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.
It was developed throughout the latter half
of the 20th century, as a collaborative effort
of scientists around the world. The current
formulation was finalized in the mid-1970s
upon experimental confirmation of the existence
of quarks. Since then, discoveries of the
top quark, the tau neutrino, and more recently
the Higgs boson, 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.
It does not incorporate the full theory of
gravitation as described by general relativity,
or account for the accelerating expansion
of the universe. The model does not contain
any viable dark matter particle that possesses
all of the required properties deduced from
observational cosmology. It also does not
incorporate neutrino oscillations. Although
the Standard Model is believed to be theoretically
self-consistent and has demonstrated huge
and continued successes in providing experimental
predictions, it does leave some phenomena
unexplained.
The development of the Standard Model was
driven by theoretical and experimental particle
physicists alike. For theorists, the Standard
Model is a paradigm 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 in an
attempt to explain experimental results at
variance with the Standard Model, such as
the existence of dark matter and neutrino
oscillations.
Historical background
The first step towards the Standard Model
was Sheldon Glashow's discovery in 1961 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
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, 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 1973–74, 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.
Particle content
The Standard Model includes members of several
classes of elementary particles, which in
turn can be distinguished by other characteristics,
such as color charge.
Fermions
The Standard Model includes 12 elementary
particles of spin-½ 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. There are
six quarks, and six leptons. Pairs from each
classification are grouped together to form
a generation, with corresponding particles
exhibiting similar physical behavior.
The defining property of the quarks is that
they carry color charge, and hence, interact
via the strong interaction. A phenomenon called
color confinement results in quarks being
perpetually bound to one another, forming
color-neutral composite particles containing
either a quark and an antiquark or three quarks.
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 them notoriously
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
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
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, known
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 that force. The Feynman
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 fails
in other situations. These include low-energy
quantum chromodynamics, bound states, and
solitons.
The gauge bosons of the Standard Model all
have spin. 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 do not have a theoretical
limit on their spatial density. 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. 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 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. Gluons are
massless. The eightfold multiplicity of gluons
is labeled by a combination of color and anticolor
charge. 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
The Higgs particle is a massive scalar elementary
particle theorized by Robert Brout, François
Englert, Peter Higgs, Gerald Guralnik, C.
R. Hagen, and Tom Kibble in 1964 and is a
key building block in the Standard Model.
It has no intrinsic spin, and for that reason
is classified as a boson.
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 explains why the photon has no mass,
while the W and Z bosons are very heavy. Elementary
particle masses, and the differences between
electromagnetism and the weak force, are critical
to many aspects of the structure of microscopic
matter. In electroweak theory, the Higgs boson
generates the masses of the leptons and quarks.
As the Higgs boson is massive, it must interact
with itself.
Because the Higgs boson is a very massive
particle and also decays almost immediately
when created, only a very high-energy particle
accelerator can observe and record it. Experiments
to confirm and determine the nature of the
Higgs boson using the Large Hadron Collider
at CERN began in early 2010, and were performed
at Fermilab's Tevatron until its closure in
late 2011. Mathematical consistency of the
Standard Model requires that any mechanism
capable of generating the masses of elementary
particles become visible at energies above
1.4 TeV; therefore, the LHC was built to
answer the question of whether the Higgs boson
actually exists.
On 4 July 2012, the two main experiments at
the LHC both reported independently that they
found a new particle with a mass of about
125 GeV/c2, which is "consistent with the
Higgs boson." Although it has several properties
similar to the predicted "simplest" Higgs,
they acknowledged that further work would
be needed to conclude that it is indeed the
Higgs boson, and exactly which version of
the Standard Model Higgs is best supported
if confirmed.
On 14 March 2013 the Higgs Boson was tentatively
confirmed to exist.
Full particle count
Counting particles by a rule that distinguishes
between particles and their corresponding
antiparticles, and among the many color states
of quarks and gluons, gives a total of 61
elementary particles.
Theoretical aspects
Construction of the Standard Model Lagrangian
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 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. 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 above.
Quantum chromodynamics sector
The quantum chromodynamics 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 Yang–Mills gauge
theory with the simple 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.
Higgs sector
In the Standard Model, the Higgs field is
a complex spinor of the group SU(2)L:
where the indices + and 0 indicate the electric
charge of the components. The weak isospin
of both components is 1.
Before symmetry breaking, the Higgs Lagrangian
is:
which can also be written as:
Tests and predictions
The Standard Model 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:
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.
In May 2012 BaBar Collaboration reported that
their recently analyzed data may suggest possible
flaws in the Standard Model of particle physics.
These data show that a particular type of
particle decay called "B to D-star-tau-nu"
happens more often than the Standard Model
says it should. In this type of decay, a particle
called the B-bar meson decays into a D meson,
an antineutrino and a tau-lepton. While the
level of certainty of the excess is not enough
to claim a break from the Standard Model,
the results are a potential sign of something
amiss and are likely to impact existing theories,
including those attempting to deduce the properties
of Higgs bosons.
On December 13, 2012, physicists reported
the constancy, over space and time, of a basic
physical constant of nature that supports
the standard model of physics. The scientists,
studying methanol molecules in a distant galaxy,
found the change in the proton-to-electron
mass ratio μ to be equal to "(0.0 ± 1.0)
× 10−7 at redshift z = 0.89" and consistent
with "a null result".
Challenges
Self-consistency of the Standard Model has
not been mathematically proven. While regularized
versions useful for approximate computations
exist, it is not known whether they converge
in the limit that the regulator is removed.
