Theoretical transition frequencies beyond 0.1 ppb accuracy in H${}_2^{+}$, HD${}^{+}$, and antiprotonic helium

Abstract

We present improved theoretical calculations of transition frequencies for the fundamental transitions $(L=0,v=1)\to (L^{\prime }=0,v^{\prime }=0)$ in the hydrogen molecular ions H${}_2^{+}$ and HD${}^{+}$ with a relative uncertainty $4\cdot 10^{-11}$ and for the two-photon transitions in the antiprotonic helium atom with a relative uncertainty $10^{-10}$. To do that, the one-loop self-energy correction of order $\alpha (Z\alpha {)}^6$ is derived in the two Coulomb center approximation, and numerically evaluated in the case of the aforementioned transitions. The final results also include a complete set of other spin-independent corrections of order $m{\alpha }^7$. The leading order corrections of ${\alpha }^2{\ln }^3(Z\alpha {)}^{-2}(Z\alpha {)}^6$ are also considered that allows to estimate a magnitude of yet uncalculated contributions.

10 pages, 2 figure, to be submitted to PRA

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• Bounding Quantum Dark Forces
• Observation and calculation of the quasi-bound rovibrational levels of the electronic ground state of H${}_2^{+}$
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• Physics beyond the Standard Model from hydrogen spectroscopy
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