Pseudoscalar meson ($J^P=0^{-}$)

A meson with zero spin angular momentum and negative parity. The pion and kaon are familiar examples. Between two pseudoscalar mesons, parity conservation in the strong interaction forces the axial current matrix element to vanish, while the vector current has pseudoscalar-to-pseudoscalar form factors. The weak decay as a whole need not conserve parity.

The vacuum-to-meson axial-current normalization defined by $⟨0|{\bar{q}}_1{\gamma }^{\mu }{\gamma }^5{q}_2|P(p)⟩=i{f}_P{p}^{\mu }$. It controls exclusive weak annihilation rates. Ratios of tau lepton decays into kaons and pions determine $f_K|V_{us}|/(f_{\pi }|V_{ud}|)$; extracting the Cabibbo-Kobayashi-Maskawa matrix ratio alone requires independent hadronic input.

In the quark model, the light-flavour triplet and its antiquark conjugate give an octet and a singlet. A colour-singlet pair with orbital angular momentum zero and total spin zero has parity minus one, giving a pseudoscalar nonet. Its six outer weights are charged pions and four kaons. At the centre the octet contains the neutral pion and octet eta direction; the additional singlet direction gives a third state at the same weight.

These neutral isospin-zero pseudoscalar mesons have $J^{PC}=0^{-+}$. Their light-quark components mix the Eta octet state and eta singlet state. The singlet axial anomaly contributes to the unusually large eta-prime mass, while flavour breaking also affects both masses and the mixing. The simple orthogonal one-angle flavour model is useful for explaining the nonet; detailed decay-constant descriptions can require more than one parameter.

The heavier physical isoscalar member of the light pseudoscalar meson nonet. It mixes the octet and singlet flavor directions, and is distinct from the lighter eta meson; both occupy the central flavor weight.

Mixing of the Eta octet state and eta singlet state to produce physical neutral pseudoscalar mass eigenstates. It limits mass identities derived by treating the physical eta meson as a pure octet state.

The lighter physical neutral pseudoscalar meson in the eta and eta prime mesons system. The pure Eta octet state is a useful approximation to its flavor content, not its exact physical mass eigenstate.

This flavour combination is the invariant scalar in the octet and singlet in a fundamental SU3 tensor product. Its isospin and flavour hypercharge vanish. Although it shares the central weight with the Eta octet state, it lies in a different irreducible representation. Physical eta mixing and the singlet axial anomaly distinguish the mass eigenstates from the pure flavour directions.