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 $11.5\text{}\text{}{\mathrm{fb}}^{-1}$ 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 $\sigma \left[{e}^{+}{e}^{-}\to \gamma {\chi }_{c1}\left(3872\right)\right]B\left[{\chi }_{c1}\left(3872\right)\to {\pi }^{+}{\pi }^{-}\eta \right]$ 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 $R=B\left[{\chi }_{c1}\left(3872\right)\to {\pi }^{+}{\pi }^{-}\eta \right]/B\left[{\chi }_{c1}\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right]<0.12$ is given. These measurements provide important inputs for understanding the internal structure of the ${\chi }_{c1}\left(3872\right)$ resonance.