Interacting dark energy (IDE) models offer a promising avenue to explore possible exchanges of energy and momentum between dark matter and dark energy, providing a dynamical extension of the standard $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) paradigm. Such interactions modify the growth of cosmic structures, imprinting distinctive signatures on the matter power spectrum that can be tested through large-scale structure (LSS) observations. In this work, we compute the one-loop corrections to the matter power spectrum in IDE models. We then reinterpret these results within the standard framework of the effective field theory of large-scale structure (EFTofLSS), which provides a consistent description of mildly nonlinear scales and allows for reliable comparisons with observational data. We investigate two commonly studied forms of the coupling function, $Q$, namely $Q=\xi \mathcal{H}{\rho }_{\mathrm{m}}$ and $Q=\xi \mathcal{H}{\rho }_{\mathrm{DE}}$, and introduce a novel interaction term, $Q=\mathrm{\Gamma }{\rho }_{\mathrm{m}}{\rho }_{\mathrm{DE}}{\theta }_{\mathrm{m}}$, characterized by the nonlinear coupling constant $\mathrm{\Gamma }$, which links the interaction strength to the velocity divergence of dark matter. This coupling function is proposed to isolate the effects solely of the IDE model on mildly nonlinear scales. Using full-shape (FS) measurements of the galaxy power spectrum from BOSS DR12, we constrain the interaction rate $\mathrm{\Gamma }$, the cosmological parameters, and the bias parameters. We find $\mathrm{\Gamma }=0.0039\pm 0.0082$, which is highly consistent with the $\mathrm{\Lambda }\mathrm{CDM}$ model. This work opens the possibility of testing IDE models at mildly nonlinear scales, potentially providing new insights for this class of models beyond the standard $\mathrm{\Lambda }\mathrm{CDM}$ framework.

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• Cosmological parameters
• Dark energy