The Particle Model

Before going any further, it is probably safe to assume that the description offered up by the current standard particle model will not be the last word in terms of the development of fundamental physics. For it would seem that there are simply too many unexplained parameters and assumptions, so in spite of the successful predictions, the suggestion remains that the theory, as a whole, might need to be refined or possibly overturn by some future paradigm. This statement is not made to be sceptical from the outset, but simply as a warning that it is all too easy to get lost in the mathematical complexity of modern quantum field theory to the point that all becomes abstraction. Today, the standard particle model can be described in terms of hundreds of exotic particles, although most of these ‘particles’ only exist for a brief moment of time within high-energy experiments. As such, the following table might be said to consist of only the primary components of the particle model within the form of a hierarchy of classes:


The top of the table is split into two halves defined by the fermion and the boson groups, while at the bottom, we have 6 classes that we might initially identify as particles, although this term is primarily a label of convenience rather than an implicit statement of tangible physicality.

Note: The comment about the actual nature of particles reflects the ongoing question about the physical ‘substance’ of elementary particles, such as an electron. At some point, the idea of physical substance appears to become meaningless, such that it might be easier to define an elementary particle as some form of localisation of energy density in spacetime. However, energy is a scalar quantity and therefore it would also need a mechanism by which it is transported to different points in spacetime, e.g. a wave of some description. However, whether this idea is still consistent with quantum theory is an open question - see Wave Theory of Everything by way of a speculative discussion.

While most of the particle classes fall under either the description of fermions or bosons, the mesons might be described as a hybrid having a structural  composition of fermion-quarks, but which act as composite bosons. However, the following definitions will try to expand on the nature of this particular ‘duality’.

We might start by simply describing fermions as a class of  ‘matter-like’ particles that have the attribute of ½-spin and obey the Pauli exclusion principle. However, fermions are then further sub-divided into either leptons or quarks. It should also be noted that each fermion has an anti-matter counterpart as originally predicted by Dirac:

  • Leptons
  • Quarks

These matter-like particles can be described as fundamental particles in as much as there is no further sub-division within the standard model. However, while leptons can exist as independent particles, quarks are only said to exist in some form of composite structure called hadrons.

While bosons are also labelled as a class of particles, they act as ‘force-carriers’ that mediate the strong, weak and electromagnetic fundamental interactions. Unlike fermions, bosons are not subject to the Pauli exclusion principle, such that an unlimited number of these ‘particles’ may occupy the same state at the same time. At this point, we shall define 3 classes of bosons:

  • Gauge Bosons
  • Conceptual Bosons
  • Composite bosons, i.e. mesons

Gauge bosons are described as the carriers of 3 of the 4 fundamental forces of nature, i.e. electromagnetic plus the weak and strong nuclear. As indicated, these force carriers are still linked to a description of elementary particles, but where the process of interaction’ is now defined in terms of a ‘gauge theory that is said to explain how a specific force is exerted via the exchange of gauge bosons. Another sub-class of bosons is identified as ‘conceptual’ because their existence has not been verified, i.e. the graviton associated with gravity and the Higgs particle associated with mass. Finally, mesons are a hybrid class that have a composite structure of 2 quarks, but might be described as mediating as a force-carrier interaction involving the strong nuclear force.

Any composite arrangement of quarks held together by the strong force is classed as a hadron. In essence, there are 2 classes of hadrons:

  • Baryons
  • Mesons

Baryons can be described in terms of protons and neutrons that consist of 3 quarks, while mesons have a composite structure requiring only 2 quarks. The details of the quark composition is given below.

As indicated, a lepton is a fundamental particle, where the electron is the best know component of the standard atomic model. In a general context, there are 2 sub-divisions of leptons, i.e. charged and neutral. The former is electron-like, while the neutral leptons are better known as neutrinos that appear to have minimal mass. The mass in all the following tables is expressed in units of MeV/c2:

Particle Symbol Charge Spin Mass Lifetime
e:electron e −1 12 0.511 Stable
μ:muon μ −1 12 105.658 2.197*10−6
Τ:tau τ −1 12 1,776.84 2.906*10−13
e:neutrino νe 0 12 < 0.0000022 Unknown
μ:neutrino νμ 0 12 < 0.17 Unknown
τ:neutrino ντ 0 12 < 15.5 Unknown

While the muon [μ] and tau [τ] can be described as being similar to an increasingly large electron, the neutrino is quite different in form, being electrically neutral with a near-zero mass. As such, the neutrino is able to pass through ordinary matter almost unaffected.

As stated, quarks combine to form composite particles called hadrons, which in turn are sub-divided into baryons, i.e. protons and neutrons, plus mesons, i.e. pions and kaons. As such, quarks are never found in isolation and therefore much of what is known about quarks has been drawn from observational inference. There are 6 basic types of quarks:

Name Symbol Mass Spin Charge
Up u 1.7 to 3.3 12 + 23
Down d 4.1 to 5.8 12 13
Strange s ~101±25 12 13
Charm c ~1,270 12 + 23
Top t ~172,000 12 + 23
Bottom b ~4,190 12 13

The basic structure of an atom can be described in terms of just 3 particles, the electron, which is a lepton with no quark sub-structure and the proton and neutron, which are baryons that have a sub-structure that consists of 3 quarks:

Name Symbol Quarks Charge Mass Mean Lifetime
neutron n udd  0 939.565 8.881*102
proton p uud +1 938.272 Stable

The quark structure of the baryon particles is held together via the strong nuclear force, which always results in a net integer charge of 0 or +1. Outside the nucleus, free neutrons are unstable and have a mean lifetime of ~881.5s, i.e. ~14 minutes-42 seconds. Free neutrons decay by emission of an electron and the electron/anti-neutrino to become a proton, which is also known as beta decay that is a type of radioactivity:

[1]      1

Although the table above declares the proton to be stable, some theories require the proton to have a half-life in the order of 1036 years, i.e. much, much longer than the present age of the universe. Within this process, the proton decays into a positron and a neutral pion, which then almost immediately decays into 2 gamma ray photons:

[2]      2

While such long timescales might appear to be of no immediate interest to humanity, aspects of this speculative decay process has relevance to cosmology, which seeks to model the future of the universe: see 'The Degenerate Era'.

This sub-class of atomic particles are composed of just one quark and one anti-quark, bound together by strong interaction. However, because the mesons are described in terms of quarks they can also be assigned a physical size, i.e. radius ~10−15m, which is about 2⁄3 the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting in the order of 10−8 seconds. There are many types of mesons, therefore the following tables simply represents 2 primary forms, the pion ( π -meson) and the kaon (K-meson):

Name Symbol Quarks Mass Lifetime
Pion π+/ π-  3 139.570 2.603*10−8
Kaon K+/K-  4 493.677 1.238*10−8

The (+/-) superscript denotes the existence of particles and anti-particles, which have opposite charge. However, there is also a charge neutral form of each particle. As a broad generalisation, charged mesons decay to form electrons and neutrinos, while uncharged mesons may decay to photons, although the complexity of each permutation can be much more involved than this outline is suggesting.