Post-selection shifts the transition frequency of helium in an atomic beam

Post-selecting output states in measurements can effectively amplify weak signals and improve precision. However, post-selection effects may also introduce unintended biases in precision measurements. Here, we investigate the influence of post-selection in the precision spectroscopy of the 2^3S - 2^3P transition of helium $⁴$He using an atomic beam. We directly observe that post-selection based on atomic positions causes a shift in the measured transition frequency, amounting to approximately -55 kHz. After accounting for this post-selection shift, we obtain a corrected frequency of 276,764,094,712.45 pm 0.86 kHz for the 2^3S₁ - 2^3P₀ transition. Combining this result with existing data for ³He, we derive a new value for the difference in squared nuclear charge radii, δr² \[r_h² - r_α²\] = 1.0733 pm 0.0021 fm². This value shows a 2.8σ deviation from measurements of muonic helium ions, potentially pointing to new physics that challenges lepton universality in quantum electrodynamics.