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The GlueX experiment at Jefferson Lab studies photoproduction of mesons usinglinearly polarized $8.5\,\text{GeV}$ photons impinging on a hydrogen targetwhich is contained within a detector with near-complete coverage for chargedand neutral particles. We present measurements of spin-density matrix elementsfor the photoproduction of the vector meson $\rho$(770). The statisticalprecision achieved exceeds that of previous experiments for polarizedphotoproduction in this energy range by orders of magnitude. We confirm a highdegree of $s$-channel helicity conservation at small squared four-momentumtransfer $t$ and are able to extract the $t$-dependence of natural andunnatural-parity exchange contributions to the production process in detail. Weconfirm the dominance of natural-parity exchange over the full $t$ range. Wealso find that helicity amplitudes in which the helicity of the incident photonand the photoproduced $\rho(770)$ differ by two units are negligible for$-t<0.5\,\text{GeV}^{2}/c^{2}$.

Measurement of Spin-Density Matrix Elements in $\rho(770)$ Production with a Linearly Polarized Photon Beam at $E_\gamma = 8.2\,-\,8.8\,\text{GeV}$