Observation of $\omega $ contribution in the $\chi_{c1} \left ( 3872 \right ) \to \pi ^{+} \pi ^{-} J/\psi $ decays

Resonant structure in the dipion mass spectrum produced via $B^{+} \to \chi _{c1}\left ( 3872 \right )K^{+}$, $\chi _{c1}\left ( 3872 \right )\to J/\psi \pi ^{+}\pi ^{-}$, with $J/\psi \to \mu ^{+}\mu ^{-}$ is analyzed using Run 1 and Run 2 data samples from the LHCb experiment. The spectrum is dominated by $\rho^{0} \to \pi ^{+} \pi ^{-}$, but cannot be discribed by this contribution alone. A significant $\omega \to \pi ^{+} \pi ^{-}$ contribution, interfering with $\rho^{0}$ is observed for the first time. This is a more significant observation ( > 7.1$\sigma $) of $\chi _{c1}\left ( 3872 \right )\to \omega J/\psi$ decays, than previously archieved with $\omega \to \pi ^{+} \pi ^{-} \pi ^{0}$ decays. The relative contribution of $\omega$ to the total $\chi _{c1}\left ( 3872 \right )\to J/\psi$ rate is at the level expected from the measured $\chi _{c1} \left ( 3872 \right ) \to \left ( \omega \to \pi ^{+}\pi ^{-}\pi ^{0} \right )J/\psi $ rate, if the interference between the $\rho^{0}$ and $\omega$ amplitudes is neglected, $\left (1.9\pm 0.4\pm 0.3 \right )%$. The interference enhances the importance of $\omega$ contribution by an order of magnitude to $\left (21.4\pm 2.3\pm 2.0\right )%$. The results support interpretations of the $\chi _{c1}\left ( 3872 \right )$ state as an exotic hadron, since its isospin violating $\rho^{0} J/\psi$ decay rate, relative to isospin conserving $\omega J/\psi$ decay, is an order of magnitude larger than expected for an ordinary charmonium state.