of Detector A for 475 MeV protons incident on WbLS-2 may be written as a similar expression, though without any WLS Cherenkov light component, as 475 MeV protons are at the Cherenkov production threshold: $$N_{up}(WbLS, 475~MeV) = N_{up}^{Scint}(WbLS, 475~MeV)% + N_{up}^{WLS(Scint)}(WbLS, 475 MeV)$$

The 2 GeV and 475 MeV protons experience stopping powers in water of 2.0 and 2.8 MeV/cm, respectively. It is possible estimate the difference in scintillation light yield at the different energies using the Birks quenching correction: $$Q(E) = \frac{\frac{dE}{dx}}{1 + k_{B}\frac{dE}{dx}}
\label{eqn:Birks}$$ where $E$ is the proton energy and $k_{B}$ is the quenching parameter. Note that equation \[eqn:Birks\] assumes a constant stopping power for the particles interacting in the tub. The corrected light yields can then be used to relate the number of scintillation photons measured using the 475 MeV proton beam with the 2 GeV proton beam: $$N_{up}(WbLS, 2~GeV) = \frac{Q(2 GeV)}{Q(475 MeV)}N_{up}(WbLS, 475~MeV) + N_{up}^{WLS(Ckov)}(WbLS, 2~GeV)
\label{eqn:WLSCkov}$$

Equations \[eqn:Up2GeV\] and \[eqn:WLSCkov\] permit the calculation of the relative contributions of the scintillation and Cherenkov processes to the measured signal in the upstream PMT. Our results indicate that in the upstream PMT for incident 2 GeV protons; for every detected photon that was produced by scintillation 