During the 1960s, everybody came to agree that protons and neutrons contain three quarks. According to the Standard Model, there is no other kind of massive particles inside the proton. A few years later, when it turned out that these quarks carry less than half of the proton’s linear momentum (indicating that there had to be other massive particles inside the proton), QCD fans proclaimed that this missing momentum was actually carried by the gluons. It is important to note here that gluon behavior is very different from that of one other massless particle, the photon, related to the electromagnetic interactions of a particle’s bound state.
In this article we’ll see that there is much more than an additional massive particle in the proton. As modern particle accelerators reach increasingly higher energy levels, this fact becomes more and more obvious.
An impactful quantum mechanical experiment
In 1913, James Franck and Gustav Hertz conducted one of the first experiments showing that the atom could not have any arbitrary energy state, but only specific energy levels. The results of this experiment supported Bohr’s atom model. Bohr’s model was later abandoned, but the results of this experiment gave a major boost for the development of the nascent Quantum Mechanics.
What did Franck and Hertz do? They fired electrons into a tube containing Argon gas or Mercury vapors, and measured the value of the electric current at the other end of the tube. The electrons were accelerated by means of an electric field.
Franck and Hertz could control the electrons’ velocity by changing the electric field. At first, the current increased consistently with the increase of electron speed. But when the electrons’ velocity reached a certain threshold, the current at the other end of the tube suddenly dropped. When they further increased the electric field and the acceleration of the electrons, the current at the end of the tube raised again, until a certain threshold, and then, when electrons’ speed crossed this new threshold, the current level dropped again.
What are the experiment’s conclusions? The atom can only have specific energy levels. When the electrons were moving slowly and their energy was too low to excite the atom, which means, to bring the atom to a higher energy level, the electrons just traveled across the atoms and reached the end of the tube with no energy loss. But when the electrons were accelerated and reached a certain velocity (and kinetic energy), their energy was high enough to excite the atom, and was transferred to the atom. This explains the first drop in current intensity. The second drop in current intensity corresponds to the loss of electrons’ kinetic energy when exciting atoms again, and so forth.
Analogous results are regularly observed in today’s particle accelerators as well, but with energy levels extremely higher than those used a century ago. The analysis of these experimental results are based on what physicists call “the cross section curve”, which refers to particle collision rates and is related to the probability to observe a specific event as a result of the collision. It turns out that the cross section depends not only on the type of particles involved in the collision but on the process energy as well.
The study of the proton structure
In the Franck-Hertz experiment, electrons colliding with atoms interacted with the atomic electrons. Exploring the proton requires much more energetic particle beams, and that for two main reasons. One reason is that in Quantum Theory, a particle’s location is not point-like, the way it had been considered in classical physics, but is described by a wave. A slowly moving particle has a relatively large wavelength. When a particle’s wavelength is larger than that of the proton size, it does not collide with an isolated quark, but rather with the whole proton. In order to study quarks, the incident particle’s wavelength should be significantly smaller than the proton’s size, and this is only possible when the incident particle moves at a very high energy.
And indeed, during the last decades scientists managed to accelerate many different particles, electrons, positrons, muons and protons reaching very high energies which significantly shortened the particle’s wavelength and allowed particles of these beams to interact with a single quark within the proton.
What happens when a proton is bombarded?
When a high energy particle beam hits the proton, there are two possible types of interactions between the incident particle and the proton. One type of collision is called “elastic collision”, where there is exchange of kinetic energy and momentum between the particles. The products of the elastic collision are the same particles which existed before the collision. The second type of collisions, called “inelastic collision”, is characterized by the creation of new particles, such as mesons, composed of a quark-antiquark pair. This phenomenon will be explained to the details in another article, dealing with the question of why there are no free quarks.
Scientists observed that when they raised the energy levels of electron- proton collisions, nearly all the collisions were “inelastic”. In fact, in the high energy range, as energy increases, the relative rate of elastic collisions decreased and reached a tiny fraction of about 1:1000. This was true until experiments in the late 1990s reached unprecedented energy levels.
Late 1990s, DESY laboratories, Germany
The results of experiments conducted at the DESY Labs in Germany were published in 1997. The experiments consisted of bombarding protons with beams of electrons or positrons, with very high energy, higher than ever before. The experiment was done by two different groups of researchers, in 2 different locations of the device. The results obtained from both experiments where similar, and surprising.
