Measurement of Production Polarization in tex2html_wrap_inline221


We present a measurement of the production polarization of tex2html_wrap_inline223 mesons produced in tex2html_wrap_inline225 collisions at tex2html_wrap_inline227 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 tex2html_wrap_inline229 collisions (roughly a factor 50 above the Color Singlet Model). A prediction of the COM is that directly produced charmonia should approach 100tex2html_wrap_inline231 transverse polarization for high transverse momentum of the onium state. We consider tex2html_wrap_inline233 mesons, reconstructed using the decay mode tex2html_wrap_inline235 in a 110 pbtex2html_wrap_inline237 data sample of tex2html_wrap_inline239 collisions. The polarization of prompt tex2html_wrap_inline241 is extracted to be tex2html_wrap_inline243 for tex2html_wrap_inline245 GeV/tex2html_wrap_inline247.

1 Introduction

Measurements of both direct tex2html_wrap_inline251 and tex2html_wrap_inline253 cross sections by CDF [1] are tex2html_wrap_inline255 times higher than Color Singlet Model predictions [2]. By ``direct'', we mean the charmonia produced directly from the tex2html_wrap_inline257 collisions, and not those from particle decays such as tex2html_wrap_inline259, tex2html_wrap_inline261, etc. One of the theoretical models which tries to explain this anomalous production is the Color Octet Model (COM) [3]. The model raises the direct production cross section by including color-octet tex2html_wrap_inline263 states in the fragmentation process. At leading order in tex2html_wrap_inline265 and at high tex2html_wrap_inline267 (tex2html_wrap_inline269, where tex2html_wrap_inline271 is the charm quark mass), the contribution to the cross section is dominated by gluon fragmentation into the color octet tex2html_wrap_inline273 states. The fragmenting gluon, being effectively on-shell at high tex2html_wrap_inline275, is transversely polarized. The tex2html_wrap_inline277 pair and subsequently the tex2html_wrap_inline279 and tex2html_wrap_inline281 mesons inherit the gluon's transverse polarization. Therefore, COM predicts the direct tex2html_wrap_inline283 and the tex2html_wrap_inline285 to approach 100tex2html_wrap_inline287 transverse polarization at high tex2html_wrap_inline289 [4]. Observation of such a polarization would support the color-octet fragmentation mechanism.


Experimentally, the tex2html_wrap_inline293 is a clean channel to test the COM. The displacement of the tex2html_wrap_inline295 vertex from the primary can be used to distinguish prompt (direct) production from B decays. In the case of the tex2html_wrap_inline299, the prompt production is contaminated with feed-down like tex2html_wrap_inline301.


Using spin formalism [5], the angular distribution in tex2html_wrap_inline305 decay is derived to be:
where tex2html_wrap_inline307 is the polarization and tex2html_wrap_inline309 denotes the angle between the tex2html_wrap_inline311 momentum in the tex2html_wrap_inline313 rest frame and the tex2html_wrap_inline315 momentum in the Lab frame. Unpolarized tex2html_wrap_inline317 mesons would have tex2html_wrap_inline319 whereas tex2html_wrap_inline321 and -1 correspond to fully transverse and longitudinal polarizations respectively. The value of tex2html_wrap_inline325 is extracted from the data by fitting the reconstructed angular distribution after acceptance corrections.

2 Data Sample Selection

This analysis is based on a 110 pbtex2html_wrap_inline327 sample of low tex2html_wrap_inline329 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 tex2html_wrap_inline331 larger than 2.0 GeV/tex2html_wrap_inline333 (in the Run 1A sample, the high tex2html_wrap_inline335 muon is required to have tex2html_wrap_inline337 larger than 2.8 GeV/tex2html_wrap_inline339). The selected dimuons are vertex constrained to form the tex2html_wrap_inline341 candidates. A tex2html_wrap_inline343 cut larger than 5.5 GeV/tex2html_wrap_inline345 is imposed on the tex2html_wrap_inline347 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 tex2html_wrap_inline349 signal tex2html_wrap_inline351 candidates. In a tex2html_wrap_inline353 mass window around the tex2html_wrap_inline355 mass, the signal to background ratio (S/B) is tex2html_wrap_inline357.

