The Quark Model

By the early 1960’s, particle accelerators were starting to suggest the existence of dozens of new particles, which Murray Gell-Mann and Yuval Ne'eman, organized into families with certain mathematical properties known as a ‘group of eight’. Based on this mathematical property, it was proposed that a certain class of fundamental particles could be explained in terms of an eight-fold pattern, which is now explained in terms of quarks.


However, it was not until the 1970’s that there was enough experimental data to support the mathematical conjecture that quarks were the building blocks of protons and neutrons. Initially, to explain the observed spectrum of hadrons, Gell-Mann and Zweig defined 3 ‘flavours’ of quarks:

  • Up (u): Charge +2/3
  • Down (d): Charge -1/3
  • Strange (s): charge -1/3

However, ordinary matter, i.e. protons and neutrons, only contain (u) and (d) quarks, where the electric charge of these particles reflects the net composition of quarks. However, at the time, this was quite a radical assumption as there was no experimental data for any elementary particle carrying unit charge smaller than an electron.

Note: In addition to the initial quarks listed above, Dirac's equation of 1928 had already implied that for every charged particle there must exists an anti-particle with the opposite charge. On this basis, it was therefore assumed that there must be anti-quarks to complement the list above.

In the context of this model, it was also assumed that quarks must interact with one another to form some sort of stable-state in order to describe the known hadrons, i.e. protons and neutrons. Within this model, a proton consisted of 2 (up) quarks, i.e. +4/3e, and 1 (down) quark, i.e. −1/3e, resulting in a net charge of (+1e). In a similar fashion, a neutron consisted of 1 (up) quark, i.e. +2/3e, and 2 (down) quarks, i.e. -2/3e, resulting in a zero net charge. While we have only identified 2 examples of baryon particles in the form of protons and neutrons, the ‘reality’ of the particle model lists dozens of examples, which we shall only briefly outline. In 1947, experimental data associated with cosmic ray interactions suggested that certain particle products, resulting from collisions, were found  to exist for much longer than expected, i.e. 10-10s versus 10-23s. The product particle was called lambda (Λ0) and its ‘strange’ property was tagged as ‘strangeness’ and used to name the third quark in the list above. As such, the lambda particle is a true baryon that consists of three quarks, i.e. up, down and strange. The expected lifetime of 10-23 seconds was calculated based on the assumption that all the quarks of a  baryon interact via the strong nuclear force. However, the observed lifetime of  10-10 seconds required an additional explanation that would involve an interaction linked to the weak nuclear force and require a new conservation law to account for the observed decays called the ‘conservation of strangeness’. However, the conservation of strangeness is not in fact an independent conservation law, but rather a combination of the conservation of charge [Q], isospin [I], and baryon number [B].

Note: For the purposes of this discussion, we can simply identify isospin as another quantum number related to the strong interaction, while the baryon [B] number is the approximate conserved quantum number of the composite particle.

Over the years, the quark model was continuously extended due to the development of ever higher energy particle accelerators to include 3 additional quarks:

  • Charm (c): Charge +2/3
  • Bottom (b): charge -1/3
  • Top (t): Charge +2/3

The charm quark was first hypothesised , in 1974, based on the observation of a meson particle with the label [J/Ψ] with a mass some 3 times larger than a proton. As a meson, the quark structure comprises of a quark and its anti-quark, but the discrepancy in the mass suggested the existence of another quark that was call ‘charm’. Subsequently, in 1977, the bottom quark was hypothesised  based on experiments that seem to identified another meson called the upsilon meson (Y) with another mass that pointed to the ‘bottom’ quark and its anti-particle. Although the existence of final ‘top’ quark was predicted in the early 1970’s, it took to 1995 to actually discover the top quark within the debris of a high-energy collision between protons and anti-protons. The mass of the top quark is over 180 times larger than a proton. Of course, aspects of the quark model can appear to be quite abstract, especially in view of the statement that quarks do not exist in isolation.

So is it meaningful to say that quarks exist ?

Clearly, quarks started out as a hypothetical concept through which the process of particle decay could be described and to some extent explained. However, it has always been recognised that the idea of quarks were accompanied by the fairly fundamental issue that they do not appear to exist in isolation. This issue sometimes goes by the name of the confinement problem that raises the following question:

Why has physics not reach an energy high enough to liberate quarks?

One answer to this question lies within the nature of the strong force, which is assumed not to diminish with distance and, in fact, there are arguments to suggest that it may actually increase with distance at the rate of about 1 GeV per 10-15 metres. As a consequence, free quarks are not observed because by the time the separation reaches a more observable scale, the energy is far above the ‘pair production’ energy for quark/anti-quark pairs.

Note: Pair production is a process by which an elementary particle and its antiparticle can be created provided there is enough energy available.

For the up and down quarks, the mass corresponds to an energy in the order of +1 MeV, therefore pair production would take place at distances much less than 10-15 metres. As such, there is the implicit suggestion that an isolated quark can never  be seen because the strong force requires so much energy to separate the quarks that the process itself produces quark plus anti-quark pairs, i.e. a meson, long before they become sufficiently separated to be observed by any known technology to-date. Therefore, it has to be recognised that the quark model, like much of quantum mechanics, is a useful model, but not necessarily a true or full description of quantum reality.

Note: Examination of both the particle and quark model does not really seem to suggest a mass-particle concept, but rather a resonant-frequency model. For it seems that if you put enough energy into a system, a new set of particles emerges. This might be seen as analogous to a wave pattern on a 1-dimensional piece of string, where the integrals of wavelength depend on the input energy-frequency of vibration. Of course, to support this suggestion you would need to explain what is vibrating in 3-dimensions and why any given resonance frequency persists. See Atomic Orbitals for some possible visualisations of this idea.