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Ultra-high finesse cavity-enhanced spectroscopy for accurate tests of quantum electrodynamics for molecules

We report the most accurate measurement of the position of the weak quadrupole S(2) 2-0 line in D$_2$. The spectra were collected with a frequency-stabilized cavity ring-down spectrometer (FS-CRDS) with an ultra-high finesse optical cavity ($\mathcal{F}$ = 637 000) and operating in the frequency-agile, rapid scanning spectroscopy (FARS) mode. Despite working in the Doppler-limited regime, we reached 40 kHz of statistical uncertainty and 161 kHz of absolute accuracy, achieving the highest accuracy for homonuclear isotopologues of molecular hydrogen. The accuracy of our measurement corresponds to the fifth significant digit of the leading term in QED correction. We observe 2.3$σ$ discrepancy with the recent theoretical value.