3 Extracting the Polarization

To study the tex2html_wrap_inline359 dependence of the polarization, we divide the data sample into three tex2html_wrap_inline361 ranges (5.5-7, 7-9 and 9-20 GeV/tex2html_wrap_inline363). Each sample is further divided into two sub-samples based on the tex2html_wrap_inline365 distribution. ct is related to the transverse decay length tex2html_wrap_inline369 as follows:
where m is the reconstructed tex2html_wrap_inline373 mass. The factor tex2html_wrap_inline375 is an average correction factor obtained from Monte Carlo studies to account for the fact that we use tex2html_wrap_inline377 instead of tex2html_wrap_inline379. 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 tex2html_wrap_inline393 for each candidate is calculated from the momentum vectors of the muons, and the mass and momentum of the reconstructed tex2html_wrap_inline395. Since the angular distribution is symmetric, the absolute value of tex2html_wrap_inline397 is used, and subdivided into 10 bins. The mass distribution in each tex2html_wrap_inline399 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 tex2html_wrap_inline401 is low. It is well known that the mass resolution depends on tex2html_wrap_inline403. Due to the kinematic correlation between tex2html_wrap_inline405 and tex2html_wrap_inline407, the mass width is also expected to have tex2html_wrap_inline409 dependence. Figure 2 shows the mass width of the tex2html_wrap_inline411 Monte Carlo versus tex2html_wrap_inline413 in the three different tex2html_wrap_inline415 ranges. In the tex2html_wrap_inline417 range tex2html_wrap_inline419 where the bin size is large, the mass width is seen to rise towards higher tex2html_wrap_inline421 bins. This distribution is then used to parameterize the kinematic width variation in the mass fits. The resultant fits to the mass distributions for tex2html_wrap_inline423 in the low ct region are shown in Figure 3, Figure 4 and Figure 5 for the three tex2html_wrap_inline427 ranges of tex2html_wrap_inline429. The tex2html_wrap_inline431 mass fits in the high ct region for the three tex2html_wrap_inline435 ranges are shown in Figure 6, Figure 7 and Figure 8 respectively. The signal event yield from the mass fits then form the tex2html_wrap_inline437 distributions.


Monte Carlo events are used to obtain a parameterization of the acceptance. tex2html_wrap_inline441 events are generated with flat angular distributions, and a tex2html_wrap_inline443 distribution given by tex2html_wrap_inline445, where C, M and N are obtained by fitting the parameterization to the Run 1A tex2html_wrap_inline453 differential cross sections [1]. Figure 9 shows the fits to the differential cross sections of the promptly produced tex2html_wrap_inline455, and of those arising from B meson decays. tex2html_wrap_inline457 mesons are decayed to dimuons and simulated through the detector. The resulting prompt and B decay acceptances as a function of tex2html_wrap_inline461 are shown in Figure 10 and Figure 11 respectively. In Figure 12, the prompt acceptance is separated into three tex2html_wrap_inline463 subranges. One sees that the acceptance extends to higher values of tex2html_wrap_inline465 as the tex2html_wrap_inline467 of the tex2html_wrap_inline469 increases. Comparisons of the tex2html_wrap_inline471 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 tex2html_wrap_inline479 mesons to get the relative fractions of prompt and B decay in different ct bins. This is based on an unbinned likelihood fit [6]. The tex2html_wrap_inline485 distributions overlaid with fit results for the three tex2html_wrap_inline487 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, tex2html_wrap_inline489 is the fitted B fraction; tex2html_wrap_inline493 is the tex2html_wrap_inline495 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 tex2html_wrap_inline517 distributions of the data by simultaneously fitting the two ct regions using a binned tex2html_wrap_inline521 fitter.

4 Results

The prompt fractions, tex2html_wrap_inline523 and tex2html_wrap_inline525 for the low and high ct regions, and the tex2html_wrap_inline529 polarizations for prompt and B decay production are summarized in the following table:


Figure 22 shows the tex2html_wrap_inline575 distributions in the low ct region with their polarization fits overlaid. The same fits for the high ct region are shown in Figure 23.

5 Systematics

We study two categories of systematic uncertainties. One is the event yield uncertainty resulted from the mass fits in the tex2html_wrap_inline581 bins. The other is the uncertainty on the tex2html_wrap_inline583 acceptance due to the modeling of the tex2html_wrap_inline585 distribution. They are summarized in the table below:


6 Conclusion

Using a sample of tex2html_wrap_inline613 events reconstructed with the CDF detector, we present a preliminary measurement of the tex2html_wrap_inline615 polarization from prompt production, as well as from B decays. The results of the three tex2html_wrap_inline619 subranges and the integrated tex2html_wrap_inline621 range are as follows:


In Figure 24, the prompt tex2html_wrap_inline661 polarization is plotted versus tex2html_wrap_inline663. Also shown is a theoretical calculation based on the Color Octet Model [4]. The measurement has large statistical uncertainties, but it appears to not support the Color Octet Model predication that the tex2html_wrap_inline665 is transversely polarized at high tex2html_wrap_inline667. Figure 25 shows the tex2html_wrap_inline669 polarization from B decay versus tex2html_wrap_inline673.


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CDF B Physics Group