Preliminary results for the measurement of the inclusive b-jet cross section in RunII, based on about 300 pb^-1 of good run data collected from February 2002 to September 2004, are presented.
Measurements of the b-jet production cross section at p-pbar colliders provide an important quantitative test of Quantum Chromodynamic. The mass of the b quark is considered to be large enough to justify perturbative expansions in the strong coupling constant. Consequently, data on b quark production are expected to be adequately described by calculations at the next-to-leading order (NLO).
Past measurements of inclusive b quark production using exclusive measurements on B+ indicated an ``excess'' with respect to the NLO QCD predictions (Data/Theory = 1.7 ± 0.5(theo) ± 0.5(expt)). The actual theorethical prediction, after further studies, shows a good agreement with new CDF measurement of the B-cross section at low Pt.
The use of jets extends the upper reach of the measurement using exclusive decays, thus allows to explore the behaviour at higher transverse momentum. In addition, theorethical uncertainties on fragmentation and decay are smaller in an inclusive b-jet analysis than in exclusive decay studies.

The analysis is restricted to jets in the central rapidity region (|y|<0.7), reconstructed with the MidPoint algorithm in a Pt range of 30 GeV to 360 GeV (uncorrected) and exploits the good tracking capabilities of the CDF detector to tag b-jets by reconstructing secondary vertex with the SecVtx algorithm.
The b-tagging algorithm uses displaced tracks associated with a jet that are within a sub-cone of 0.4 in the eta-phi space with respect to the jet axis.
The search for secondary vertices is defined in two steps, or passes, with selection based on the significance of the impact parameter and of the decay lenght Lxy. The sign of Lxy is used to distinguish heavy flavour candidates from mistagged jets, and only positively tagged jets (Lxy>0) are considered. Notice that SecVtx is optimized for jet cone R=0.4. In order to avoid an increase in mistagging, we keep a subcone of 0.4 in the selection of tracks used for the reconstruction of the secondary vertex.
The measurement is corrected in average for detector effects and compared to the leading order Monte Carlo predictions from Pythia (tune A).

Five different datasets are used: Single Tower 05 (ST05), Jet20, Jet50, Jet70, Jet100, where the number indicates the nominal trigger threshold on the towers and on the jets respectively.
The behaviour of each trigger sample has been studied in order to define a range in Pt of jets where effects due to trigger inefficiency can be neglected and trigger bias avoided: trigger efficiency as a function of measured jet Pt for each data sample is shown, together with the 99% efficiency threshold (here is the eps version of the plot).

We use Monte Carlo to define the average detector effects on the jet energy and to correct the Pt scale. With the MidPoint algorithm, it is possible to form jets at the hadron level in MC, using informations from stable particles in the HEPG bank. Those jets can then be compared to jets reconstructed with calorimetric information, with energy deposit in the towers.
At hadronic level, particles with momentum above 1 GeV are used as seeds and no further selections are applied on other particles included in the proto-jet reconstructions and same jet kinematics scheme is used.

In order to extract the correction factors to compansate for energy losses at calorimeter level, we use a procedure to match hadronic and calorimetric jets based on a selection in the Y-phi space. For the transverse momentum, a scatter plot of calorimetric jet Pt vs. hadronic jet Pt is plotted. the profile is shown in figure below (here eps )

The procedure has been implemented only for events with a positively tagged jet; these corrections are therefore not to be considered valid for b-jets, but for general tagged ones, since to derive the cross section we are interested in the number of tagged jets divided by b-tagging efficiency and multiplied by fraction of b-jets tagged.

The resulting correction function is also reported (here eps ).

The two-dimensional SecVtx algorithm is used to tag jets: we consider positively tagged jets, defined to have a positive distance, in the transverse plane, from the primary reference vertex to the secondary vertex relative to the direction of the jet. The b tagging efficiency is the fraction of tagged b jets with respect to all b jets in a given Pt bin.
To measure directly the b tagging efficiency from data, it is necessary to determine the heavy flavor content of the sample before and after the tagging procedure. For this purpose, the approach that CDF has adopted up to now is to use the 8 GeV inclusive electron data sample, because of the good capability in electron identification and the enhancement in heavy flavor content; this comes as a consequence of the trigger sensitivity to semileptonic decays of B and C hadrons and it does not depend on displaced vertex.
Since the electron jet Pt range between 15 GeV and 60 GeV (raw energy) in this sample, the direct measurement of the btagging efficiency cannot be used in this analysis, where the range in Pt of the jets is much wider.
Therefore, it is necessary to use a bin-by-bin b tagging efficiency distribution taken from the Monte Carlo. Thus, a direct measurement of the b tagging efficiency from electron data and from a Monte Carlo sample generated to match the data as closely as possible, is performed to define the ratio of Data/MC efficiencies (scale factor, SF). The scale factor is then used to scale the b-tag efficieny of the MC dijet samples.
The resulting b-tagging efficiency is shown in figure below (here eps ): the error bars refer to the statistical error of the Monte Carlo, the grey band is the systematic error on the Scale factor, dominated by the Pt dependence. A combination of the two sources is finally used as global systematic.

Several techniques have been developed to determine the heavy flavour content of a tagged jet in order to extract the fraction of bjets. Here we use the shape of the SECVTX vertex mass distribution as discriminating quantity.
The secondary vertex is usually found for long-lived b or c hadrons. But due to the presence of neutral particles and energy lost because of detector resolution, a full reconstruction of the invariant mass is not possible. Still the invariant mass of tracks used to find the secondary vertex constitutes a good discrimination between jets containing b, c or light quarks. Using the Pythia MC, we obtain b, c and lights-jets distributions (templates) for masses of positively tagged jets. Light-jets and c-jets are then merged and considered together since the b fraction is the only flavor content of interest. The same distribution from data is fitted to a linear combination of the 2 components (b and non-b) with the routine TFractionFitter (ROOT). The fit is performed considering independently each bin in Pt, since the b-tagging efficiency depends on it as the purity of the tagging procedure. An example (for a single bin) of fit results and monte carlo distributions of secondary vertex mass for b and non-b tagged jet can be found below ( eps1, eps2). The b-tagged jet fraction distribution bin by bin is shown below ( eps ).

The main sources of systematic uncertainties are shown in the table below.

The plot shows the inclusive b-jet cross section over a Pt range between 38 and 400 GeV (corrected jets). Statistical error on the last 6 bins is dominated by the error on b-tagged jets fraction ( eps ).

Comparison with Pythia Tune A Monte Carlo is shown below ( eps ).

Ratio Data/Pythia Tune A monte carlo is shown below ( eps ).