a large (&gt;10) mean number of detected photoelectrons. The effect on the remaining data is estimated to be &lt;10% and is included in the systematic uncertainty discussed in section \[sec:Results\].

![The measured photoelectron distributions for identical measurements using the two different photomultipliers (represented as the red and blue traces) in Detector A. The solid traces represent measurements taken downstream of the 2 GeV proton beam on a water target, and the dashed traces represent measurements taken upstream of the 475 MeV proton beam on a WbLS-2 target. The photomultiplier responses are similar for small and large numbers of photoelectrons.[]{data-label="fig:PMTresponse"}](PMTAblue_PMTBred_IdenticalMeasurements_withLegend_FatLines.pdf){width="0.8\columnwidth"}

   Instrument   Sample     Incident Proton Energy
  ------------ -------- -----------------------------
   Detector A   Water         2 GeV and 475 MeV
   Detector A   WbLS-2        2 GeV and 475 MeV
   Detector B   Water    210 MeV, 475 MeV, and 2 GeV
   Detector B   WbLS-1   210 MeV, 475 MeV, and 2 GeV
   Detector B   WbLS-2   210 MeV, 475 MeV, and 2 GeV
   Detector B     LS     210 MeV, 475 MeV, and 2 GeV

  : A summary of the proton beam exposures.

\[tab:BeamMeas\]

The data readout in all measurements was achieved using a CAEN V1729A 14 bit waveform digitizer sampling at 1 gigasamples per second. The raw waveforms were stored for 