Results for the measurement of the inclusive b-jet cross section in RunII, based on 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 use of jets extends the upper reach of the measurement using exclusive decays, thus allows to explore the behaviour at higher transverse momentum. The analysis is performed on jets within the central rapidity region (|y|<0.7); jets are reconstructed using the MidPoint cone-based algorithm, in a Pt range of 38 GeV to 400 GeV/c (corrected transverse momentum) 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 L2D. The sign of L2D is used to distinguish heavy flavour candidates from mistagged jets, and only positively tagged jets (L2D>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.

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).

At least one primary vertex is required with z-position within 50 cm around the nominal interaction point. Beam related background events and cosmic rays are rejected by a cut on the missing transverse energy significance, taken between 2 and 7 GeV$^{1/2}$ for the different data samples. Monte Carlo simulation studies show that the requirement above preserves more than 98% of b-jet production events.
The measured jet transverse momentum includes additional contributions due to multiple proton-antiproton interactions per bunch crossing. In CDF, multiple interactions are revealed through the presence of additional primary vertices inside the tracking volume. The transverse momentum deposited in the calorimeter in a 0.7 cone is measured as a function of the average number of primary vertices in Minimum Bias events: a correction factor 0.93+-0.14 GeV/c is extrapolated as momentum to be subtracted from the measured jet Pt, for each additional primary vertex.

We use Monte Carlo Pythia Tune A inclusive jet samples to define the average detector effects on the jet transverse momentum. 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 and it is extracted from Pythia Monte Carlo jet samples.
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.
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. The scale factor 0.91+-0.06 is used to scale the b-tag efficieny of the MC inclusive jet samples.
The resulting b-tagging efficiency is shown in figure below (here eps ): the grey band is the systematic error on the Scale factor.

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 invariant mass of all charged tracks attached to the secondary vertex (M secvtx)
The secondary vertex is usually found for long-lived B or D 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) using a maximum likelihood method. 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 (here is the eps ). The b-tagged jet fraction distribution bin by bin is shown below (here is the eps ).

The main sources of systematic uncertainties are summerized in the following and reported in the figure below (here is the eps ):

--> A 3% variation on the measured tagged jet Pt accounts for jet energy scale uncertainties and introduces an uncertainty on the cross section between +10%/-8% for low Pt jets and +39%/-22% for high Pt jets.

--> A +-10 % jet energy resolution uncertainty leads to a +-6 % effect on the measured cross section.

--> The unfolding factors contribution to systematics mainly derives by the dependence on the Pt spectrum, as evaluated repeating the procedure with un-weighted Pythia Monte Carlo events: uncertainty on the cross section is between 5% and 15% as increasing the jet Pt.

--> Systematic uncertainty related to the b-fraction is +14%/-15% for low Pt, +47%/-50% for high Pt, the lowest error for jets of the intermediate Pt region (+8%/-10% for 90 GeV/c jets). The main contributions are related to:

• mixing composition of non-b templates in terms of the c-tagged and non-heavy flavor-tagged jet fraction: effects are between 5% and 10% as increasing Pt jets;
• dependence of secondary vertex mass shape on heavy quark multiplicity within the jet cone: the uncertainty on the mixing between double and single b(c)-jets as foreseen in Pythia Monte Carlo simulations leads to an uncertainty between +2 and -5% in the whole Pt range;
• statistic of the Monte Carlo templates, arising to an uncertainty between 7% and 12% going from low to high corrected transverse momentum.
• effects related to different Monte Carlo generators used for Msecvtx templates, or to different implemented fragmentation models: contributions are less than 1%.

--> The b-tagging efficiency uncertainty leads to an effect of about +-7% for the whole Pt jet range. Major contributions derive from uncertainties on the semileptonic decay branching ratio and differences in the scale factor due to the lower charged particle multiplicity of semileptonic B-hadron decays (3%); background estimate (3%); amount of electrons from conversions (3%); dependence of the b-tagging efficiency scale factor on the jet transverse momentum (5%). The dependence of the b-tagging efficiency on the number of b-quarks within the same jet cone is studied using Pythia Monte Carlo samples: b-tag efficiency for jets with 2 b-quarks inside the cone is found to be between 5 and 15% higher than the one for single b-quark jets. Effects on inclusive b-tagging efficiency are small: a 50% uncertainty given to the fraction of single and double b-quarks jets as derived from Monte Carlo results in a 1% systematic error on the efficiency.

