Beam performance and data-constrained optical modeling of a UV-transmitting acrylic Cherenkov counter for hadron identification

A threshold Cherenkov counter based on ultraviolet-transmitting (UVT) acrylic has been developed for hadron identification in the S-2S spectrometer at J-PARC. Three 730 mm $\times$ 100 mm $\times$ 50 mm radiators were beam tested: polished UVT acrylic without WLS, UVT acrylic roughened on the four long surfaces without WLS, and polished UVT acrylic containing 10 ppm by mass bis-MSB as a wavelength shifter (WLS). The polished/WLS prototype gave the largest two-ended photoelectron yield among the tested configurations. At a 1-photoelectron software-SUM threshold, its measured detection efficiency remained above 99% throughout the scanned longitudinal range, with no significant degradation up to an average extracted-particle rate of approximately $2.5\times10^{5}~{\rm s^{-1}}$ during beam delivery. Beam observables constrained a Geant4 optical model with one common detector response scale and no PMT-specific response tuning. The model reproduces the observed response hierarchy and main longitudinal trends. In the central |y| < 200 mm region, simulated and measured MPV estimators for the calibration configurations typically agree within about 15%, while larger deviations occur toward the radiator ends, especially for rough/no-WLS. With the calibrated parameters fixed, the model was used to compare unmeasured detector configurations and quantify the momentum dependence of $K^{+}$/p discrimination. In the central, normal incidence geometry, a 90% $K^{+}$-survival working point is predicted to keep proton survival below 3% up to about 1.8 GeV/c. The measurements and constrained extrapolations support the polished UVT/WLS configuration for S-2S and quantify its expected particle-identification reach beyond the simple threshold regime.