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Fermion

Higgs candidate decaying to 2 tau leptons in the ATLAS detector

Elementary particles

An elementary particle or fundamental particle is a particle not known to have any substructure, thus it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made. In the Standard Model of particle physics, the elementary particles include
the fundamental fermions and the fundamental bosons. Although elementary particles are not made up of smaller particles, some of them may change or convert to particles lighter than them via certain decay reactions. Historically, atoms were once regarded as elementary particles. The word “atom” means “that which cannot be cut” from the Greek word atomos. Later, hadrons such as protons and neutrons were considered elementary. A central feature in elementary particle theory is the early 20th-century idea of “quanta,” which revolutionized the understanding of electromagnetic radiation and brought about quantum mechanics. For mathematical purposes, elementary particles are normally treated as point particles, although some particle theories, such as string theory, point out that elementary particles have a finite non-zero size.

Fermi–Dirac statistics

Quantum statistics tell us about the distribution of uniform particles among quantum states. This means that all microscopic particles in the system are assumed to be indistinguishable, i.e. we cannot label the particles. Swapping the particles does not change the system. A branch of physics in quantum statistics, Fermi–Dirac statistics describe the distribution of particles in a
system consisting of many identical particles that obey the Pauli exclusion principle. It is named after Enrico Fermi and Paul Dirac, who discovered it independently. Fermi–Dirac statistics apply to identical particles having quasi-integer-integer spin in a system in thermal equilibrium.
Additionally, the particles in this system are known to have negligible mutual interaction. This allows many-particle systems to be described in terms of single-particle energy states. The result is the F–D distribution of particles in these states and includes the condition that no two particles can remain in the same state, which has a great effect on the properties of the system.
Particles that obey the F–D statistic are known as Fermions. This usually applies to electrons, which are fermions with spin ½.

FERMION

Particles with integer spin are bosons, while particles with half-integer spin are fermions. Besides this spin characteristic fermions have another specific property: they possess conserved baryon or lepton quantum numbers. As a quantum number given to elementary particles, baryons and leptons have particle number 1, antiparticle -1 and all other observable particles 0. Both elementary particle numbers are a conserved quantum number in all particle
reactions. In contrast to bosons, as a consequence of the Pauli principle only one fermion can occupy a particular quantum state at any given time. If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles; although in the current state of particle physics the distinction between the two concepts is unclear. Each of these fermions also has an anti-particle associated with it, so there are a total of 24 different fundamental fermions. The anti-particle is similar to the original particle, but with opposite electrical charge. The “up,” “charm,” and “top” quarks have an electrical charge of +2/3. Their anti-particles have charge -2/3 (anti-up, anti-charm, anti-top). The other three quarks (down, strange and bottom) have charge -1/3, and their anti-particles have charge +1/3. The electron, muon, and tau leptons all have charge of -1, and their anti-particles (anti-electron or “positron”, anti-muon, anti-tau) have charge +1. All the neutrinos and
anti-neutrinos have charge 0. The main difference between quarks or leptons with the same charge is their mass.

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