Measurement of the Dipion Mass Spectrum in $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ Decays

We measure the dipion mass spectrum in $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ decays using $360{\mathrm{pb}}^{-1}$ of $\overline{p}p$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected with the CDF II detector. The spectrum is fit with predictions for odd $C$-parity (${}^{3}S_1$, ${}^{1}P_1$, and ${}^{3}D_J$) charmonia decaying to $J/\psi {\pi }^{+}{\pi }^{-}$, as well as even $C$-parity states in which the pions are from ${\rho }^0$ decay. The latter case also encompasses exotic interpretations, such as a $D^0{\overline{D}}^{*0}$ molecule. Only the ${}^{3}S_1$ and $J/\psi \rho$ hypotheses are compatible with our data. Since ${}^{3}S_1$ is untenable on other grounds, decay via $J/\psi \rho$ is favored, which implies $C=+1$ for the $X(3872)$. Models for different $J/\psi -\rho$ angular momenta $L$ are considered. Flexibility in the models, especially the introduction of $\rho -\omega$ interference, enables good descriptions of our data for both $L=0$ and 1.

Figure 1

Examples of slices in dipion mass $m_{\pi \pi }$ of the $J/\psi {\pi }^{+}{\pi }^{-}$ mass distributions and their $X(3872)$ fits. The raw yields $N_X$ prior to efficiency corrections are quoted, and the arrow in the first panel marks the $X(3872)$ mass.

Figure 2

The CDF dipion mass spectrum for the $\psi (2S)$ with a fit of a QCD multipole expansion calculation for ${}^{3}S_1$ [22].

Figure 3

The dipion mass spectrum for the $X(3872)$ and fits to various hypotheses (see text). The fitted curve for the ${}^{1}P_1$ model is scaled up by a factor of 5 for better visibility.

Figure 4

A blowup of the $X(3872)$ spectrum with $J/\psi \rho$ fits which include $\rho -\omega$ interference (95° phase) with relative amplitudes set by ${\mathcal{R}}_{3/2}=1.0$. Fits for both $L=0$ (lines) and 1 (shaded regions) are shown, along with their decomposition into $\rho$, $\omega$, and interference terms. The inset shows $L=1$ fit probabilities as a function of $\varphi$ and $R_X$ in 5% contours.