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

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