Search for the light hadron decay ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}\eta$

With a data sample corresponding to an integrated luminosity of 11.5~fb${}^{-1}$ collected with the BESIII detector operating at the BEPCII storage ring, for the first time the light hadron decay ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}\eta$ is searched for. While no significant signal is observed, the upper limits at the 90% confidence level for $\sigma [e^{+}{e}^{-}\to \gamma {\chi }_{c1}(3872)]\mathcal{B}[{\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}\eta ]$ at center-of-mass energies from 4.13 to 4.34 GeV are determined. By normalizing to the ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}J\mathrm{/}\psi$ decay channel, a 90% confidence level upper limit for the branching fraction ratio $\mathcal{R}=\mathcal{B}[{\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}\eta ]\mathrm{/}\mathcal{B}[{\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}J\mathrm{/}\psi ]<0.12$ is given. These measurements provide important inputs for understanding the internal structure of the ${\chi }_{c1}(3872)$ resonance.