Summary
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.
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Yamada, M. Consistency and inconsistency of the pion wave function. Lett. Nuovo Cimento 41, 405–408 (1984). https://doi.org/10.1007/BF02739592
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DOI: https://doi.org/10.1007/BF02739592