Extended Data Table 4 Ratios \({{{\mathcal{R}}}}\) of spin-averaged transition frequencies

From: Test of charged baryon interaction with high-resolution vibrational spectroscopy of molecular hydrogen ions

  1. The unprimed ratios are dimensionless while the primed ratios \({{{{\mathcal{R}}}}}_{m,n}^{{\prime} }\) are dimensional and weakly depend on R∞. The omitted unit for column 5, rows 1 and 3, is Hz0.13, and for column 8, rows 1 and 3, is Hz0.14. In rows 6 - 8, the uncertainties due to the different fundamental constants are given individually, without considering correlations between the constants. The fractional uncertainties of the theoretical spin frequency values applied to the experimental frequencies are not included in row 2 but are listed in row 5, in the subsection of the theory values. In the total fractional uncertainty of the experiment - theory comparison (row 10), correlations between the uncertainties of the fundamental constants have been ignored, since they do not alter the result substantially. The lower half of the table (rows 11 - 19) presents the fractional contributions of various energy contributions to the theoretical ratios, as well as the normalized sensitivities on the mass ratios. The spin theory uncertainty is calculated assuming that the hyperfine theory uncertainties of the individual frequencies are not correlated, while for the QED theory uncertainty a correlation coefficient rQED = 0.95 is assumed. Taking into account the correlations of the hyperfine coefficients does not significantly change the experimental ratios and the total spin theory uncertainty.
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