Characterization of the Polarization Beam Response of SPT-3G Using Point Sources

Precise measurements of cosmic microwave background polarization require rigorous control of instrumental systematics. For the South Pole Telescope's third-generation camera (SPT-3G), accurate characterization of the beam is critical for understanding the polarized mm-wave sky. Here, we present direct measurements of SPT-3G's polarized beam response using observations of 100 polarized extragalactic point sources. Previous SPT-3G CMB power spectrum analyses introduced a phenomenological parameter $\beta_\mathrm{pol}$ to describe the degree of polarization preserved in beam sidelobes. These analyses found evidence for significant depolarization driven by the requirement of polarization power spectrum consistency between different frequency bands. Our direct measurements yield $\beta_\mathrm{pol}=0.90\pm0.10$ at 95 GHz, $1.01\pm0.12$ at 150 GHz, and $0.81\pm0.29$ at 220 GHz, indicating minimal sidelobe depolarization. We validate these results through extensive systematic tests including Bayesian posterior sampling versus frequentist bootstrap resampling, real-space versus Fourier-space analysis, and variations on temperature-to-polarization leakage handling, covariance determination, and source selection. When compared to values inferred from previous cosmological analyses, which favored significant depolarization to resolve inter-frequency power spectrum inconsistencies, we find a mild tension of $1.9\sigma$. However, this apparent discrepancy is dependent on the beam modeling, as our point source-based analysis derives much of its constraining power on $\beta_\mathrm{pol}$ from higher multipoles than the power spectrum analysis. These measurements therefore admit three explanations for the frequency-dependent residuals observed in the power spectrum analysis: a statistical fluctuation, the need for more sophisticated polarized beam models, or systematics other than beam depolarization.