier) C9, 1-141 (1973).

External links

• New Scientist story: Standard Model may be found incomplete
• The Universe Is A Strange Place, a lecture by Frank Wilczek
• Observation of the Top Quark at Fermilab
• PDF version of the Standard Model Lagrangian (after electroweak symmetry breaking, with no explicit Higgs boson)
• PDF, PostScript, and LaTeX version of the Standard Model Lagrangian with explicit Higgs terms
• The particle adventure.

Category:Fundamental physics concepts Category:Particle physics *