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Virtual Delbr\"uck scattering and the Lamb shift in light hydrogen-like atoms

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arxiv 1909.04116 v1 pith:JPCWQAJP submitted 2019-09-09 physics.atom-ph hep-ph

classification physics.atom-phhep-ph
keywords light-by-lightalphaeffectivescatteringatomscontributiondelbrenergy
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abstract

We return to the problem of evaluation of the light-by-light contribution to the energy levels of the hydrogen atom. We find an additional contribution directly related to the Delbr\"uck scattering amplitude. The new correction is larger than the previously included light-by-light terms at order~$\alpha^2 (Z\alpha)^6\ln(Z\alpha)\, m_e$. We consider the effective potential in position space using an effective field theory approach and evaluate light-by-light corrections to the energy levels of states with non-zero orbital momentum as well as to the weighted difference of $s$ states. We also determine the large distance asymptotic behaviour of the effective potential induced by the light-by-light scattering in muonic atoms.

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    A five-stage EFT tower factorizes QED corrections to muon conversion and decay-in-orbit near the endpoint, yielding a resummed NLL-corrected signal shape.

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