In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, the C parity or charge parity is a
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 th ...
of some particles that describes their behavior under the symmetry operation of
charge conjugation
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-sy ...
.
Charge conjugation changes the sign of all quantum charges (that is, additive
quantum numbers), including the
electrical charge
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
,
baryon number
In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as
::B = \frac\left(n_\text - n_\bar\right),
where ''n''q is the number of quarks, and ''n'' is the number of antiquarks. Baryo ...
and
lepton number
In particle physics, lepton number (historically also called lepton charge)
is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction.
Lepton number ...
, and the flavor charges
strangeness,
charm,
bottomness
In physics, bottomness (symbol ''B''′ using a prime as plain ''B'' is used already for baryon number) or beauty is a flavour quantum number reflecting the difference between the number of bottom antiquarks (''n'') and the number of botto ...
,
topness
Topness (''T'', also called truth), a flavour quantum number, represents the difference between the number of top quarks (t) and number of top antiquarks () that are present in a particle:
:T = n_\text - n_\bar
By convention, top quarks have a ...
and
Isospin
In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions ...
(''I''
3). In contrast, it doesn't affect the
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
,
linear momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass a ...
or
spin of a particle.
Formalism
Consider an operation
that transforms a particle into its
antiparticle
In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
,
:
Both states must be normalizable, so that
:
which implies that
is unitary,
:
By acting on the particle twice with the
operator,
:
we see that
and
. Putting this all together, we see that
:
meaning that the charge conjugation operator is
Hermitian {{Short description, none
Numerous things are named after the French mathematician Charles Hermite (1822–1901):
Hermite
* Cubic Hermite spline, a type of third-degree spline
* Gauss–Hermite quadrature, an extension of Gaussian quadrature m ...
and therefore a physically observable quantity.
Eigenvalues
For the eigenstates of charge conjugation,
:
.
As with
parity transformations, applying
twice must leave the particle's state unchanged,
:
allowing only eigenvalues of
the so-called ''C-parity'' or ''charge parity'' of the particle.
Eigenstates
The above implies that
and
have exactly the same quantum charges, so only truly neutral systems – those where all quantum charges and the magnetic moment are zero – are eigenstates of charge parity, that is, the
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
and particle–antiparticle bound states like the neutral pion, η or the positronium.
Multiparticle systems
For a system of free particles, the C parity is the product of C parities for each particle.
In a pair of bound
meson
In particle physics, a meson ( or ) is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, ...
s there is an additional component due to the orbital angular momentum. For example, in a bound state of two
pions
In particle physics, a pion (or a pi meson, denoted with the Greek letter pi: ) is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the lightest mesons and, more gene ...
, π
+ π
− with an orbital
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
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
Spectroscopic notation provides a way to specify atomic ionization states, atomic orbitals, and molecular orbitals.
Ionization states
Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by ...
2''S''+1L
''J'' (see
term symbol In quantum mechanics, the term symbol is an abbreviated description of the (total) angular momentum quantum numbers in a multi-electron atom (however, even a single electron can be described by a term symbol). Each energy level of an atom with a giv ...
), where ''S'' is the total spin quantum number, ''L'' the total
orbital momentum quantum number and ''J'' the
total angular momentum quantum number
In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).
If s is the particle's sp ...
.
Example: the ''positronium'' is a bound state
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
-
positron similar to a
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, ...
. The ''parapositronium'' and ''orthopositronium'' correspond to the states
1S
0 and
3S
1.
* With ''S'' = 0 spins are anti-parallel, and with ''S'' = 1 they are parallel. This gives a multiplicity (2''S''+1) of 1 or 3, respectively
* The total
orbital angular momentum quantum number is ''L'' = 0 (S, in spectroscopic notation)
*
Total angular momentum quantum number
In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).
If s is the particle's sp ...
is ''J'' = 0, 1
* C parity η
''C'' = (−1)
''L'' + ''S'' = +1, −1, respectively. Since charge parity is preserved, annihilation of these states in
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
s (''η
C''(γ) = −1) must be:
:
Experimental tests of C-parity conservation
*
: The neutral pion,
, is observed to decay to two photons,γ+γ. We can infer that the pion therefore has
, but each additional γ introduces a factor of -1 to the overall C parity of the pion. The decay to 3γ would violate C parity conservation. A search for this decay was conducted using pions created in the reaction
.
*
: Decay of the
Eta meson
The eta () and eta prime meson () are isosinglet mesons made of a mixture of up, down and strange quarks and their antiquarks. The charmed eta meson () and bottom eta meson () are similar forms of quarkonium; they have the same spin and parity ...
.
*
annihilations
See also
*
G-parity In particle physics, G-parity is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles.
''C''-parity applies only to neutral systems; in the pion triplet, only π0 has ''C''-parity. On the othe ...
References
{{C, P and T
Quantum mechanics
Quantum field theory