Electromagnetic properties of ground-state and excited-state pseudoscalar mesons

The axial-vector Ward-Takahashi identity places constraints on particular properties of every pseudoscalar meson. For example, in the chiral limit all pseudoscalar mesons, except the Goldstone mode, decouple from the axial-vector current. Nevertheless, all neutral pseudoscalar mesons couple to two photons. The strength of the π_n⁰γγ coupling, where n=0 denotes the Goldstone mode, is affected by the Abelian anomaly's continuum contribution. The effect is material for n≠0. The γ^*π_nγ^* transition form factor, T_πn(Q²), is nonzero ∀n, and T_πn(Q²)≈(4π²/3)(f_πn/Q²) at large Q². For all pseudoscalars but the Goldstone mode, this leading contribution vanishes in the chiral limit. In this instance the ultraviolet power-law behavior is 1/Q⁴ for n≠0, and we find numerically T_π1(Q²)≃(4π²/3)(-〈q̅ q〉/Q⁴). This subleading power-law behavior is always present. In general its coefficient is not simply related to f_πn. The properties of n≠0 pseudoscalar mesons are sensitive to the pointwise behavior of the long-range piece of the interaction between light quarks.