Measurement of $b$-jet shapes in inclusive jet production in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We present a measurement of the shapes of $b$-jets using $300{\mathrm{pb}}^{-1}$ of data obtained with the upgraded Collider Detector at Fermilab (CDF II) in $p\overline{p}$ collisions at center-of-mass energy $\sqrt{s}=1.96\mathrm{TeV}$. This measurement covers a wide transverse momentum range, from 52 to $300\mathrm{GeV}/c$. Samples of heavy-flavor enhanced jets together with inclusive jets are used to extract the average shapes of $b$-jets. The $b$-jets are expected to be broader than inclusive jets. Moreover, $b$-jets containing a single $b$-quark are expected to be narrower than those containing a $b\overline{b}$ pair from gluon splitting. The measured $b$-jet shapes are found to be significantly broader than expected from the pythia and herwig Monte Carlo simulations. This effect may arise from an underestimation of the fraction of $b$-jets originating from gluon splitting in these simulations. The jet shape distributions provided in this paper could be compared to any full Monte Carlo simulation and could be used to further constrain the various parameters.

Figure 1

Fraction of $b$-jets that contain more than one $b$-quark inside the same jet cone. The pythia Tune A MC simulation predictions are compared to NLO calculations for two different hadronization and factorization scales. The NLO calculations are shown binned with the same binning as used for the pythia Tune A MC simulation.

Figure 2

Measured detector level jet shapes in data for the tagged ( gray full triangles) and inclusive (open squares) data samples for each $p_T$ bin. The jet algorithm used, MidPoint cone 0.7 $f_{\mathrm{merge}}$ 0.75, is described in Sec. 3.

Figure 3

Top panel: Normalized secondary vertex mass distributions for $b$- (black solid line) and $\mathrm{non}b$-jets ( gray dashed line) as obtained from pythia Tune A. Middle panel: Secondary vertex mass distribution in data (black open squares) compared to the fitted distribution (histogram) for the second $p_T$ bin. Bottom panel: Extracted $b$-jet purity in data as a function of jet $p_T$ using the templates obtained from pythia Tune A (black solid lines) and from herwig ( gray dashed lines). The error bars indicate the statistical uncertainties only.

Figure 4

Total uncertainties on the integrated $b$-jet shape measurements for each of the four jet $p_T$ and $r$ bins (thick black lines). Also shown are the statistical uncertainties ( gray bands) and the five dominant sources of systematic uncertainties: dependence on the particular MC model for the unfolding (thin black line), dependence on the detector simulation description (dashed thin black line), dependence on the single $b$-quark, $f_{1b}$ (thick gray line), and single $c$-quark, $f_{1c}$ (dotted thick gray line), jet fractions in MC simulation, and the dependence on the jet energy scale, JES (dot-dashed black line). The uncertainties are added in quadrature.

Figure 5

Measured integrated $b$-jet shapes for each of the four $p_T$ bins considered. The results are shown as black open squares where the error bars represent the statistical and total uncertainties. The statistical uncertainties are smaller than the squares. The results are compared to pythia Tune A (solid lines) and herwig (dashed lines) predictions using the default $f_{1b}$ fractions (black lines). Also shown are the pythia Tune A predictions for the inclusive jet shapes (gray lines).

Figure 6

This plot shows the same data points as in Fig. 5. The results are compared to pythia Tune A (solid lines) and herwig (dashed lines) predictions if $f_{1b}$ is decreased by 0.2 (black lines). Also shown are the pythia Tune A and herwig predictions for single and double $b$-quark jets (upper light gray and lower dark gray lines, respectively).

Figure 7

Ratios of the hadron level integrated $b$-jet shapes for various Monte Carlo predictions over the measured values. The light gray bands represent the total uncertainties on the measured $b$-jet shapes and the dark gray bands show the statistical uncertainties. pythia Tune A and herwig predictions using the default $f_{1b}$ fractions are shown as gray lines (solid lines for pythia Tune A, dashed ones for herwig). pythia Tune A and herwig predictions using $f_{1b}$ fractions 0.2 below the default values are also reported (black lines).

Figure 8

Fractional $p_T$ outside a cone of radius $r=0.2$ around the jet axis as a function of the $p_T$ of the jet. The results for $b$-jets are shown as black open squares and compared to different pythia Tune A and herwig predictions. The error bars on the plots represent the total and statistical uncertainties. The statistical uncertainties are smaller than the squares. Top panel: The results are compared to pythia Tune A (solid lines) and herwig (dashed lines) predictions using the default $f_{1b}$ fractions (black lines). Also shown are the pythia Tune A predictions for the inclusive jet shapes ( gray lines) as well as the previously published inclusive jet shape results (triangles). Bottom panel: The measured values are shown along with the expected distributions if $f_{1b}$ is decreased by 0.2 (black lines). Also shown are the pythia Tune A and herwig predictions for single and double $b$-quark jets (upper light gray and lower dark gray lines, respectively).