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 other hand, strong interaction does not see electrical charge, so it cannot distinguish amongst π+, π0 and π−. We can generalize the C-parity so it applies to all charge states of a given multiplet:

𝒢^(π+π0π−)=ηG(π+π0π−)

where ηG = ±1 are the eigenvalues of G-parity. The G-parity operator is defined as

𝒢^=𝒞^e(iπI^2)

where 𝒞^ is the C-parity operator, and I^2 is the operator associated with the 2nd component of the isospin "vector", which in case of isospin I=1/2 takes the form I^2=iσ2/2, where σ2 is the second Pauli matrix. G-parity is a combination of charge conjugation and a π rad (180°) rotation around the 2nd axis of isospin space. Given that charge and isospin are preserved by strong interactions, so is G. Weak and electromagnetic interactions, though, does not conserve G-parity.

Since G-parity is applied on a whole multiplet, charge conjugation has to see the multiplet as a neutral entity. Thus, only multiplets with an average charge of 0 will be eigenstates of G, that is

Q¯=B¯=Y¯=0

(see Q, B, Y).

In general

ηG=ηC(−1)I

where ηC is a C-parity eigenvalue, and I is the isospin.

Since no matter whether the system is fermion–antifermion or boson–antiboson, ηC always equals to (−1)L+S, we have

ηG=(−1)S+L+I.

## See also

* Quark model

## References

* T. D. Lee and C. N. Yang (1956). "Charge conjugation, a new quantum number G, and selection rules concerning a nucleon-antinucleon system". Il Nuovo Cimento 3 (4): 749–753. doi:10.1007/BF02744530. Bibcode: 1956NCim....3..749L.
* Charles Goebel (1956). "Selection Rules for NN̅ Annihilation". Phys. Rev. 103 (1): 258–261. doi:10.1103/PhysRev.103.258. Bibcode: 1956PhRv..103..258G.

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