Parity-Violating Photoproduction of ${\mathit{\pi }}^{\pm }$ on the $\mathit{\Delta }$ Resonance

We analyze the real-photon asymmetry $A_{\gamma }^{\pm }$ for the parity-violating (PV) ${\pi }^{\pm }$ production on the $\Delta$ resonance via the reactions $\overrightarrow{\gamma }+p\to {\Delta }^{+}\to {\pi }^{+}+n$ and $\overrightarrow{\gamma }+d\to {\Delta }^0+p\to {\pi }^{-}+p+p$. This asymmetry is nonvanishing due to a PV $\gamma N\Delta$ coupling constant, $d_{\Delta }^{\pm }$. We argue that an experimental determination of this coupling would be of interest for hadron dynamics, possibly shedding light on the $S$-wave/ $P$-wave puzzle in the hyperon nonleptonic decays and the violation of Hara’s theorem in weak radiative hyperon decays.