Elementary Particles

6. PARTICLE CLASSIFICATION

It is important to now understand how the Standard Model particles are classified in order to comprehend some of their more colorful properties. The earliest classification scheme for particles (protons, neutrons, electrons) was based on their masses. But quarks cannot be classified this way because they possess certain unusual properties which other particles do not. For example, unlike other particles, quarks are never seen as free particles. Hence one needs other strategies for particle classification. The two important concepts necessary for classification are (a) spin and (b) the Pauli Exclusion Principle. Later in this article, a different classification scheme called the Eightfold way will be introduced—all of these classification schemes are designed to bring out certain important characteristics of the particles and their interactions much in the same spirit as Mendeleev’s periodic table of elements that was based on recurring chemical properties ordered by their atomic number.

6.1 SPIN

All moving charges produce magnetic fields. In a series of atomic beam experiments conducted in the 1920s, Otto Stern and Walther Gerlach attempted to measure the magnetic fields produced by the electrons orbiting nuclei in atoms. The rapid spinning of the electrons produced tiny magnetic fields independent of those from their orbital motions. The word ‘spin’ was used to describe this apparent rotation of subatomic particles.

However, the analogy breaks down there as it is misleading to conjure up an image of the electron as a small spinning object. Really, spin is a quantum mechanical concept and each subatomic particle has an intrinsic angular momentum or spin that is measured in multiples of a unit called h-bar (ℏ), equal to the Planck constant (h = 6.626\times 10^{-34} \mbox{J.s}) divided by 2\pi. For electrons, quarks, neutrons, and protons, the multiple is ½.

6.2 PAULI EXCLUSION PRINCIPLE

The Exclusion Principle asserts that no two electrons in an atom can be at the same time in the same quantum state or configuration. Proposed in 1925 by the Austrian physicist Wolfgang Pauli to account for the observed patterns of light emission from atoms, the exclusion principle subsequently has been generalized to include a whole class of particles of which the electron is only one member.

Particles are either fermions or bosons depending on whether they possess half-integer or integer spin. Fermions obey the Pauli Exclusion Principle, which means that two of them cannot occupy the same quantum state, but no such restrictions apply to bosons:

  • Fermions. Half-integer spin particles are called fermions
    • Obey the Fermi-Dirac Statistics. The Fermi–Dirac statistics describes a distribution of particles in certain systems comprising many identical particles that obey the Pauli Exclusion Principle.
    • No two-particles can exactly be at the same time in the same state or configuration (Pauli Exclusion Principle)
    • Examples: The fundamental matter particles (quarks and leptons, as well as most composite particles, such as protons and neutrons) are fermions. Therefore, due to the Pauli Exclusion Principle, these particles cannot co-exist in the same location. This is a very important property of ordinary matter!
  • Bosons. Integer spin particles are called bosons
    • Obey Bose-Einstein Statistics. The Bose-Einstein Statistics describes how indistinguishable particles that do not obey the Pauli Exclusion Principle occupy a set of available discrete energy states.
    • Examples: The force carrier particles of fundamental interactions. Composite particles with even numbers of fermion constituents (such as mesons). The nucleus of an atom is a fermion or boson depending on whether the sum of the number of protons and neutrons is odd or even. This property explains the strange behavior of very cold helium, which is a superfluid (meaning it has no viscosity, among other things) because its nuclei are bosons and may pass through each other.

Fermions of the Standard Model make up matter and are responsible for their size and shape. They interact with each other using the four fundamental forces and their associated gauge bosons. Fermions can push and pull one another by exchanging or tossing bosons back and forth, or they can decay into other fermions by emitting some bosons. Fermions are very standoffish; everyone must be in a different state. Bosons, on the other hand, are very clannish; they prefer to be in the same state.

In short, the particles of the Standard Model can be classified into two groups: fermions and bosons. Fermions are the building blocks of matter. They all obey the Pauli Exclusion Principle. Bosons are force-carriers, occupying the right-hand column of the Standard Model. They carry the electromagnetic, strong, and weak forces between fermions.

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