G parity
The G-parity is a multiplicative quantum number , which can take the values +1 and -1. It generalizes the C parity to particle multiplets .
This makes sense because the C parity is only defined for neutral systems (e.g. in the pion triplet only the π 0 C parity), but the strong interaction acts independently of the electrical charge (equally on π 0 , π - and π + ).
Since the G parity is applied to a whole multiplet, the charge conjugation sees the multiplet as a neutral whole. Hence only multiplets with mean charges of 0 can be eigen-states of G , i.e. H. only multiplets for which the following applies:
with the electric charge Q, the baryon number B and the hypercharge Y.
Formulation with operators
Here η G are the eigenvalues of G parity (for pions in particular is ).
The operator of G parity is defined as:
with the operator of the C parity and the second component of the isospin . The G parity is thus a combination of charge conjugation and a 180 ° rotation around the 2-axis in isospin space.
Formulation with eigenvalues
In general
with eigenvalue η C of C parity and the isospin I .
For fermion- antifermion systems this becomes
with the total spin S and the total angular momentum quantum number L.
and for boson- antiboson systems
- .
Invariance and conservation
The G -parity is invariant under the strong interaction, since this receives both charge conjugation and isospin. However, under the electromagnetic and the weak interaction , G parity is not invariant.
Since it is a multiplicative quantum number, the G parity for a system of n pions is:
- .
This results in an interesting consequence of the conservation of G for processes in which only pions appear : under the strong interaction, the number of pions can only change by an even number.
literature
- TD Lee and CN Yang : Charge conjugation, a new quantum number G, and selection rules concerning a nucleon-antinucleon system . In: Il Nuovo Cimento . 3, No. 4, 1956, pp. 749-753. doi : 10.1007 / BF02744530 .
- Charles Goebel: Selection Rules for NN̅ Annihilation . In: Phys. Rev. . 103, No. 1, 1956, pp. 258-261. doi : 10.1103 / PhysRev.103.258 .
- Christoph Berger: Particle Physics - An Introduction . Springer, Berlin 1992, pp. 110f, ISBN 978-3-540-54218-6