C parity
Encyclopedia
In physics
, C parity or charge parity is a multiplicative quantum number
of some particles that describes its behavior under a symmetry operation of charge conjugation (see C-symmetry
).
Charge conjugation changes the sign of all quantic charges (i.e., additive quantum number
s):
On the contrary, does not affect:
As a result, a particle is substituted by its antiparticle.
For the eigenstates of charge conjugation
and
is called the C parity or charge parity.
The above implies that
and 
have exactly the same quantum charges, so only truly neutral systems —those where all quantum charges and magnetic moment are 0— are eigenstates of charge parity, that is, the photon
and particle-antiparticle bound states: neutral pion, η, positronium... The neutron is not an eigenstate because it has a magnetic moment
, and so does not have an associated C parity.
For a system of free particles, the C parity is the product of C parities for each particle.
In a pair of bound boson
s there is an additional component due to the orbital angular momentum. For example, in a bound state of two pions, π+ π− with an orbital angular momentum
L, exchanging π+ and π− inverts the relative position vector, which is identical to a parity
operation. Under this operation, the angular part of the spatial wave function contributes a phase factor of (−1)L, where L is the angular momentum quantum number associated with L.
.
With a two-fermion
system, two extra factors appear: one comes from the spin part of the wave function, and the second from the exchange of a fermion by its antifermion.
Bound states can be described with the spectroscopic notation
2S+1LJ (see term symbol
) , where S is the total spin quantum number, L the total orbital momentum quantum number
and J the total angular momentum quantum number.
Example: the positronium is a bound state electron
-positron
similar to an hydrogen
atom
. The parapositronium and ortopositronium correspond to the states 1S0 and 3S1.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, C parity or charge parity is a multiplicative quantum number
Multiplicative quantum number
In quantum field theory, multiplicative quantum numbers are conserved quantum numbers of a special kind. A given quantum number q is said to be additive if in a particle reaction the sum of the q-values of the interacting particles is the same before and after the reaction. Most conserved quantum...
of some particles that describes its behavior under a symmetry operation of charge conjugation (see C-symmetry
C-symmetry
In physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry.-Charge reversal in electromagnetism:...
).
Charge conjugation changes the sign of all quantic charges (i.e., additive quantum number
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
s):
- electrical charge
- baryon number and lepton numberLepton numberIn particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0...
- flavor charges: strangenessStrangenessIn particle physics, strangeness S is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic reactions, which occur in a short period of time...
, charm, bottomnessBottomnessIn physics, bottomness also called beauty, is a flavour quantum number reflecting the difference between the number of bottom antiquarks and the number of bottom quarks that are present in a particle: B^\prime = -Bottom quarks have a bottomness of −1 while bottom antiquarks have a...
(formerly `beauty'), topness (formerly `truth') - IsospinIsospinIn physics, and specifically, particle physics, isospin is a quantum number related to the strong interaction. This term was derived from isotopic spin, but the term is confusing as two isotopes of a nucleus have different numbers of nucleons; in contrast, rotations of isospin maintain the number...
3rd-component
On the contrary, does not affect:
- massMassMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
- linear momentum
- spinSpin (physics)In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
J - complex conjugation K
As a result, a particle is substituted by its antiparticle.
For the eigenstates of charge conjugation
and
is called the C parity or charge parity.The above implies that
and have exactly the same quantum charges, so only truly neutral systems —those where all quantum charges and magnetic moment are 0— are eigenstates of charge parity, that is, the photonPhoton
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
and particle-antiparticle bound states: neutral pion, η, positronium... The neutron is not an eigenstate because it has a magnetic moment
Magnetic moment
The magnetic moment of a magnet is a quantity that determines the force that the magnet can exert on electric currents and the torque that a magnetic field will exert on it...
, and so does not have an associated C parity.
For a system of free particles, the C parity is the product of C parities for each particle.
In a pair of bound boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s there is an additional component due to the orbital angular momentum. For example, in a bound state of two pions, π+ π− with an orbital angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
L, exchanging π+ and π− inverts the relative position vector, which is identical to a parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
operation. Under this operation, the angular part of the spatial wave function contributes a phase factor of (−1)L, where L is the angular momentum quantum number associated with L.
.With a two-fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
system, two extra factors appear: one comes from the spin part of the wave function, and the second from the exchange of a fermion by its antifermion.
Bound states can be described with the spectroscopic notation
Spectroscopic notation
Spectroscopic notation provides various ways to specify atomic ionization states, as well as atomic and molecular orbitals.-Ionization states:Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by the element's symbol followed by a Roman numeral...
2S+1LJ (see term symbol
Term symbol
In quantum mechanics, the Russell-Saunders term symbol is an abbreviated description of the angular momentum quantum numbers in a multi-electron atom. It is related with the energy level of a given electron configuration. LS coupling is assumed...
) , where S is the total spin quantum number, L the total orbital momentum quantum number
Azimuthal quantum number
The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital...
and J the total angular momentum quantum number.
Example: the positronium is a bound state electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
-positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
similar to an hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
. The parapositronium and ortopositronium correspond to the states 1S0 and 3S1.
- With S = 0 spins are anti-parallel, and with S = 1 they are parallel. This gives a multiplicity (2S+1) of 1 or 3, respectively
- The total orbital angular momentum quantum numberAzimuthal quantum numberThe azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital...
is L = 0 (S, in spectroscopic notation) - Total angular momentum quantum number is J = 0, 1
- C parity ηC = (−1)L + S = +1, −1, respectively. Since charge parity is preserved, annihilation of these states in photonPhotonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s (ηC(γ) = −1) must be:1S0 → γ + γ 3S1 → γ + γ + γ ηC: +1 = (−1) × (−1) −1 = (−1) × (−1) × (−1)