We present a measurement of the production polarization of mesons produced in collisions at with the CDF detector at Fermilab. This measurement is a sensitive test of the Color Octet Model (COM) suggested as the explanation for the unexpectedly large cross section for charmonium production in collisions (roughly a factor 50 above the Color Singlet Model). A prediction of the COM is that directly produced charmonia should approach 100 transverse polarization for high transverse momentum of the onium state. We consider mesons, reconstructed using the decay mode in a 110 pb data sample of collisions. The polarization of prompt is extracted to be for GeV/.
Measurements of both direct and cross sections by CDF  are times higher than Color Singlet Model predictions . By ``direct'', we mean the charmonia produced directly from the collisions, and not those from particle decays such as , , etc. One of the theoretical models which tries to explain this anomalous production is the Color Octet Model (COM) . The model raises the direct production cross section by including color-octet states in the fragmentation process. At leading order in and at high (, where is the charm quark mass), the contribution to the cross section is dominated by gluon fragmentation into the color octet states. The fragmenting gluon, being effectively on-shell at high , is transversely polarized. The pair and subsequently the and mesons inherit the gluon's transverse polarization. Therefore, COM predicts the direct and the to approach 100 transverse polarization at high . Observation of such a polarization would support the color-octet fragmentation mechanism.
Experimentally, the is a clean channel to test the COM. The displacement of the vertex from the primary can be used to distinguish prompt (direct) production from B decays. In the case of the , the prompt production is contaminated with feed-down like .
Using spin formalism , the angular distribution
is derived to be:
where is the polarization and denotes the angle between the momentum in the rest frame and the momentum in the Lab frame. Unpolarized mesons would have whereas and -1 correspond to fully transverse and longitudinal polarizations respectively. The value of is extracted from the data by fitting the reconstructed angular distribution after acceptance corrections.
This analysis is based on a 110 pb sample of low dimuon triggers collected by CDF during 1992-95. Both muons are required to pass standard quality cuts and to be reconstructed in the silicon vertex detector (SVX). In addition, they are required to have larger than 2.0 GeV/ (in the Run 1A sample, the high muon is required to have larger than 2.8 GeV/). The selected dimuons are vertex constrained to form the candidates. A cut larger than 5.5 GeV/ is imposed on the candidates. The reconstructed dimuon mass distribution after the selection cuts is shown in Figure 1. It is fitted with a gaussian plus linear background. We find signal candidates. In a mass window around the mass, the signal to background ratio (S/B) is .
To study the dependence of the polarization, we divide the
data sample into three ranges (5.5-7, 7-9 and 9-20
Each sample is further divided
into two sub-samples based on the distribution.
ct is related to the transverse decay length as follows:
where m is the reconstructed mass. The factor is an average correction factor obtained from Monte Carlo studies to account for the fact that we use instead of . The low ct region (-0.1<ct<0.01 cm) is prompt enriched whereas the high ct region (ct>0.01 cm) is dominated by B decays.
The value of for each candidate is calculated from the momentum vectors of the muons, and the mass and momentum of the reconstructed . Since the angular distribution is symmetric, the absolute value of is used, and subdivided into 10 bins. The mass distribution in each bin is fit with a gaussian and linear background to determine the number of observed signal events. The values of the mean and width of the gaussian signal function are constrained as the event yield at large is low. It is well known that the mass resolution depends on . Due to the kinematic correlation between and , the mass width is also expected to have dependence. Figure 2 shows the mass width of the Monte Carlo versus in the three different ranges. In the range where the bin size is large, the mass width is seen to rise towards higher bins. This distribution is then used to parameterize the kinematic width variation in the mass fits. The resultant fits to the mass distributions for in the low ct region are shown in Figure 3, Figure 4 and Figure 5 for the three ranges of . The mass fits in the high ct region for the three ranges are shown in Figure 6, Figure 7 and Figure 8 respectively. The signal event yield from the mass fits then form the distributions.
Monte Carlo events are used to obtain a parameterization of the acceptance. events are generated with flat angular distributions, and a distribution given by , where C, M and N are obtained by fitting the parameterization to the Run 1A differential cross sections . Figure 9 shows the fits to the differential cross sections of the promptly produced , and of those arising from B meson decays. mesons are decayed to dimuons and simulated through the detector. The resulting prompt and B decay acceptances as a function of are shown in Figure 10 and Figure 11 respectively. In Figure 12, the prompt acceptance is separated into three subranges. One sees that the acceptance extends to higher values of as the of the increases. Comparisons of the distributions between the data and the Monte Carlo are shown in Figure 13 and Figure 14 for prompt and B decay. We see they have good agreement.
We fit the ct distribution of the mesons to get the relative fractions of prompt and B decay in different ct bins. This is based on an unbinned likelihood fit . The distributions overlaid with fit results for the three ranges are shown in Figure 15, Figure 16 and Figure 17 for events in the mass signal region, and in Figure 18, Figure 19 and Figure 20 for events in the sidebands. In the figures, is the fitted B fraction; is the purity (including both prompt and B) in the mass signal region. Figure 21 shows the relative purity for the prompt and B decay components as a function of ct. The two curves cross each other near ct = 0.01 cm. This motivates us to divide the ct distribution into two regions with a low ct region dominated by the prompt component and a high ct region dominated by the B component.
The prompt and B decay production polarizations are extracted from the distributions of the data by simultaneously fitting the two ct regions using a binned fitter.
The prompt fractions, and for the low and high ct regions, and the polarizations for prompt and B decay production are summarized in the following table:
Figure 22 shows the distributions in the low ct region with their polarization fits overlaid. The same fits for the high ct region are shown in Figure 23.
We study two categories of systematic uncertainties. One is the event yield uncertainty resulted from the mass fits in the bins. The other is the uncertainty on the acceptance due to the modeling of the distribution. They are summarized in the table below:
Using a sample of events reconstructed with the CDF detector, we present a preliminary measurement of the polarization from prompt production, as well as from B decays. The results of the three subranges and the integrated range are as follows:
In Figure 24, the prompt polarization is plotted versus . Also shown is a theoretical calculation based on the Color Octet Model . The measurement has large statistical uncertainties, but it appears to not support the Color Octet Model predication that the is transversely polarized at high . Figure 25 shows the polarization from B decay versus .