To know the Nature of Nature

Knowing the nature, in its most intimate structure, satisfies the human curiosity. Obeys the human instinct of wanting to know his origins and the composition of its habitat.

When inquiring the intimate structure of the nature, the ancient philosophers, today the physicists, invented the concept of atom. The concept is famous and badly interpreted. The first ideas can be traced back to the ancient Greeks. Their ideas were merely speculative. Or to say it in terms less rigorous, their ideas, plausibles, were based on the experimental evidences presented by the external world. The diffusion of odors, the evaporation of the water from the pond, the spread out of the perfume of the flowers in the air, the partition of dirt into smaller pieces, etc. were with out doubt sources of inspiration and of irrefutable evidences about the existence of the atoms. The rest they got by way of speculative thinking. Guided by plausible philosophical principles. Like the beauty, the simplicity, the order, etc.

The ideas of the ancient Greeks are very modern. The parallelism between their system of the world, animated by forces and particles, and ours is awesome. The methods are very different. Theirs is static. It does not correct by itself. The modern is dynamics, it corrects by itself, and it carries knowledge far away. It is the experimental method.

The experimental confirmation, that passed all tests, about the existence of the atoms is a modern success. It has close to one hundred years. The experimental test of the existence of the elementary particles is still more modern. It has no more than fifty years. Still in 1908 it was doubted the existence of the atoms. J.B. Perrin proposed that, the erratic motion of the suspended particles, the Brownian motion, was caused by the collisions of the atoms with the suspended molecules. Eminents thinkers, as E. Mach, never accepted the existence of the atoms. They went to grave with out been convinced.

We presented, in the Section 2, that history of the atoms and of the particles. We introduce, in this section, the history of the subsequent discoveries. The first one is to meditate, the second one is to expand. To research.

The existence, based on indirect evidences, of the quarks was accepted in a short time. The discovery of the particle $J/\Psi$, in 1974, was crucial. The discovery of the state $\Psi^\prime$definitely convinced the physicists. This is an excited state of $\Psi$, called charmonium. It was the discovery of the quark $c$.

For those that doubted of the existence of the quarks, according to the most brilliant minds of the time, all the disputes about the existence of the quarks must be solved in the laboratory. All the efforts must be encouraged to show the existence of the quarks. This is, to build particle accelerators potent enough as to reveal the existence of the quarks. To show the quarks. In this way Fermilab was born. And other centers of research in particles in the world began to operate with the same purpose.

Using the experimental facilities of Fermilab, Leon Lederman and coworkers discovered the particle upsilon $(\Upsilon)$ in 1978. It was the discovery of the quark $b$. At the same time, they discovered the states $\Upsilon^\prime$ and $\Upsilon^{\prime \prime}$.

After those discoveries few physicists doubted about the existence of quarks.

The model of quarks was invented by Gell-Mann. And many physicists followed him.

For example, in his courses and conferences, G. Zweig showed the enormous simplicity gained, by the hypothesis of the quarks, in the understanding of the resonances and in decay spectrum. Zweig was an enthusiast of the quark theory. He contributed to the model.

For some, the unique thing that the quark model could not explain was itself. The simplicity proposed by the quark model was extreme. However, the model presented some difficulties. The laws for the interactions between quarks were unknown. The rules for combining quarks appeared arbitrarily. Without bases.

The lack of bases was more evident trying to understand the structure of the baryons. Specially, the structure of $\Omega^-$. This baryon is composed of three strange quarks. According to the quark model, the wave function must be symmetric. However, according to the Pauli principle, must be antisymmetric. The demands of the Pauli exclusion principle were of much weight. This principle is the base of all atomic spectroscopy. The dilemma was solved by W. Greenberg.

W. Greenberg suggested that the quarks, at that time, $u,d,$ and $s$ must be able to be in three different states. That is, be distinguishable or be able to be distinguished. He call them color states. And every thing agreeded naturally with the exclusion principle. The wave function for $\Omega^-$ becomes antisymmetric. The color must be an intrinsic property of the baryons. The baryons are colorless; the quarks have color. The states are three, according to the experimental evidences. They are blue, green, and red. These have nothing to do with the visual sensation of color. These are just a name for three different states.

