in CDF Run II using
Text for the blessed web page - CDF note 6285
The CDF Collaboration
October 9, 2003
Using 
of the Run-II 
data sample collected from
February to September 2002, a measurement of the inclusive b-hadron
production cross-section in the decay channel is performed, where 
denotes all b-hadrons that decay to .
The b-fraction is extracted using an
unbinned likelihood fit to the proper decay length of the in
bins of 
for 
GeV/c. The b-fractions
obtained are applied to the measurement of the inclusive
cross-section to obtain a measurement of the differential
production cross-section as a function of
.
The first measurement of the total b-hadron cross-section at a
hadronic machine has been extracted from the measurement of the
cross-section with transverse momenta > 1.25 GeV/c and
<17.0 GeV/c using a Monte Carlo modeling of the decay kinematics of
b hadrons to charmonium. We find
nb
where denotes both hadron and anti-hadron
states. The total single b-quark cross-section integrated over the
rapidity range |y|<1 is
b.
The Run I central b production cross-section results, which included only b
hadrons with 
GeV, were more than a factor of two greater than NLO QCD
predictions. Dozens of theoretical explanations were offered: NNLO corrections
were large, intrinsic 
effects are large, extreme value of the
renormalization scales are required, new methods of resummation and
fragmentation were required. These theories can broadly be categorized as
``size" theories and ``shape" theories. An inclusive measurement of bottom quark
production over all transverse momenta can help resolve this ambiguity.
This is done by taking the previously measured total cross-section (CDF
Note 6288), and determining the fraction of these particles that are bottom
hadron decay products by measuring the position of the vertex relative
to the b-hadrons (). The long-lived events have daughters
hundreds or thousands of microns from the primary vertex, unlike directly
produced charmonium which has the vertex at the proton-antiproton
interaction point. We use an unbinned maximum liklihood fit to statistically
separate the two components. A MC simulation is used to model the distribution
of the proper decay length of the s from . The shape of the prompt
proper decay length distribution is modeled by a double Gaussian.
The combination of the inclusive cross-section and the fraction of
those 's that are daughters in different transverse
momentum bins (along with the appropriate branching fractions) is then used to
extract the b-hadron differential cross-section as a function of
. An unfolding method using MC templates of the transverse momentum
distribution of b-hadrons is used to obtain the b-hadron differential
cross-section distribution as a function of 
. We use the number of
s from in the momentum range 
GeV/c to
extract the total inclusive cross-section down to 
Gev/c.
This section summarizes the numbers which have been blessed for this analysis.
The following figures have been blessed for the b-hadron cross-section measurement More text can be found in CDF note 6285
Figure 1: b-fraction fit in 1.25-1.5 GeV/c bin
Figure 2: b-fraction fit in 5.0-5.5 GeV/c bin
Figure 3: b-fraction fit in 10.0-12.0 GeV/c bin
Figure 4: b-hadron differential cross-section as a function of
Figure 5: acceptance versus 
for 
GeV/c
Figure 6: Examples of b-hadron transverse
momentum distributions in various J/psi momentum bins.
Figure 7:
Differential cross-section as a
function of
Figure 8:
Differential cross-section as a
function of
Figure 9: Differential cross-section as a
function of 
Figure 10: Differential cross-section as a
function of
Measurement of the b-Hadron Inclusive Cross-section
in CDF Run II using
Text for the blessed web page - CDF note 6285
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