One of the fundamental rules admitted since about a century states that in processes obeying electromagnetic laws, the probability of a collision between an electron (and similar particles) and a proton decreases as the incident particle’s energy increases.
For this reason, physicists expected to see a decrease in the cross-section curve for higher energies. But relative to the expected decreasing values, the results showed an unexpected increase in the number of events, which is incoherent with the Standard Model. The discovery was followed by the publication of 2 papers expressing astonishment with regard to these findings [1, 2].
What are the possible explanations for such an increase in the number of events? One possibility would be that in analogy to the Franck-Hertz experiment, there are other entities inside the proton capable of absorbing this energy only above a certain threshold. This explanation obviously contradicts the Standard Model. The groups conducting the experiments concluded, quite reasonably, that their findings may be accidental, because there was not enough data collected.
Early 2000s, the Tevatron particle detector, Illinois
About 10 years ago, an experiment was conducted in the Tevatron Particle Accelerator in the State of Illinois, USA, in which a proton beam collides with another proton (or anti-proton) beam. The energy levels of these beams were higher than those reached at DESY, and the results were clear cut: the cross-section curve does move up when the beam’s energy goes beyond a certain threshold! Furthermore, the rate of elastic collisions increased as well. In other words, a change of tendency was observed both in the total and the elastic cross sections, and their curves changed directions and started increasing .
This finding has been known for several years now and is supported by earlier results. It clearly indicated that there are massive particles inside the proton, which get “excited” at this high energy level and produce this tendency change on the curve. In analogy to the Franck-Hertz experiment, these massive particles can only occupy specific energy levels, and react to the collision only when the energy of the incident particle is high enough to excite them and move them to a higher energy level.
Scientists currently prefer ignoring this finding, probably because it contradicts the Standard Model. Very few scientists complain about the fact that the Standard Model does not provide an explanation to this phenomenon [4, 5].
Comay’s model naturally accounts for this finding. Inside the proton there is a core attracting particles to it, whereas moderately high energy experiments could only detect the quarks located in the external shell. But the proton has additional inner quark shells, in analogy to a multi-electron atom, containing filled up inner electron shells. Only incident particles with a sufficiently high kinetic energy would be able to excite the inner shells.
Something more about elastic scattering
The consensus today is that high energy scattering of electrons on protons indicates that the interaction actually takes place between the electron and a single quark inside the proton. As we mentioned above, in such a case, the relative rate of elastic collision should decrease with the increase of the energy, and become negligible for very high energies. This means that if a quark gets heavily hit by an electron, the proton almost always undergoes an inelastic collision. But it turns out that in high energy proton-proton collisions, the proportion of elastic scattering events is about 15% and it does not decrease as energy increases. These results lead to two conclusions:
a. The proton contains a rigid component which is not a quark, and which can resist high energy collisions and maintain the proton’s integrity.
b. This component is electrically neutral and is therefore not revealed in electron- proton scattering.
These conclusions validate the existence of a core inside the proton. This core contains closed quark shells and it contributes to the fact that the proportion of elastic collisions in proton-proton scattering is far from being negligible.
The near future, CERN
The proton beam of the LHC particle collider at CERN reached even higher energy levels, which will allow us to observe the cross section curve as energy goes up. According to Comay , if the number of inner shells is small, or if the energy needed to excite quarks in even deeper shells is higher than the experimental energy, than the elastic cross section will start decreasing again. It’s hard to tell if the energy levels obtained during the upcoming CERN experiment will be able to bring out the next zone on the curve in which the elastic scattering cross section goes down.
Most of the proton momentum is not carried by the 3 external quarks. Following the experimental discovery of this fact, QCD provided an unnatural explanation to the phenomenon.
In high energy proton-proton collisions, the elastic collision rate increases with the energy. Standard Model has no explanation for this phenomenon.
Comay’s model provides a straightforward and natural explanation for these phenomena.
 C. Adloff et al., Z. Phys C74, 191 (1997)
 J. Breitweg et al., Z. Phys C74, 207 (1997)
 C. Amsler et al. (Particle Data Group) Physics Letters B667, 1 (2008) see p.12 in http://pdg.lbl.gov/2009/reviews/rpp2009-rev-cross-section-plots.pdf
 A. A. Arkhipov
 E. Comay, Prog. in Phys. 2, 56 2010