The Constituent Counting Rule and Omega Photoproduction

The constituent counting ruling (CCR) has been found to hold for numerous hard, exclusive processes. It predicts the differential cross section at high energies and fixed $\cos \theta_{c.m.}$ should follow $ \frac{d \sigma}{dt} \sim \frac{1}{s^{n-2}}$, where $n$ is the minimal number of constituents involved in the reaction. An in-depth examination of applying the CCR to the reaction $\gamma p \rightarrow \omega p$ at $\theta_{c.m.}\sim 90^\circ$ is provided. CLAS data with an energy range of $s = 5 - 8$ GeV$^2$, where the CCR has been shown to work in other reactions, is used in this analysis. The data selected to test the CCR is done so on the basis of momentum transfer, the Mandelstam variable $t$. A Taylor-series expansion of the fitting function is implemented to take advantage of data from nearby angle bins in the analysis. Na\"{i}vely, this reaction would have $n=9$ (or $n=10$ if the photon is in a $q\bar{q}$ state) and scaling of $\sim s^{-7}$ ($s^{-8}$) is expected. Instead, a scaling of $s^{-(9.08 \pm 0.11)}$ was observed.