Extended Data Table 2 Contributions to the ab initio spin averaged frequency f5(theor)

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

  1. The computation, using NRQED theory, follows refs. 2. For the present transition frequency, a total of 41 individual contributions were calculated for both upper and lower rovibrational levels by V. I. Korobov. The relative order is relative to the transition frequency itself. The main contribution to \({f}_{5}^{({{{\rm{theor}}}})}\) is the accurate solution of the non-relativistic three-body problem (relative order α0). This is complemented by contributions that scale, relative to the main contribution, as the 2nd to 6th power of the fine-structure constant α. The term of relative order α2 includes the effects of overlap of the electron’s wavefunction with the finite-size proton and deuteron. These effects contribute –70.0(3)CODATA18 kHz and –465.9(3)CODATA18 kHz, respectively, to the transition frequency. We point out that the contribution of relative order α6 includes also a recently calculated term that scales as \({R}_{\infty }{\alpha }^{6}{(\log {\alpha }^{-2})}^{2}\), amounting to 10.02 kHz for the transition frequency. Additional contributions are from muon-antimuon and hadronic vacuum polarization in the electron propagator2. The fractional contributions are indicated in ED Table 1, column 2, rows 12 to 17.
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