Study of the lineshape of the $\chi_{c1}(3872)$ state.

A study of the lineshape of the $\chi_{c1}(3872)$ state is made using a data sample corresponding to an integrated luminosity of $3\,$fb$^{-1}$ collected in $pp$ collisions at centre-of-mass energies of $7$ and $8\,$TeV with the LHCb detector. Candidate $\chi_{c1}(3872)$ mesons from $b$-hadron decays are selected in the $ J/\psi \pi^+ \pi^-$ decay mode. Describing the lineshape with a Breit--Wigner function, the mass splitting between the $\chi_{c1}(3872)$ and $\psi(2S)$ states, $\Delta m$, and the width of the $\chi_{c1}(3872)$ state, $\Gamma_{\mathrm{BW}}$, are determined to be \begin{eqnarray*} \Delta m & = & 185.588 \pm 0.067 \pm 0.068\,{\mathrm{MeV}} \,, \\ \Gamma_{\mathrm{BW}} & = & \phantom{00}1.39\phantom{0} \pm 0.24\phantom{0} \pm 0.10\phantom{0}\,{\mathrm{MeV}} \,, \end{eqnarray*} where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired lineshape, two poles for the $~\chi_{c1}(3872)~$state in the complex energy plane are found. The dominant pole is compatible with a quasi-bound $D^0\bar{D}^{*0}~$state but a quasi-virtual state is still allowed at the level of $2~$standard deviations.