The color became to be the key for the physicists could understand the structure of the baryons in terms of quarks. Or for they could accept quarks model as true model. When the physicists measured the color, they got a number consistent with three, in agreement with Greenberg suggestion.

Not only the color, but the quarks too, must fit the experimental criteria we stated previously. The experimental evidence have a prime role in physics. And it has to be applied to the quark model. Or to the quarks. The quarks must be an experimental reality.

And they are an experimental evidence. The dispersion experiments of electrons by protons, of J. Friedman, D. Taylor, and H. Kendall, and coworkers, provided the experimental basis for the model of quarks. The high rate of inelastic collisions observed in their experiments made at SLAC, showed that inside the proton there are electric charged, and very dense, localizations of matter. R. P. Feynman call them partons. If it were assumed that the electrons were dispersed for massive localizations inside the protons, then could be easy to understand the so big observed cross sections of elastic dispersions. This is, the SLAC experiments were observing not a tender structure of the proton, but a hard structure very well defined and localized. Those were the quarks or the partons, or whatever they must be called.

Assuming the hypothesis of quarks as valid, of course supported by the experimental evidence of J. Friedman, D. Taylor, and H. Kendall, B. Bjorken and M. Paschos got the consequences of the dispersion of electrons and of the dispersion of neutrinos. The predictions agreed with the experimental results. The quarks were an operative reality, at least. The objective reality of the quarks were very different from that obtained up to that time for other particles.

The predictions added more questions. The quarks behaved as if they were free inside the proton. But they could not be obtained as free states. Up to this time, they have not shown themselves as a free particles. Maybe they never will show up as free states.

The experimental evidence laid the quarks inside the protons. However, constantly at the experiments, at energies enough they did not appear free. The acquired mentality in the past decades on particles, demanded that the quarks to be real must appear free. If they could no be observed as free particles, the quarks could be seen only as a computational fictions. The quarks inside the proton behaved as free particles. And remained confined, inside a structure, forming the proton, the neutron, and other baryons.

The non-Abelian gauge theories can accommodate the behaviour of the quarks inside the baryons. In those theories, the interaction between two quarks decreases when less is their separation, and become more intense while more aparted they are. This behaviour of the strong forces is called asymptotic freedom. That characteristic of the strong forces was the key to understand the experimental results of J. Friedman, D. Taylor, and H. Kendall.

In this way, the quantum chromodynamics (QCD) was born in hands of Gell-Mann and others. With the name he emphasized the role of the color concept played in the theory. After the reinforced theory by the experimental evidence of the quark $c$ -the experimental evidence of charmonium-, the image about the constitution of matter changed. The actual image about the matter was consolidated.

That image we have presented in the Section 3. It is schematized in the Figure 6.

The actual elementary particles are the leptons: $(e,\nu_e)$, $(\mu,\nu_{\mu})$, $(\tau,\nu_{\tau})$. And the quarks: $(u,d)$,$(s,c)$, $(b,t)$. All of them are fermions of spin $\frac{1}{2}$ in Planck constant divided by $2\pi$ units. They have no internal structure. The quarks are color triplets. They are influenced by the strong force. The leptons have no color charge. They experiment the weak force. They do not experiment the strong force.

The physicists discovered the top quark in 1997. At Fermilab, inside the experiments $D0$ and $CDF$. Maybe there are baryons and mesons conformed by the top quark. They have not been detected.

The lepton tau was detected in 1974 at SLAC. The neutrino associated to the tau was indirectly detected in 1997. The channel disintegration of the $\tau$ and of the $Z^0$ was the channel of the discovery.

At Fermilab it is performed the experiment DONUT -Direct Observation of NU Tau-. This experiment will detect the neutrino associated with the lepton tau directly. A beam of neutrinos associated with the tau interacts with the protons of the target to produce tau leptons.

The student can consult the $www$ page of this experiment, inside the Fermilab $www$ page.

The forces complement the scenario of the constitution of matter. They are four, as we stated before. Attributes or properties of those forces are gauge asymmetry. They determine the character of the elementary forces.

