We report a measurement of the $pi^-$ photoproduction beam asymmetry for the reaction $vec{gamma} p rightarrow pi^- Delta^{++}$ using data from the GlueX experiment in the photon beam energy range 8.2--8.8 GeV. The asymmetry $Sigma$ is measured as a function of four-momentum transfer $t$ to the $Delta^{++}$ and compared to phenomenological models. We find that $Sigma$ varies as a function of $t$: negative at smaller values and positive at higher values of $|t|$. The reaction can be described theoretically by $t$-channel particle exchange requiring pseudoscalar, vector, and tensor intermediaries. In particular, this reaction requires charge exchange, allowing us to probe pion exchange and the significance of higher-order corrections to one-pion exchange at low momentum transfer. Constraining production mechanisms of conventional mesons may aid in the search for and study of unconventional mesons. This is the first measurement of the process at this energy.
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