0.0         4.5 $\pm$ 0.5
   WbLS-2          2000 MeV            Downstream        21.5 $\pm$ 0.3       20.4 $\pm$ 2.0
   WbLS-2          2000 MeV             Upstream         7.7 $\pm$ 0.2         7.3 $\pm$ 0.7

\[tab:MeansDetA\]

The simulated results used the optimised values of WbLS-2’s light yield and quenching from the Detector B analysis. Whilst fairly good agreement is obtained using these values, the shape of the simulated photoelectron distribution is in general broader than that of the measured distribution. The cause for this behaviour is not fully understood. We have also performed a $\chi^2$ optimisation of the simulated distribution to the measured one by adjusting the simulated light yield using the 475 MeV proton irradiation data. These results suggest an optimal light yield of 109.0 $\pm$ 1.0 and 110.2 $\pm$ 1.0 photons per MeV using the downstream and upstream PMTs, respectively. The uncertainties relate only the statistical uncertainty arising from the $\chi^2$ analysis of the simulated data, and we estimate an additional 10% systematic uncertainty. This good agreement with the Detector B analysis suggests that the model can consistently describe different measurement geometries.

![image](NumPE_MeasVsSim_ALL_150812_v2_dashed.pdf){width="\textwidth"}

For the 2 GeV proton measurements, many more photons were observed in the downstream PMT than the upstream PMT due to the directional Cherenkov radiation. However, 