Data analysis techniques, differential cross sections, and spin density matrix elements for the reaction $\gamma p \rightarrow \phi p$

See paper for full list of authors - 38 pages, 36 figures. arXiv admin note: substantial text overlap with arXiv:1006.0374High-statistics measurements of differential cross sections and spin density matrix elements for the reaction $\gamma p \to \phi p$ have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies ($\sqrt{s}$) from 1.97 to 2.84 GeV, with an extensive coverage in the $\phi$ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the $\phi$ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- ($\phi \to K^+ K^-$) and neutral- ($\phi \to K^0_S K^0_L$) $K\overline{K}$ decay modes of the $\phi$. Further, for the charged mode, we differentiate between the cases where the final $K^-$ track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed $\phi$ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide $\sqrt{s}$ bins for the charged- and the neutral-mode, respectively. Possible effects from $K^+ \Lambda^\ast$ channels with $p K\overline{K}$ final-states are discussed. These present results constitute the most precise and extensive $\phi$ photoproduction measurements to date and in conjunction with the $\omega$ photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction