On this web page we present a limit on the mass splitting for the hypothesis that the measured X(3872) signal is produced by two different states with slightly different mass and we show an improved measurement of its mass.
The results were blessed in the B Physics Meeting on July 24, 2008.

We select X(3872) and &psi(2S) candidates in the decay mode J/&psi&pi&pi using an artificial neural network and a cut on the number of candidates per event.

To test the hypothesis whether the observed X(3872) signal stems from two different states, we fit the X(3872) mass signal with a Breit-Wigner function convoluted with a resolution function determined from simulation. Both functions contain a width scale factor that is a free parameter in the fit and therefore sensitive to the shape of the mass signal. The measured width scale factor is compared to the values seen in pseudo experiments which assume two states with given mass difference and ratio of events. The resolution in the simulated events is corrected for the difference between data and simulation measured for the &psi(2S).
The result of this hypotheses test shows that data is very well consistent with only one state. Under the assumption of two states with equal amount of observed events we set a limit of

&Delta m < 3.2 (3.6) MeV/c² at 90% (95%) C.L.

Since our signal is consistent with one peak we proceed and measure the X(3872) mass in an unbinned maximum likelihood fit. The systematic uncertainties are determined from the difference between the measured &psi(2S) mass and its world average value, the potential variation of the &psi(2S) mass as a function of kinematic variables and the difference in Q value between X(3872) and &psi(2S). Systematic effects due to the fit model are negligible. The measured X(3872) mass is:

m(X(3872)) = 3871.61 +- 0.16 (stat) +- 0.19 (syst) MeV/c².

The analysis is described in more detail in a public note.

The following figures are available for download:

• Figure 1 (eps, gif): Distribution of neural network output for signal and background events
• Figure 2 (eps, gif): Optimization of cut on the neural network output based on significance defined by number of selected MC events devided by square root of data events in the signal region
• Figure 3 (eps, gif): Effect of the neural network selection on the mass spectrum
• Figure 4 (eps, gif): Optimization of cut on the number of candidates per event based on significance defined by number of signal events devided by square root of signal plus background events in the signal region in data
• Figure 5 (eps, gif): Effect of the cut on the number of candidates on the mass spectrum
• Figure 6 (eps, gif): Distribution of width scale factor in simulated events with &Delta m = 0 compared to the value seen in data
• Figure 7a (eps, gif): Distribution of width scale factor in simulated events with &Delta m = 3.2 MeV/c² (90% C.L. limit) compared to the value seen in data
• Figure 7b (eps, gif): Distribution of width scale factor in simulated events with &Delta m = 3.6 MeV/c² (95% C.L. limit) compared to the value seen in data
• Figure 8 (eps, gif): 90% and 95% C.L. limits on the width scale factor as a function of the mass difference &Delta m
• Figure 9 (eps, gif): 90% and 95% C.L. upper limits on the mass difference &Delta m as function of the ratio of the two states
• Figure 10 (eps, gif): Projection of the unbinned maximum likelihood mass fit for the X(3872)
• Figure 11 (eps, gif): Projection of the unbinned maximum likelihood mass fit for the &psi(2S)
• Figure 12a (eps, gif): Dependence of the &psi(2S) mass on the transverse momentum of the &psi(2S)
• Figure 12b (eps, gif): Dependence of the &psi(2S) mass on the transverse momentum of the J/&psi
• Figure 13a (eps, gif): Dependence of the &psi(2S) mass on the transverse momentum of the &mu⁺
• Figure 13b (eps, gif): Dependence of the &psi(2S) mass on the transverse momentum of the &mu^-
• Figure 14a (eps, gif): Dependence of the &psi(2S) mass on the transverse momentum of the &pi⁺
• Figure 14b (eps, gif): Dependence of the &psi(2S) mass on the transverse momentum of the &pi^-
• Figure 15 (eps, gif): Dependence of the &psi(2S) mass on the transverse momentum of the dipion system
• Figure 16 (eps, gif): Overview of X(3872) mass measurements
• Figure 17 (eps, gif): Limit on mass difference derived from the mass measurements of CDF and B-factories