Deep-Inelastic Processe−+γ→e−+nπ+nπ−

The deep-inelastic process $e^{-}+\gamma \to e^{-}+n{\pi }^{+}n{\pi }^{-}$ is considered. The differential cross section for this process is calculated using the matrix element for $\gamma +\gamma \to n{\pi }^{+}n{\pi }^{-}$ which has been derived by Terazawa in the soft-pion limit. Expressions are given for the photon structure functions, $W_1^{\gamma }(q^2, \nu )$ and $W_2^{\gamma }(q^2, \nu )$, due to the contribution of the $n{\pi }^{+}n{\pi }^{-}$ hadronic system. The photon structure functions derived are seen to obey the Bjorken limiting assumption.