The Standard Model



Before a precise investigation of the history of the universe, we must make a detour via the infinitesimal : to understand the beginning of a very hot and very dense universe, we must know its constituent elements, and how do they evolve. That's the aim of the standard model.

The theoretical scope of the standard model is the quantum field theory which allows to describe the fundamental interactions between particles, along with respecting the principles of special relativity and of quantum mechanics.

According to the quantum mechanics, in order to observe a microscopic structure, we must transfer it an energy. The more accurate is the wished resolution, the higher must be this energy.
But, according to the special relativity, this energy can transform into new particles : the fermions - which are the bases of ordinary matter - can be producted or destroyed by pairs of particle/antiparticle, the bosons - messengers of the forces - can be producted in any arbitrary number.


The forces in presence

There are four fundamental forces in the universe :

Compared scales of the four fundamental forces
Compared evolution of the four fundamental forces upon the distance.

The fact that the gluons, which are the transmitters of the strong nuclear interaction, carry a colour charge (the charge of the strong interaction) gives rise to the particular behaviour of the strong force.

On a great scale, only gravitation and electromagnetism can play a part. However, the universe is globally neutral, so the electromagnetic interaction, due to its repulsive and attractive feature, ends up being cancelled.
That's why gravitation is the main force in the universe.

The family of particles

Historically, when people realized that an atom was not indivisible, two types of particles were revealed : neutrons and protons on one hand, which are the elements of the atomic nucleus, and the electron, very much lighter, which, roughly speaking, orbits around this nucleus.

Successive splitting of the matter

In the 1930's, other particles, the muons, were discovered in the cosmic rays. Muons are very much like the electrons, but two hundred times more massive.

In the 1950's, following the predictions of Wolfgang Pauli, neutrinos were discovered : they are very light particles - if they really have a mass, and very weakly interacting with the matter.

In 1968, thanks to the linear accelerator, we noticed that neutrons and protons were in fact made of more elementary "bricks", which were called quarks. Two types were discovered : the u quark (u for up) and the d quark (d for down).

By increasing the energy of the accelerators, thus the mass of the particles within reach, four other types of quark were discovered : the c type(charmed), the s type (strange), the t type (top) and the b type (bottom). Notice that the name given to these particles has absolutely no physical meaning.
Each of these quarks appears in three varieties, named red, green and blue, corresponding to a particular load of the strong nuclear interaction. One more time, the names have no report with the usual colors, they are only a convenient way to call them.

From all these discovery, we can draw a diagram. Particles are organized in three groups, called families.

Fermions : parts of the matter
1st family 2nd family 3rd family E F C
electron 0,511 muon 106 tauon 1784 -1 0
0? muonic
0? tauonic
0? 0 ½ 0
quark u 5 quark c 1300 quark t 174.000 2/3 ½ couleurs
quark d 10 quark s 200 quark b 4300 -1/3 couleurs

Compared diagram of the families of elementary particles.
Beside each particle, its mass is writen in Mev/c².

The column 'E' indicates the electromagnetic charge of the particle,
the column 'W' its weak charge,
the column 'S' its color charge (strong interaction)

For every particle, there exists an anti-particle with the same mass, but with an opposite electrical charge.
The antiparticle of an electron, for example, is called a positron. It has the same mass, but a positive electrical charge.


In the same way, quantum mechanics, especially quantum field theory, indicates that a force between two particles can only take place through an exchange of other particles, called virtual particles.
For each interaction, there is a messenger particle. This particle is of boson type - as opposed to fermions.
The photon does not carry an electromagnetic charge, but the bosons W± and the gluons carry a charge of their corresponding interaction.

Interactions and mediator bosons
electromagnetic force weak interaction chromodynamics strong nuclear interaction gravitation
photon bosons W±, Zo gluons graviton ?
mass = 0 mass = 80/90 mass = 0 mass = 0



The standard model consists of a set of algorithms, based upon the perturbation theory, allowing to calculate, by means of successive approximations and with a finite and steady number of experimentaly deduced parameters, the probabilities of reactions of the leptons, the quarks, the photons and the mediator bosons in electromagnetic and weak interactions (electroweak theory), and the probabilities of reactions of the quarks and the gluons in strong interaction at a high energy (Quantum Chromodynamics, QCD).

The standard model succeeded in all its experimental testings. It allowed us to anticipate a great number of experimental discoveries, like the existence of the quarks, the gluons or the bosons W± and Zo.
However, this model lets appear some weaknesses, especially :


The unification of the forces

For the physicists, four interactions is too much. And their dream would be to show that these four forces are only four different aspects of one and the same interaction.

In the 70's, several physicists - in particular Steven Weinberg, Abdus Salam and Sheldon Glashow - present an audacious hypothesis : electromagnetism and the weak interaction would be the same force. This hypothesis was experimentaly confirmed by the discovery of the W± and Zo bosons and of the "exchanges" between particles.

transmutation d'un électron
For example, an electron can transform into an electronic neutrino, by radiating a W- boson. This one, by interacting with a u quark, will transform it into a d quark.

In order to obtain this identification of the two interactions, it is necessary to work with very high energies : you need to use an energy equivalent to a temperature of 1015 K in order to succed. This is one hundred thousand times the temperature of the core of our Sun.

By extrapolating this result, the so called 'Great Unification Theories' foresee that the electroweak and strong interactions would be joined when the energy would be equivalent to 1028 K. Such an energy is of course far beyond the reach of the current particle accelerators, and such a theory still remains to write.
And if we continue, the 'Theory of Everything' imagines an unification with gravitation. But the required energy would be about 1032 K, the Plank energy.

Unification of the forces

Of course, the four forces appear nowadays under four separate interactions, and we are unable to re-create this unification with our technological means. But, if the universe has been hot enough in its beginning, this situation may have existed.


References :
The standard model (CERN) Histoire, actualité & horizons du modèle standard (G. Cohen-Tannoudji )