Electromagnetic properties of ground-state 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 ${\ensuremath{\pi}}_{n}^{0}\ensuremath{\gamma}\ensuremath{\gamma}$ coupling, where $n=0$ denotes the Goldstone mode, is affected by the Abelian anomaly's continuum contribution. The effect is material for $n\ensuremath{\ne}0$. The ${\ensuremath{\gamma}}^{*}{\ensuremath{\pi}}_{n}{\ensuremath{\gamma}}^{*}$ transition form factor, ${\mathcal{T}}_{{\ensuremath{\pi}}_{n}}({Q}^{2})$, is nonzero $\ensuremath{\forall}n$, and ${\mathcal{T}}_{{\ensuremath{\pi}}_{n}}({Q}^{2})\ensuremath{\approx}(4{\ensuremath{\pi}}^{2}/3)({f}_{{\ensuremath{\pi}}_{n}}/{Q}^{2})$ 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 behavior is $1/{Q}^{4}$ for $n\ensuremath{\ne}0$, and we find numerically ${\mathcal{T}}_{{\ensuremath{\pi}}_{1}}({Q}^{2})\ensuremath{\simeq}(4{\ensuremath{\pi}}^{2}/3)(\ensuremath{-}\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}/{Q}^{4})$. This subleading power-law behavior is always present. In general its coefficient is not simply related to ${f}_{{\ensuremath{\pi}}_{n}}$. The properties of $n\ensuremath{\ne}0$ pseudoscalar mesons are sensitive to the pointwise behavior of the long-range piece of the interaction between light quarks.