Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2005-03-16
Phys.Rev.C71:065204,2005
Physics
Nuclear Physics
Nuclear Theory
13 pages, 5 figures
Scientific paper
10.1103/PhysRevC.71.065204
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 \pi_n^0 \gamma \gamma coupling, 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 \gamma* \pi_n \gamma* transition form factor, T_{\pi_n}(Q^2), is nonzero for all n, and T_{\pi_n}(Q^2) \approx (4\pi^2/3) (f_{\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 behaviour is 1/Q^4 for n \neq 0, and we find numerically T_{\pi_1}(Q^2) \simeq (4\pi^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_{\pi_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.
Hoell Arne
Krassnigg Andreas
Maris Pieter
Roberts Christopher D.
Wright Stewart V.
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