The Standard Model of particle physics is
the theory describing three of the four known
fundamental forces (the electromagnetic, weak,
and strong interactions, and not including
the gravitational force) in the Universe,
as well as classifying all known elementary
particles. It was developed in stages throughout
the latter half of the 20th century, through
the work of many scientists around the world,
with the current formulation being finalized
in the mid-1970s upon experimental confirmation
of the existence of quarks. Since then, confirmation
of the top quark (1995), the tau neutrino
(2000), and the Higgs boson (2012) have added
further credence to the Standard Model. In
addition, the Standard Model has predicted
various properties of weak neutral currents
and the W and Z bosons with great accuracy.
Although the Standard Model is believed to
be theoretically self-consistent and has demonstrated
huge successes in providing experimental predictions,
it leaves some phenomena unexplained and falls
short of being a complete theory of fundamental
interactions. It does not fully explain baryon
asymmetry, incorporate the full theory of
gravitation as described by general relativity,
or account for the accelerating expansion
of the Universe as possibly described by dark
energy. 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 and their non-zero masses.
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 and
non-perturbative behavior. 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.
== 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 interaction, 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 Z0 bosons were
discovered experimentally in 1983; and the
ratio of their masses was found to be as the
Standard Model predicted.The theory of the
strong interaction (i.e. quantum chromodynamics,
QCD), to which many contributed, acquired
its modern form in 1973–74 when asymptotic
freedom was proposed (a development which
made QCD the main focus of theoretical research)
and experiments confirmed that the hadrons
were composed of fractionally charged quarks.The
term "Standard Model" was first coined by
Abraham Pais and Sam Treiman in 1975, with
reference to the electroweak theory with four
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).
== 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.
All particles can be summarized as follows:
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 ===
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, 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. A phenomenon called
color confinement results in quarks being
very strongly 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 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 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 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 around atomic nuclei, ultimately
constituted of up and down quarks. Second-
and third-generation 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, 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
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
(and with it the concept of a "force-mediating
particle") fails in other 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-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).
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 Peter Higgs in 1964,
when he showed that Goldstone's 1962 theorem
(generic continuous symmetry, which is spontaneously
broken) provides a third polarisation of a
massive vector field. Hence, Goldstone's original
scalar doublet, the massive spin-zero particle,
was proposed as the Higgs boson. (see 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 gauge bosons,
which have integer spin).
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
(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 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
(LHC) 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 becomes visible at energies above
1.4 TeV; therefore, the LHC (designed to collide
two 7 TeV proton beams) was built to answer
the question of whether the Higgs boson actually
exists.On 4 July 2012, two of the experiments
at the LHC (ATLAS and CMS) both reported independently
that they found a new particle with a mass
of about 125 GeV/c2 (about 133 proton masses,
on the order of 10×10−25 kg), which is
"consistent with the Higgs boson". It was
later confirmed to be the searched-for Higgs
boson.
== 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 (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 depends
on 19 parameters, whose numerical values are
established by experiment. The parameters
are summarized in the table (made visible
by clicking "show") above (note: the Higgs
mass is at 125 GeV, the Higgs self-coupling
strength λ ~ ​1⁄8).
==== 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
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(i\gamma
^{\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
ψi is the Dirac spinor of the quark field,
where i = {r, g, b} represents color,
γμ are the Dirac matrices,
Gaμ is the 8-component (
a
=
1
,
2
,
…
,
8
{\displaystyle a=1,2,\dots ,8}
) SU(3) gauge field,
Taij are the 3 × 3 Gell-Mann matrices,
generators of the SU(3) color group,
Gaμν are the field strength tensors for
the gluons,
gs is the strong coupling constant.
==== Electroweak sector ====
The electroweak sector is a Yang–Mills gauge
theory with the symmetry group U(1) × SU(2)L,
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(i\partial
_{\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 SU(2) gauge field,
τL→ are the Pauli matrices – infinitesimal
generators of the SU(2) group – with subscript
L to indicate that they only act on left-chiral
fermions,
g' and g are the U(1) and SU(2) coupling constants
respectively,
W
a
μ
ν
{\displaystyle W^{a\mu \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 SU(2) gauge fields.
The Higgs mechanism is responsible for the
generation of the gauge boson masses, and
the fermion masses result from Yukawa-type
interactions with the Higgs field.
==== Higgs sector ====
In the Standard Model, the Higgs field is
a complex scalar of the group SU(2)L:
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 hypercharge (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}}=\left|\left(\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 ====
The Yukawa interaction terms are
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 ==
The Standard Model describes three of the
four fundamental forces in nature; only gravity
remains unexplained. In the Standard Model,
a force is described as an exchange of bosons
between the objects affected, such as a photon
for the electromagnetic force and a gluon
for the strong interaction. Those particles
are called force carriers or messenger particles.
== Tests and predictions ==
The Standard Model (SM) predicted the existence
of the W and Z bosons, gluon, and the top
and charm quarks and predicted many of their
properties before these particles were observed.
The predictions were experimentally confirmed
with good precision.The SM also predicted
the existence of the Higgs boson, found in
2012 at the Large Hadron Collider, as the
last particle of the SM.
== Challenges ==
Self-consistency of the Standard Model (currently
formulated as a non-abelian gauge theory quantized
through path-integrals) has not been mathematically
proven. While regularized versions useful
for approximate computations (for example
lattice gauge theory) exist, it is not known
whether they converge (in the sense of S-matrix
elements) 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:
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 Standard Model does not
consistently explain the canonical theory
of gravitation, general relativity, 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 physicists 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 (coupled to the
Higgs) 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. There are also issues of quantum
triviality, which suggests that it may not
be possible to create a consistent quantum
field theory involving elementary scalar particles.
The model is inconsistent with the emerging
Lambda-CDM model of cosmology. Contentions
include the absence of an explanation in the
Standard Model of particle physics for the
observed amount of cold dark matter (CDM)
and its 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 (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 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
Lagrangian
Open questions: CP violation, Neutrino masses,
Quark matter, Quantum triviality
Quantum field theory
Standard Model: Mathematical formulation of,
Physics beyond the Standard Model
== Notes and references
