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

We present an analysis of the mass of the $X(3872)$ reconstructed via its decay to $J/\psi {\pi }^{+}{\pi }^{-}$ using $2.4{\mathrm{fb}}^{-1}$ of integrated luminosity from $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$, collected with the CDF II detector at the Fermilab Tevatron. The possible existence of two nearby mass states is investigated. Within the limits of our experimental resolution the data are consistent with a single state, and having no evidence for two states we set upper limits on the mass difference between two hypothetical states for different assumed ratios of contributions to the observed peak. For equal contributions, the 95% confidence level upper limit on the mass difference is $3.6\mathrm{MeV}/c^2$. Under the single-state model the $X(3872)$ mass is measured to be $3871.61\pm 0.16(\mathrm{stat})\pm 0.19(\mathrm{syst})\mathrm{MeV}/c^2$, which is the most precise determination to date.

Figure 1

Invariant mass distribution of the $X(3872)$ candidates. The points show the data distribution, the full line is the projection of the unbinned maximum-likelihood fit, and the dashed line corresponds to the background part of the fit. The inset shows an enlargement of the region around the $X(3872)$ peak. Residuals of the data with respect to the fit are displayed below the mass plot.

Figure 2

Distribution of the width scale $t$ for generated experiments using the single-state hypothesis (histogram). Also shown is the measured value from data (vertical line).

Figure 3

The upper limit on the mass difference $\Delta m$ between two states as a function of the fraction $f_1$ of the yield of the lower mass state.