Direct Measurement of the ${}^{212}\mathrm{P}\mathrm{b}$ and ${}^{214}\mathrm{P}\mathrm{b}$ $\beta$ Decay Branching Ratios with the XENONnT Experiment

We present precision measurements of ${}^{212}\mathrm{P}\mathrm{b}$ and ${}^{214}\mathrm{P}\mathrm{b}$ $\beta$ decay branching ratios using ${}^{220}\mathrm{R}\mathrm{n}$ and ${}^{222}\mathrm{R}\mathrm{n}$ calibration data from the XENONnT detector, a dual-phase liquid xenon time projection chamber. Characterizing these isotopes is critical, as they lead to significant low-energy backgrounds in rare-event searches. We report ground-state branching ratios of $(14.75\pm 0.20(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-0.40}^{+0.14}(\mathrm{s}\mathrm{y}\mathrm{s}))\mathrm{\%}$ for ${}^{212}\mathrm{P}\mathrm{b}$ and $(9.8\pm 0.3(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-0.2}^{+0.8}(\mathrm{s}\mathrm{y}\mathrm{s}))\mathrm{\%}$ for ${}^{214}\mathrm{P}\mathrm{b}$, providing the most precise direct measurements of these transitions to date. These results contribute to enhancing background modeling for dark matter and neutrino experiments, improving sensitivity to solar neutrinos and physics beyond the Standard Model.