For over 40 years the standard model of particle physics has successfully described the interactions of elementary particles and is one of the best tested theories to date. It describes three of the four forces of nature, the electromagnetic force, the weak force and the strong force. The inclusion of gravity remains a challenge but as elementary particles have very low masses, it can be neglected for practically all measurements.
Descriptions of the standard model can be found in various textbooks, the following overview is mainly based on [1].
The theoretical background for the standard model is Quantum Field Theory (QFT), which is a relativistic description of quantum mechanics and can therefore be used to describe microscopic particles at high velocities/energies. A fundamental property of elementary particles is their spin, which is also used to classify them into two groups, fermions and bosons. The former have a half-integer spin value while the latter have a full-integer value. A list of all fermions in the standard model can be found in table2.1.
In total there are 12 fermions, six leptons and six quarks. While they all have the same spin, they differ in mass, electric charge and the forces they interact with. Quarks are
the only particles that interact with the strong force. The fermions are further classi-fied in three generations. Across these generations one particle ”type” differs only in its mass, the muon for example has the same quantum numbers as the electron but its mass is over 200 times larger. For all fermions there is an anti-particle which has the same properties except for their charge related quantum numbers. The anti-particle for the electron is the positron which has an electric charge of +1instead of−1.
All other particles are composites of two or three quarks, called mesons and baryons.
The lightest meson is the pion π0, which consists of an up and anti-up quark (or down and anti-down). The proton is an example for a baryon with the quark content uud.
There are, of course, many more mesons and baryons, forming what is sometimes called a particle zoo.
Symbol Generation EM charge Mass [MeV/c2] Fermion Name
Lepton
electron e− I -1 0.5109989461(31)
muon µ− II -1 105.6583745(24)
tau τ− III -1 1776.86(12)
Table 2.1.: Fermions in the standard model and their properties. Not shown are the anti-particles which have the opposite electric charge but are identical otherwise.
Values for the masses taken from [2].
2.1.1. Quantum Electrodynamics (QED)
As mentioned before the standard model covers three forces of nature. These forces are mediated by gauge bosons. A list of all gauge bosons can be found in table2.2. The gauge boson of the electromagnetic force is the massless photon, it interacts with all particles that carry an electric charge. That means that neutrinos do not feel the electromagnetic force while all other fermions do. Electromagnetic interactions are described in the theory of Quantum Electrodynamics (QED). In 1960 Richard Feynman introduced a way to graphically represent these interactions using what is called Feynman diagrams.
2.1. Standard Model of Particle Physics An example of such a diagram can be seen in fig. 2.1. The same formalism can be used to describe the other forces in the standard model as well. These diagrams can easily be translated into mathematical expressions to be evaluated.
γ e−
e+
µ+
µ−
Figure 2.1.: Simple QED Feynman diagram showing the interaction of an incoming elec-tron and posielec-tron through a photon, producing a muon/anti-muon pair.
2.1.2. Quantum Flavourdynamics (QFD)
Quantum Flavourdynamics (QFD) describes the weak force which has two gauge bosons, the W± boson and the Z boson. The former comes in a positively and negatively charged form. In contrast to the photon they are not massless but have a mass of
≈ 80GeV (W±) and ≈ 90GeV (Z). Another key difference is that they interact with all fermions, including the neutrinos. As the W is electrically charged and the Z is not, weak interactions are divided into charged and neutral current interactions. While neutral current interactions do not allow flavour changes, charged current interactions do. Another important distinction between them is the fact that the W boson only interacts with left-handed particles and right-handed anti-particles. The corresponding property of a particle is calledchirality. For massless particles the chirality is equivalent to thehelicity of a particle, which describes whether the spin of the particle is oriented in the same or opposite direction of its movement. For massive particles, however, the helicity depends on the observer, as there is always an inertial frame of reference in which the particle moves ”backwards”. Mathematically, this behaviour is described by the introduction of left-handed doublets to which the W boson couples:
u
Figure 2.2 shows Feynman diagrams of charged and neutral current interactions. Here the aforementioned flavour change during the W− interaction is visible (µ−→νµ).
W−
Figure 2.2.: Decay of muon into an electron (left) and neutrino/anti-neutrino production via a Z boson (right).
2.1.3. Quantum Chromodynamics (QCD)
The carrier of the strong force is the gluon, which is massless like the photon. The gluon only interacts with quarks, as they are the only fermions that carry a colour charge.
Conceptually, this charge is similar to the electromagnetic charge, but there are three types of charge (”colours”) instead of one, they are usually called red, blue and green.
While quarks carry one of these colours, their anti-particle pendants carry an anti-colour, like anti-red. The gluon itself does carry a colour and an anti-colour, which is another difference to the photon which does not carry an electric charge itself.
The theory that describes the strong force and its interactions is fittingly called quan-tum chromodynamics (QCD), which is mathematically based on an SU(3) gauge group.
As this is a non-abelian gauge group, the gluon can couple to itself. An example of this self-coupling can be seen in fig.2.3.
u
u
Figure 2.3.: Example of gluon-gluon self coupling. Two gluons fuse together and produce an up/anti-up quark pair.
2.1.4. Higgs boson
The last boson is the Higgs boson, which is special compared to the others. It is not connected to one of the three forces mentioned above and is the only boson that has a spin of 0. In 2012 it was discovered at the LHC [3] by the ATLAS [4] and CMS [5]
collaborations. The theoretical prediction of the particle was made in the 1960s by Peter Higgs [6] and others [7,8]. He described a mechanism of spontaneous symmetry
2.2. CKM Matrix