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

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