Soft Pionization by Two Photons

Abstract

Using the soft-pion technique with partial conservation of the axial-vector current and the algebra of currents, we express the amplitudes for $\gamma +\gamma \to n{\pi }^{+}+n{\pi }^{-}$ in terms of the spectral functions of the vector and axial-vector currents and calculate the cross sections for $\gamma +\gamma \to n{\pi }^{+}+n{\pi }^{-}$, $e^{\pm }+e^{-}\to e^{\pm }+e^{-}+n{\pi }^{+}+n{\pi }^{-}$, and $e^{+}+e^{-}\to n{\pi }^{+}+n{\pi }^{-}+\gamma$. Gauge invariance is maintained throughout the calculation if, and only if, Weinberg's first sum rule is valid.