The $\sigma$ exchange effect in the Lamb shift of muonic hydrogen by two photons and two pions exchange

Hai-Qing Zhou

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arXiv · 1608.06460

The $\sigma$ exchange effect in the Lamb shift of muonic hydrogen by two photons and two pions exchange

Hai-Qing Zhou

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Abstract

Based on the simple phenomenological $\sigma \pi \pi$, $\sigma N N$ and $\pi \pi \gamma$ interactions, we estimate the $\sigma$ exchange effect in the Lamb shift of muonic hydrogen. We at first calculate the effective couplings of $\sigma\mu\mu$ by two photons and two pions exchange, then calculate the corresponding corrections to the energy shift of the 2S/2P states of muonic hydrogen. We find the correction to the energy shift of 2S state is about -14$\mu$eV by the current used parameters, which is about $44\%$ of the usual two photons exchange contribution, and is larger than the current experimental precision, and should be considered in the experimental analysis.

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Hai-Qing Zhou. 2016-08-23. The $\sigma$ exchange effect in the Lamb shift of muonic hydrogen by two photons and two pions exchange. https://arxiv.org/abs/1608.06460

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