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

Using a data sample corresponding to an integrated luminosity of $10.9{\mathrm{fb}}^{-1}$ collected at center-of-mass energies from 4.16 to 4.34 GeV with the BESIII detector, we search for the decay ${\chi }_{c1}\left(3872\right)\to {\pi }^{+}{\pi }^{-}{\chi }_{c1}$ in the radiative production $e^{+}{e}^{-}\to \gamma {\chi }_{c1}\left(3872\right)$. No significant signal is observed, and the ratio for the branching fraction of ${\chi }_{c1}\left(3872\right)\to {\pi }^{+}{\pi }^{-}{\chi }_{c1}$ to ${\chi }_{c1}\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi$ is measured as $R\equiv \frac{B\left[{\chi }_{c1}\right(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{c1}]}{B\left[{\chi }_{c1}\right(3872)\to {\pi }^{+}{\pi }^{-}J/\psi ]}<0.18$ at 90% confidence level. An upper limit on the product of the cross section $\sigma [e^{+}{e}^{-}\to \gamma {\chi }_{c1}(3872\left)\right]$ and the branching fraction $B\left[{\chi }_{c1}\right(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{c1}]$ at each center-of-mass energy is also given. These measurements favor the nonconventional charmonium nature of the ${\chi }_{c1}\left(3872\right)$ state.