--> Other systematic uncertainties related to the selection criteria contribute for less than 1% to the total error.

--> Finally, the 5.8% uncertainty on the total luminosity is included.

The overall systematic error is +25%/-25% for the first bin, +73%/-68% for the last bin; the lowest error is found for jets of the intermediate Pt region -- about 90 GeV/c -- and is +17%/-20%.

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 bins is dominated by the error on b-tagged jets fraction (here is the eps ).

The cross section is first compared with Pythia and Herwig, and the ratio Data/MC are reported in the figures below (here are the Pythia eps ) and Herwig eps ). Herwig Monte Carlo does not include any special tuning on the underlying event, while Pythia samples have been created using a special set of parameters (Tune A) resulting from special studies on underlying events in CDF RunI data. The behaviour of the two generators is very different also for this reasons, so that a comparison with Leading Order Monte Carlo cannot be considered conclusive.

The data distribution is compared to Next-to-Leading Order perturbative QCD predictions for b-jet production as from Nucl. Phys. B483, 321 (1997) -- M.Mangano and S.Frixione. The following processes are taken into account:
At Leading Order (LO):

• g + g -> Q + Qbar
• q + qbar -> Q + Qbar

• g + g -> Q + Qbar + g
• q + qbar -> Q + Qbar + g
• q + g -> Q + Qbar + q

Input to this calculation are the b-quark bare mass (4.75 GeV/c2), the PDFs (CTEQ6M), the renormalization scale, chosen equal to the factorization scale μ_R = μ_F = &mu, and the parton clustering algorithm. The value of &mu is set to μ₀/2 = [sqrt(P_T**2+m_b**2)]/2, where the choice is mainly driven by the scale used in NLO pQCD predictions for inclusive jet cross section in CDF; however, rather than the scale being proportional to the natural scales of the process (P_T,m_b), no theoretical constraints exist, as well as for the choice of equalizing μ_R and μ_F. A cone size equal to 0.7 is used: to mimic the merging/splitting mechanism of a jet cone algorithm, not present for the parton jets in the NLO prediction, a multiplicative parameter, Rsep=1.3, has been introduced. To compare data particle level jets with parton jets, effects related to non-perturbative effects as fragmentation and underlying events must be accounted for: the theoretical prediction includes additional bin-by-bin correction factors, C_HAD. The Midpoint clustering algorithm is applied to the hadron and parton level outputs of Pythia dijet Monte Carlo samples, generated with and without underlying event, and the factors are defined as the ratio between hadron jet Pt distribution and the parton level one, obtained after turning off beam renmant interactions and string fragmentation. The correction is 18% for low Pt jets and it decreases becoming negligeble for jet Pt above 120 GeV/c.
Different sources of uncertainty are considered for the theoretical predictions. The main contribution is related to the renormalization and factorization scales: μ_R = μ_F = &mu are variated between μ₀/4 < μ < μ₀, leading to an effect on the predicted cross section of about 40%-50% for jet Pt below 150 GeV/c, of 20% for jet Pt above 300 GeV/c. Uncertainties related to the PDF are computed using the Hessian method and vary between 7% at low Pt and 20% for jet Pt of 350 GeV/c. A 10% systematic contribution accounts for the clustering uncertainties. Systematic uncertainties related to the correction factors C_HAD and to the dependence on the b-quark mass value are negligeble (less than 2%).
The NLO pQCD prediction and the relative systematic uncertainty is reported in figure below (here is the eps ).

Figure below (here is the eps ) shows the ratio data/theory, being the grey band the total systematic error from data. Systematic error on the theory are shown around one. For b-jets having transverse momentum below 90 GeV/c, good consistency between the measured cross section and NLO pQCD prediction is found; for b-jets with Pt above 90 GeV/c, agreement is observed within the systematic uncertainties.
The big uncertainties related to renormalization and factorization scales suggest that not-included higher order contributions might play a major role in b-jet production calculations.