Analysis of the Quantum Numbers $J^{PC}$ of the X(3872) Particle

We present an analysis of angular distributions and correlations of the $X(3872)$ particle in the exclusive decay mode $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ with $J/\psi \to {\mu }^{+}{\mu }^{-}$. We use $780{\mathrm{pb}}^{-1}$ of data from $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected with the CDF II detector at the Fermilab Tevatron. We derive constraints on spin, parity, and charge conjugation parity of the $X(3872)$ particle by comparing measured angular distributions of the decay products with predictions for different $J^{PC}$ hypotheses. The assignments $J^{PC}=1^{++}$ and $2^{-+}$ are the only ones consistent with the data.

Figure 1

The $J/\psi {\pi }^{+}{\pi }^{-}$ mass spectrum after optimizing the selection cuts, fitted by a double Gaussian function for the $\psi (2S)$ (left), a Gaussian function for the $X(3872)$ particle (right), and a second order polynomial for the combinatorial background.

Figure 2

Definition of the decay angles. The polar angles ($\theta$) are calculated from the parent momenta and the child momenta in the corresponding parent rest frame.

Figure 3

Measured 3D angular distribution with acceptance corrected predictions for $J^{PC}=0^{++}$ (solid line), $1^{++}$ (dotted line), $2^{-+}$ (dashed line), and $1^{--}$ (dash-dotted line). The plot is divided into $2\times 2$ regions, corresponding to intervals of $|\cos ({\theta }_{J/\psi })|$ and $|\cos ({\theta }_{\pi \pi })|$. Each region shows the distribution of $||\Delta \Phi -\pi |-\frac{\pi }{2}|$ in 3 bins. The bin contents have been scaled to the same bin volume.

Figure 4

Total ${\chi }^2$ for different analysis variations on the y-axis, explained in the text. Vertical bars are added for visual guidance. The ${\chi }^2$ values of the spin 0 states are all above 100. The $2^{--}$ and $3^{+-}$ states have the same angular distribution as the $1^{+-}$ state.