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. Here we provide an in-depth analysis of the reaction $\gamma p \rightarrow \omega p$ at $\theta_{ c.m.}\sim 90^\circ$ using CLAS data with an energy range of $s = 5 - 8$ GeV$^2$, where the CCR has been shown to work in other reactions. We argue for a stringent method to select data to test the CCR and utilize a Taylor-series expansion to take advantage of data from nearby angle bins in our analysis. Na\"{ i}vely, this reaction would have $n=9$ (or $n=10$ if the photon is in a $q\bar{ q}$ state) and we would expect a scaling of $\sim s^{ -7}$ ($s^{ -8}$). Instead, a scaling of $s^{ -(9.08 \pm 0.11)}$ was observed. Explanations for this apparent failure of the na\"{ i}ve CCR assumptions are examined.
Categories: hep-ph nucl-ex nucl-th