Cross-section
Cross-section
CDF Collaboration
Using a 39.7 pb
Run-II data sample collected from February to
October 2002, a new measurement of the inclusive
cross-section has been performed. The 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 
dependent differential cross
section has been calculated for events with rapidity |y|<0.6. The
total integrated cross section for inclusive production in
interactions at C.O.M. energy, 
GeV/c
,
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 
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 threshold of > 1.4 GeV/c. This has
extended the low transverse momentum range of triggered 
events down to 
GeV/c. A new
measurement of the total inclusive cross-section using Run-II
data has been carried out.
The 
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
.
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 
invariant
mass distribution for all the selected events in the range 
GeV/c with rapidity |y|<0.6.
From a fit to a double Gaussian and a 
order polynomial
background, the total number of reconstructed for this study
is 
with an average width of 
GeV/c. The mass sideband subtracted transverse momentum
distribution of reconstructed events
in shown in Figure 2 .
The data sample is divided into thirty ranges of transverse
momentum, covering the range 0-17 GeV/c. In each range, the total
number of s reconstructed with rapidity |y|<0.6 is measured.
To estimate the correct yield, the 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 .
The CMU muon detector covers the pseudo-rapidity range of
. 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 
and rapidity, 
is defined as 
where 
and y' are the generated true values of the
momentum and rapidity including the radiated photon.
The acceptance as a function of and is shown in Figures
6. and 7.
The yield in each bin is corrected for the 2-D
acceptance, 
, Level 1 single muon
trigger efficiency, 
, and the muon
selection cuts, using an event by
event weighing.
The differential cross section is then calculated as follows:
where 
, 
is the correction
factor for y smearing,
is the combined L3, offline
tracking and muon reconstruction efficiency, 
is the
integrated luminosity, and 
is the bin size of the
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 crossection as a function of , for
. The systematic uncertainties shown are the
dependent uncertainties only. The correlated 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,
with systematic uncertainties is shown in Figures
10. and 11.
The integrated cross section obtained from an integral of the
differential cross section is:
