Tomographic beta-gamma spectroscopy of nuclear beta decay

Nuclear $β$ decay, a sensitive probe of nuclear structure and weak interactions, has become a precision test bed for physics beyond the Standard Model, driven by recent advances in spectrometric techniques. Here we introduce tomographic $β$-$γ$ spectroscopy (TBGS) of nuclear $β$ decay, a method that detects the energies of $β$, $γ$, and internal conversion electrons while simultaneously reconstructing the energy deposition vertices. Using the PandaX-4T detector operated as a TBGS, we obtain a precise and unbiased decay scheme of $^{214}$Pb, a key background isotope in searches for dark matter and Majorana neutrinos. For the first time, transitions of $^{214}$Pb to both the ground and excited states of $^{214}$Bi are measured concurrently, revealing discrepancies in branching ratios of up to 4.7$σ$ relative to previous evaluations. Combined with state-of-the-art theoretical spectral-shape calculations, these results establish a new benchmark for background modelling in rare-event searches and highlight the potential of TBGS as a versatile tool for fundamental physics and nuclear applications.