The quantum chromodynamics describes the strong forces. The electroweak theory describes the weak and electromagnetic forces. Both theories are non-Abelian gauge theories.

The first experimental confirmations of the electroweak theory were made by A. Lagarrique and coworkers in 1973. They were working at CERN. They reported the first signal of neutral electroweak currents. The discovery of the bosons W and Z and the construction of sources of Z at the CERN and at the SLAC, showed the success of the gauge theory to describe the interactions of leptons and quarks.

According to the electroweak theory, the world must be composed of quarks and leptons. Each pair of quarks, for example the $u$ and the $d$ is accompanied by a pair of leptons, for example the electron and the neutrino associated to the electron.

There are three pairs of quarks accompanied by their respective pair of leptons. The physicists do not know if that are all the pairs that exist. Experimentally we know that there are no leptons more light than the known leptons. However could be leptons more heavy than Z boson. If they exist, they could not be produced in the decay of Z boson.

The neutrinos have a very small mass. It is different from zero. Apparently they are not themselves their antiparticles. We still do not know what is the property that makes them distinguishable, besides their mass.

It could be that the three generations of quarks and leptons are every thing that exist. The past history has shown us that always that it has been considered concluded the image of the matter, appear by surprise new forms, new states.

It could be exotic forms of matter. Like the matter called dark. It could be distinct from the ordinary matter. It is not very much what we know about it, besides its existence. And constitutes most of the suspected total mass of the whole universe. With high probability, we even no suspect how the global universe is.

The supersymmetric theories are the most popular candidates to extend the electroweak theory. These theories require of spin zero particles. They must be affiliated with the pairs of quarks and leptons.

The quarks and leptons are smaller than $10^{-19}~meters$ in their radius. Have no internal structure, up to where it could be experimented.

The Table 9 illustrates all conserved quantities in the domain of the elementary particles. All those quantities are inside the context of the standard model of the elementary interactions. Some, like the angular momentum, the electric charge, and the energy are known in the world of the macroscopic physics.

Any event that would violated those laws would be evidence of physics beyond the standard model. For example, inside the standard model the laws 7, 8, and 9, are separated because the neutrinos have zero mass. This is a supposition of the standard model. If the neutrinos have mass different from zero, as some experiments claim to have shown, then the laws 7, 8, and 9 are violated. And the conservation laws 7, 8, and 9 must be degraded to approximated valid laws.

If we do not content ourselves in describing the material world as we found it. But we aspire to know why the nature is as it is. We have in front of us a series of problems. All of them without solution for the moment.

What makes an electron an electron? What is the origin of the electric charge? Why three generations of matter? Is the electric charge related with the mass? What is that relation? What is the origin of the fundamental forces? Is there a unique force? Is there a unique particle? There are no experimental evidences to assume that there are more families of particles. However, the imposed conditions by the history of particles indicate that could be more families of particles. The history of the molecules, of the atoms, of the protons, indicates that the quarks could be composed. The ideas induced by the aesthetics, suggested that the number of families must be limited. The complex world must be fabricated of small number of simple components. If the quarks and the leptons are composed of particles even more smaller, we will find them. We will find the relations between the quarks and the leptons.

Some theories, that extend the theories experimentally confirmed, propose that the quarks and the leptons are composed. There are no indications of the level of energy where those particles must be searched for. But we can characterized the yields that they must leave if they are composed.

At the energy enough, during collisions of quarks and leptons, the constituents must approach up to touch them. Penetrate them. Interchange their components. In the dispersion of quarks by quarks, the interchange of gluons of the QCD, the strong force, must be replaced for a force of contact. Its magnitude must be determined by the size of the quarks.

For example, in $\bar p p$ collisions, the new contribution must give origin to an excess of hadronic jets at high transversal momenta or transversal energy. There the dispersion of quarks antiquarks is dominant. The form of the jets must be completely different from the form predicted by the QCD. If the leptons have similar components to the quarks, a similar excess must appear in the dileptonic production $\bar q q \to l^+l^-$. At high enough energies the effects of the excited quarks and excited leptons must be present. At those energies, characteristic phenomena of quark size must be present.