Accurate Charge Radius Measurement of $^{14}$C Confronts \textit{Ab Initio} Theory

Located at the neutron shell closure $N = 8$, the long-lived radioactive isotope \(^{14}\mathrm{C} \) plays a critical role in geochronology and nuclear structure studies. Despite its widespread use, the nuclear charge radius of $^{14}$C has remained less precisely known compared to its stable counterpart $^{12}$C. Here, we report a high-precision determination of the $^{14}$C charge radius using collinear laser spectroscopy at the COALA setup at TU Darmstadt, improving upon the precision of previous muonic measurements by a factor $5$ and revealing a $1.9σ$ discrepancy of combined uncertainty, indicating a likely underestimated uncertainty in the muonic determination. This measurement challenges state-of-the-art \textit{ab initio} nuclear theory calculations, including auxiliary field diffusion Monte Carlo, the valence-space in-medium similarity renormalization group, and the no-core shell model, augmented by neural-network techniques. With $^{12}$C and $^{14}$C now forming one of the most precisely characterized even-even isotope pairs, these results also enable improved QED tests.