Cross-section 
Cross-section
Tomohiro Yamashita
Okayama University
Slawomir Tkaczyk, Ting Miao, Dmitri Litvintsev,
Jonathan Lewis, Mary Bishai
Fermi National Accelerator Laboratory
Thomas LeCompte
Argonne National Laboratory
James Kraus
University of Illinois
Yuri Gotra
University of Pittsburgh
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 dominates and color-octet matrix elements dominate the
color-singlet matrix element contribution [3]. The results
agree well with 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 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. <a href="dimumasscorr.eps">Figure 1</a>. 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 <a href="ptjpsi_allphi.eps">Figure 2</a>.
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 <a href="mass_bin1_bless.eps">3</a>. <a href="mass_bin21_bless.eps">4</a>. and <a href="mass_bin29_bless.eps">5</a>.
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
<a href="accept_pt_log.eps">6</a>. and <a href="accept_y_1pt20_491_1.eps">7</a>.
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 such that:
where 
is the number of signal events obtained from the fit to the
invariant mass distribution of the reweighed events.
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 
summarizes the different contributions to the
systematic uncertainties to be applied to the cross-section measurement.
Table: Source of systematic uncertainty in the cross-section measurement
The cross-section values are listed
in Table .
Table: 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 
.
The differential cross-section results are displayed in
Figures <a href="xsec_syst1_bless2.eps">8</a>. and <a href="xsec_syst2_bless2.eps ">9. The invariant cross-section,
with systematic uncertainties is shown in Figures
<a href="xsec_ptsqr_syst1_bless2.eps">10</a>. and <a href="xsec_ptsqr_syst2_bless2.eps">11</a>.
The integrated cross section obtained from an integral of the
differential cross section is:
Measurement of the Run-II Inclusive Cross-section
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