The Standard Model (SM) of particle physics

The SM describes all particles and fields observed until now, except the gravitational field. These are fields of three types: fermions (quarks, leptons, neutrinos), gauge fields (field of the electromagnetic, weak and strong interactions). Moreover, it contains some not yet observed Higgs field(s).

Fermions

The SM contains 24 fermions, which appear in some well-defined structured way. Why they appear in such a way is unknown. This is one of the puzzles of the SM, and our approach allows to solve it.

First, all fermions appear in pairs - so-called "electroweak doublets".
Second, they appear in three almost identical generations.
Third, each generation contains three quark doublets (with three colors) and one lepton doublet.

Thus, the structure of the 24 fermions of the SM can be described by the following table:

	red quarks	green quarks	blue quarks	leptonic sector
1. generation	(down,up)	(down,up)	(down,up)	(electron e, neutrino ν_e)
2. generation	(strange, charmed)	(strange, charmed)	(strange, charmed)	(myon μ, neutrino ν_μ)
3. generation	(bottom,top)	(bottom,top)	(bottom,top)	(τ-meson τ, neutrino ν_τ)

Only three generations?

If there are three generations, why not more? Maybe some more generations will be found in future experiments? The probability is low, because there are good empirical arguments against the existence of more generations. Of course, if the mass of all particles of the next generation would be larger than the heaviest particle we are able to create in our accelerators now, there would be no disagreement with observation. For most of the particles of the next generation this would be a quite natural assumption, with one exception: the next neutrino. Even if it would be much larger than the heaviest neutrino, by some factor which is of order of the mass relations between different quarks or leptons, it would be nonetheless light in comparison with the particles we can observe today, that means, light enough to be observable today. People have looked for some effects, which would be caused by such a particle, and havn't found them.

Thus, it seems likely that the known three generations are not simply the beginning of some infinite series of generations, but that there are exactly three generations.

The natural question is, why three? Why not four, or five? The answer given in our approach is, that we have three generation because we live in a three-dimensional space.

Masses

In our cellular lattice model, we do not consider the masses, nor for the fermions, nor for the gauge fields. This has to be left to future research.

The mass terms make the whole picture of the SM much less beautiful. Essentially, the "mass matrix" consists of a lot of parameters measured in particle accelerators. The nature of these parameters is unknown, and physicists hope, that some more fundamental theory allows to explain these values. At least at the current moment, the cellular lattice model does not fulfill such hopes. Therefore I see no reason to introduce these mass terms here. We consider here only the massless version of the SM.

(Professionals may have noticed that I have (incorrectly) used the denotations for the mass eigenstates of the quarks to describe the electroweak doblets. The correct denotations would be a little more complex, but the difference is only relevant for nonzero masses.)

Gauge fields

The gauge group of the standard model is SU(3) x SU(2) x U(1), and it consists of following three parts:

The color group SU(3), which defines the strong interactions between the quarks. The main effect in our life is, that it holds three quarks together, to form protons and neutrons. Moreover, it gives the nuclear forces between them, which hold protons and neutrons together in atomic nuclei. It's action depends only on the color of the quark. That means, it acts on all quarks inside the same doublet in the same way. The action also does not depend on the generation of the quark.
The weak group SU(2)_L describes weak interactions, which appear in our everyday life as radioactivity. It acts only inside the electroweak doublets. Its action does not depend on any other properties, nor on the generation, nor on the color of a quark, nor is there a difference between quarks and leptons. Moreover, it acts only on the so-called "left-handed" parts of the fermions.
The electromagnetic field is a gauge group U(1). For the purpose of our approach it is useful to describe the EM charge as a combination of two different charges:
- The baryon charge I_B distinguishes quarks from leptons. It is 1/3 for each quark, so that three quarks give a baryon with baryon charge 1). It is constant on doublets, similar to the colors of the quarks. A gauge group with this charge would form, together with the color group SU(3), the group U(3). (The group U(3) is a little bit easier to define than SU(3), in correspondence with the shorter denotation.)
- The shifted isospin charge I₃-1/2 has the values 0 and -1 inside the electroweak doublets. This charge is defined in the same way on all doublets, independent of their generation, color, or baryon charge. This characterization makes it close to the weak interactions.
The EM charge Q is, now, a simple linear combination of these two charges:
Q = 2 I_B + (I₃-1/2)

These are already all particles of the SM which have been observed, up to now, in particle accelerators.

The Higgs sector

There is, yet, some other part of the SM, known as the Higgs sector. The Higgs particle has not been observed until now. Moreover, there are lots of different theoretical variants for the Higgs particle(s). There is only some agreement that some Higgs sector is necessary. So that, if it will not be observed in near future, this would be considered to be problematic.

There is, yet, not much what can be said about the Higgs sector in our cellular lattice model, because this has to be, together with the mass terms, left to future research.

The point is that the Higgs sector is the mechanicsm which gives, during some symmetry breaking, the SM particles it's masses. In our lattice model, we also need some sort of symmetry breaking, to give the particles mass. But this symmetry breaking may be very different from the mechanism given by the Higgs mechanism. So, it is not clear at all, if there has to be some Higgs particle in our approach too.