In physics, the C parity or charge parity is a multiplicative quantum number of some particles that describes their behavior under the symmetry operation of charge conjugation.
Charge conjugation changes the sign of all quantum charges (that is, additive quantum numbers), including the electrical charge, baryon number and lepton number, and the flavor charges strangeness, charm, bottomness, topness and Isospin (I3). In contrast, it doesn't affect the mass, linear momentum or spin of a particle.
Consider an operation
l{C}
lC|\psi\rangle=|\bar{\psi}\rangle.
1=\langle\psi|\psi\rangle=\langle\bar{\psi}|\bar{\psi}\rangle=\langle\psi|l{C}\daggerlC|\psi\rangle,
lC
lCl{C}\dagger=1.
l{C}
l{C}2|\psi\rangle=l{C}|\bar{\psi}\rangle=|\psi\rangle,
l{C}2=1
l{C}=l{C}-1
l{C}=l{C}\dagger,
For the eigenstates of charge conjugation,
lC|\psi\rangle=ηC|{\psi}\rangle
As with parity transformations, applying
l{C}
l{C}2|\psi\rangle=ηCl{C}|{\psi}\rangle=
| 2 | |
| η | |
| C |
|\psi\rangle=|\psi\rangle
ηC=\pm1
The above implies that for eigenstates,
\operatorname{lC}|\psi\rangle=|\overline{\psi}\rangle=\pm|\psi\rangle~.
lC~.
For a system of free particles, the C parity is the product of C parities for each particle.
In a pair of bound mesons there is an additional component due to the orbital angular momentum. For example, in a bound state of two pions, with an orbital angular momentum, exchanging and 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, where is the angular momentum quantum number associated with .
lC|\pi+\pi-\rangle=(-1)L|\pi+\pi-\rangle
lC|f\barf\rangle=(-1)L(-1)S+1(-1)|f\barf\rangle=(-1)L|f\barf\rangle~.
Bound states can be described with the spectroscopic notation (see term symbol), where is the total spin quantum number (not to be confused with the S orbital), is the total angular momentum quantum number, and the total orbital momentum quantum number (with quantum number etc. replaced by orbital letters S, P, D, etc.).
| Orbital : | 1S0 | → | 3S1 | → | ||||
| : | +1 | = | (−1) × (−1) | −1 | = | (−1) × (−1) × (−1) |
\pi0 → 3\gamma
\pi0
| 2 | |
| η | |
| C=(-1) |
=1 ,
\pi-+p → \pi0+n~.
η → \pi+\pi-\pi0
p\bar{p}