A key question related to the consistency
is the Yang–Mills existence and mass gap
problem.
Experiments indicate that neutrinos have mass,
which the classic Standard Model did not allow.
To accommodate this finding, the classic Standard
Model can be modified to include neutrino
mass.
If one insists on using only Standard Model
particles, this can be achieved by adding
a non-renormalizable interaction of leptons
with the Higgs boson. On a fundamental level,
such an interaction emerges in the seesaw
mechanism where heavy right-handed neutrinos
are added to the theory. This is natural in
the left-right symmetric extension of the
Standard Model and in certain grand unified
theories. As long as new physics appears below
or around 1014 GeV, the neutrino masses can
be of the right order of magnitude.
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:
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 some new physics is present at
high energy scales. In these cases in order
for the weak scale to be much smaller than
the Planck scale, severe fine tuning of the
parameters is required; there are, however,
other scenarios that include quantum gravity
in which such fine tuning can be avoided.
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 and
gives contributions to dark energy which are
many orders of magnitude too large. It is
also difficult to accommodate the observed
predominance of matter over antimatter. 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 widely accepted or verified.
See also
Fundamental interaction:
Quantum electrodynamics
Strong interaction: Color charge, Quantum
chromodynamics, Quark model
Weak interaction: Electroweak theory, Fermi
theory of beta decay, Weak hypercharge, Weak
isospin
Gauge theory: Nontechnical introduction to
gauge theory
Generation
Higgs mechanism: Higgs boson, Higgsless model
J. C. Ward
J. J. Sakurai Prize for Theoretical Particle
Physics
Lagrangian
Open questions: BTeV experiment, CP violation,
Neutrino masses, Quark matter
Penguin diagram
Quantum field theory
Standard Model: Mathematical formulation of,
Physics beyond the Standard Model
Unparticle physics
Notes and references
References
Further reading
R. Oerter. The Theory of Almost Everything:
The Standard Model, the Unsung Triumph of
Modern Physics. Plume. 
B.A. Schumm. Deep Down Things: The Breathtaking
Beauty of Particle Physics. Johns Hopkins
University Press. ISBN 0-8018-7971-X. 
Introductory textbooks
I. Aitchison, A. Hey. Gauge Theories in Particle
Physics: A Practical Introduction. Institute
of Physics. ISBN 978-0-585-44550-2. 
W. Greiner, B. Müller. Gauge Theory of Weak
Interactions. Springer. ISBN 3-540-67672-4. 
G.D. Coughlan, J.E. Dodd, B.M. Gripaios. The
Ideas of Particle Physics: An Introduction
for Scientists. Cambridge University Press. 
D.J. Griffiths. Introduction to Elementary
Particles. John Wiley & Sons. ISBN 0-471-60386-4. 
G.L. Kane. Modern Elementary Particle Physics.
Perseus Books. ISBN 0-201-11749-5. 
Advanced textbooks
T.P. Cheng, L.F. Li. 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.
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. Group structure of gauge
theories. Cambridge University Press. ISBN 0-521-34785-8. 
Nagashima Y. Elementary Particle Physics:
Foundations of the Standard Model, Volume
2. 920 рапуы
Schwartz, M.D. Quantum Field Theory and the
Standard Model 952 pages
Langacker P. The standard model and beyond.
670 pages Highlights group-theoretical aspects
of the Standard Model.
Journal articles
E.S. Abers, B.W. Lee. "Gauge theories". Physics
Reports 9: 1–141. Bibcode:1973PhR.....9....1A.
doi:10.1016/0370-1573(73)90027-6. 
M. Baak et al.. "The Electroweak Fit of the
Standard Model after the Discovery of a New
Boson at the LHC". The European Physical Journal
C 72. arXiv:1209.2716. Bibcode:2012EPJC...72.2205B.
doi:10.1140s10052-012-2205-9. 
Y. Hayato et al.. "Search for Proton Decay
through p → νK+ in a Large Water Cherenkov
Detector". Physical Review Letters 83: 1529.
arXiv:hep-ex/9904020. Bibcode:1999PhRvL..83.1529H.
doi:10.1103/PhysRevLett.83.1529. 
S.F. Novaes. "Standard Model: An Introduction".
arXiv:hep-ph/0001283 [hep-ph].
D.P. Roy. "Basic Constituents of Matter and
their Interactions — A Progress Report".
arXiv:hep-ph/9912523 [hep-ph].
F. Wilczek. "The Universe Is A Strange Place".
Nuclear Physics B - Proceedings Supplements
134: 3. arXiv:astro-ph/0401347. Bibcode:2004NuPhS.134....3W.
doi:10.1016/j.nuclphysbps.2004.08.001. 
External links
"The Standard Model explained in Detail by
CERN's John Ellis" omega tau podcast.
"LHC sees hint of lightweight Higgs boson"
"New Scientist".
"Standard Model may be found incomplete,"
New Scientist.
"Observation of the Top Quark" at Fermilab.
"The Standard Model Lagrangian." After electroweak
symmetry breaking, with no explicit Higgs
boson.
"Standard Model Lagrangian" with explicit
Higgs terms. PDF, PostScript, and LaTeX versions.
"The particle adventure." Web tutorial.
Nobes, Matthew "Introduction to the Standard
Model of Particle Physics" on Kuro5hin: Part
1, Part 2, Part 3a, Part 3b.
"The Standard Model" The Standard Model on
the CERN web site explains how the basic building
blocks of matter interact, governed by four
fundamental forces.
