Measurement of the Run-II Inclusive tex2html_wrap_inline253 Cross-section

CDF Collaboration


Using a 39.7 pbtex2html_wrap_inline257 Run-II data sample collected from February to October 2002, a new measurement of the inclusive tex2html_wrap_inline253 cross-section has been performed. The tex2html_wrap_inline253 events were collected using the CMU-CMU di-muon triggers, and the raw yields were corrected by the geometric and kinematic acceptance, trigger efficiency and reconstruction efficiency. A tex2html_wrap_inline263 dependent differential cross section has been calculated for events with rapidity |y|<0.6. The total integrated cross section for inclusive tex2html_wrap_inline253 production in tex2html_wrap_inline269 interactions at C.O.M. energy, tex2html_wrap_inline271 GeV/ctex2html_wrap_inline273, is measured to be:


Non-relativistic quarkonia bound states are best described by Non-Relativistic QCD ( NRQCD) theoretical models which are used to predict the hadroproduction cross-sections  [1]  [2]. At large transverse momenta, fragmentation type production is expected to dominate and color-octet matrix elements dominate the color-singlet matrix element contribution  [3]. Using color-octet matrix elements extracted from data, the model can accomodate the Run I data at the Tevatron for tex2html_wrap_inline277 GeV/c. At low transverse momenta, soft gluon effects and non-fragmentation effects from other octet matrix elements that are difficult to calculate theoretically become important and cause theory predictions and data to diverge. The Run-II CDF detector has an improved dimuon trigger with a lower tex2html_wrap_inline263 threshold of > 1.4 GeV/c. This has extended the low transverse momentum range of triggered tex2html_wrap_inline283 events down to tex2html_wrap_inline285 GeV/c. A new measurement of the total inclusive tex2html_wrap_inline253 cross-section using Run-II data has been carried out.

Data sample and event selection

The tex2html_wrap_inline289 sample used for this analysis was collected using the Level 1 and Level 3 Central Muon (CMU) di-muon triggers. The single muon trigger efficiency as a function of the muon transverse momentum is shown here. The data sample used was collected during the stable running period of February to October 2002 and corresponds to a total luminosity of tex2html_wrap_inline291.

tex2html_wrap_inline289 decays were reconstructed from tracks reconstructed in the Central Outer Tracker (COT) drift chamber and matched to track-stubs in the Central Muon Chambers (CMU). The invariant mass was calculated from the sum of the four-momenta of the two muons. Figure 1 shows the tex2html_wrap_inline295 invariant mass distribution for all the selected events in the range tex2html_wrap_inline297 GeV/ctex2html_wrap_inline273 with rapidity |y|<0.6. From a fit to a double Gaussian and a tex2html_wrap_inline303 order polynomial background, the total number of tex2html_wrap_inline253 reconstructed for this study is tex2html_wrap_inline307 with an average width of tex2html_wrap_inline309 GeV/ctex2html_wrap_inline273. The mass sideband subtracted transverse momentum distribution of reconstructed tex2html_wrap_inline289 events in shown in Figure 2 .

The data sample is divided into thirty ranges of tex2html_wrap_inline253 transverse momentum, covering the range 0-17 GeV/c. In each range, the total number of tex2html_wrap_inline253s reconstructed with rapidity |y|<0.6 is measured. To estimate the correct yield, the tex2html_wrap_inline253 invariant mass signal distribution including the radiative tail from internal bremsstrahlung is fitted using mass template shapes obtained from a MC simulation of the COT. The fits to the COT invariant mass distributions in three of the transverse momentum ranges are shown in Figures 3 . 4 . and 5 .

Detector Acceptance

The CMU muon detector covers the pseudo-rapidity range of tex2html_wrap_inline323. In this region the coverage of the central tracking chamber, COT is 100% and the CDF detector acceptance is driven by the muon detector geometry and kinematic reach. A full GEANT simulation of the CDF detector is used to estimate the acceptance correction.

The acceptance efficiency as a function of reconstructed tex2html_wrap_inline325 and rapidity, tex2html_wrap_inline327 is defined as
where tex2html_wrap_inline331 and y' are the generated true values of the tex2html_wrap_inline253 momentum and rapidity including the radiated photon.

The acceptance as a function of tex2html_wrap_inline325 and tex2html_wrap_inline327 is shown in Figures 6. and 7.


Cross Section Results

The tex2html_wrap_inline253 yield in each tex2html_wrap_inline263 bin is corrected for the 2-D acceptance, tex2html_wrap_inline349, Level 1 single muon trigger efficiency, tex2html_wrap_inline351, and the muon selection cuts, using an event by event weighing. The tex2html_wrap_inline253 differential cross section is then calculated as follows:
where tex2html_wrap_inline359, tex2html_wrap_inline361 is the correction factor for y smearing, tex2html_wrap_inline365 is the combined L3, offline tracking and muon reconstruction efficiency, tex2html_wrap_inline367 is the integrated luminosity, and tex2html_wrap_inline369 is the bin size of the tex2html_wrap_inline263 bin.

Table 1 summarizes the different contributions to the systematic uncertainties to be applied to the cross-section measurement.

Table 1: Source of systematic uncertainty in the cross-section measurement

The cross-section values are listed in Table 2.

Table 2: The differential tex2html_wrap_inline253 crossection as a function of tex2html_wrap_inline263, for tex2html_wrap_inline677. The systematic uncertainties shown are the tex2html_wrap_inline263 dependent uncertainties only. The correlated tex2html_wrap_inline263 independent systematic uncertainty in each bin is +/- 6.7%.

The differential cross-section results are displayed in Figures 8. and 9. The invariant cross-section, tex2html_wrap_inline685 with systematic uncertainties is shown in Figures 10. and 11.

The integrated cross section obtained from an integral of the differential cross section is:


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