Simulation of the spatial shift in detector response for polarized protons within a calorimeter

Measurement of the helicity dependent elastic electron-proton scattering cross section provides a key means of investigating parity violation within the proton. However, such measurements exhibit potential instrumental effects associated with the detection of polarized recoiled protons. In particular, spin-orbit interactions within a massive detector induce a systematic spatial shift in the detector signal. In this study, we determine the size of this shift using the Geant4 simulation toolkit. For a typical hadron calorimeter, we found a polarization dependent shift on the order of 0.01-0.1 mm, multiple orders of magnitude smaller than the typical spatial resolution seen in hadronic calorimeters. Additionally, we provide the custom modifications required of the Geant4 source code to implement the quasi-elastic scattering of polarized protons incident on nuclei in the detector. The modifications are readily extendable to generic matter sources, and can be used for the study of additional spin dependent observables in Geant4.