Measurement of Spin-Density Matrix Elements in $\phi (1020)\to K_S^0{K}_L^0$ Photoproduction with a Linearly Polarized Photon Beam at $E_{\gamma }=8.2-8.8$ GeV

We measure the spin-density matrix elements (SDMEs) for the photoproduction of $\phi (1020)$ off of the proton in its decay to $K_S^0{K}_L^0$, using 105 pb${}^{-1}$ of data collected with a linearly polarized photon beam using the GlueX experiment. The SDMEs are measured in nine bins of the squared four-momentum transfer $t$ in the range $-t=0.15-1.0$ GeV${}^2$, providing the first measurement of their $t$-dependence for photon beam energies $E_{\gamma }=8.2-8.8$ GeV. We confirm the dominance of Pomeron exchange in this region, and put constraints on the contribution of other Regge exchanges. We also find that helicity amplitudes where the helicity of the photon and the $\phi (1020)$ differ by two units are negligible.