G parity

Template:Short description In particle physics, G parity is a multiplicative quantum number that results from the generalization of C parity (charge conjugation) to multiplets of particles.

It was introduced by Louis Michel in 1953 as isotopic parity, and later introduced as G parity by T.D. Lee and C.N. Yang in 1956.

Description

Charge conjugation or C parity applies only to neutral systems. For example, in the pion triplet, only the neutral pion 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:

$𝒢:\left(\begin{array}{c}{\pi }^{+}\\ {\pi }^0\\ {\pi }^{-}\end{array}\right)={\eta }_G\left(\begin{array}{c}{\pi }^{+}\\ {\pi }^0\\ {\pi }^{-}\end{array}\right)$

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

$\widehat{𝒢}=\widehat{𝒞}{e}^{(i\pi {\hat{I}}_2)}$

where $\widehat{𝒞}$ is the C parity operator, and ${\hat{I}}_2$ is the operator associated with the 2nd component of the isospin "vector", which in case of isospin $I=1/2$ takes the form ${\hat{I}}_2={\sigma }_2/2$, where ${\sigma }_2$ is the second Pauli matrix. G-parity is a combination of charge conjugation and a π radians (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

$\overline{Q}=\overline{B}=\overline{Y}=0,$

where Q is the electric charge of the multiplet, B is the baryon number and Y of the hypercharge.

In general

${\eta }_{\mathrm{G}}={\eta }_{\mathrm{C}}(-1{)}^I$

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

Since no matter whether the system is fermion–antifermion or boson–antiboson, ${\eta }_{\mathrm{C}}$ always equals to $(-1{)}^{L+S}$, we have

${\eta }_{\mathrm{G}}=(-1{)}^{S+L+I}$.

See also

• Quark model

References

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