Consistency and inconsistency of the pion wave function
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The Van Royen-Weisskopf relation is extended to incorporate the second-order electromagnetic decay of the neutral pion. Using this result, we connect the decay rate of the process π0 → 2γ to the square of the absolute value of the pion wave function at zero distance ¦ϕ(0)¦2 through the effective quark propagator. This connection is compared with the result from the anomalous Ward-Takahashi identity for the axial vector current. It is shown that previously noticed disagreement on ϕ(0)¦2 of the pion wave function is solved if the quark propagator is parametrized like a free propagator with a mass of the same order as the constituent quark mass.
PACS14.40 Mesons and meson resonances
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- (7).Particle Data group:Rev. Mod. Phys.,56, No. 2, Part. II (1984)Google Scholar