Electromagnetic properties of ground and excited state pseudoscalar mesons

Abstract

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_n^0 γγcoupling, where n=0 denotes the Goldstone mode, is affected by the Abelian anomaly's continuum contribution. The effect is material for n \neq 0. The γ* π_n γ* transition form factor, T_{π_n}(Q^2), is nonzero for all n, and T_{π_n}(Q^2) \approx (4π^2/3) (f_{π_n}/Q^2) at large Q^2. For all pseudoscalars but the Goldstone mode, this leading contribution vanishes in the chiral limit. In this instance the ultraviolet power-law behaviour is 1/Q^4 for n \neq 0, and we find numerically T_{π_1}(Q^2) \simeq (4π^2/3) (-<\bar q q>/Q^4). This subleading power-law behaviour is always present. In general its coefficient is not simply related to f_{π_n}. The properties of n \neq 0 pseudoscalar mesons are sensitive to the pointwise behaviour of the long-range piece of the interaction between light-quarks.