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Based on the simple phenomenological $\sigma \pi \pi$, $\sigma N N$ and $\pi\pi \gamma$ interactions, we estimate the $\sigma$ exchange effect in the Lambshift of muonic hydrogen. We at first calculate the effective couplings of$\sigma\mu\mu$ by two photons and two pions exchange, then calculate thecorresponding corrections to the energy shift of the 2S/2P states of muonichydrogen. 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 usualtwo photons exchange contribution, and is larger than the current experimentalprecision, and should be considered in the experimental analysis.

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