Data-Driven Modeling of Electron Recoil Nucleation in PICO C$_3$F$_8$ Bubble Chambers

The primary advantage of moderately superheated bubble chamber detectors is their simultaneous sensitivity to nuclear recoils from WIMP dark matter and insensitivity to electron recoil backgrounds. A comprehensive analysis of PICO gamma calibration data demonstrates for the first time that electron recoils in C$_3$F$_8$ scale in accordance with a new nucleation mechanism, rather than one driven by a hot-spike as previously supposed. Using this semi-empirical model, bubble chamber nucleation thresholds may be tuned to be sensitive to lower energy nuclear recoils while maintaining excellent electron recoil rejection. The PICO-40L detector will exploit this model to achieve thermodynamic thresholds as low as 2.8 keV while being dominated by single-scatter events from coherent elastic neutrino-nucleus scattering of solar neutrinos. In one year of operation, PICO-40L can improve existing leading limits from PICO on spin-dependent WIMP-proton coupling by nearly an order of magnitude for WIMP masses greater than 3 GeV c$^{-2}$ and will have the ability to surpass all existing non-xenon bounds on spin-independent WIMP-nucleon coupling for WIMP masses from 3 to 40 GeV c$^{-2}$.