Measurement of b-quark jet shapes at CDF
This analysis presents preliminary results on the integrated jet shapes of b-quark jets.
The data used for this analysis were taken between February 2002 and September 2004 and represent an integrated luminosity of about 300 pb^-1.
This is the first time that b-quark jet shapes have been measured at hadron colliders.
This measurement shows that, despite relatively large systematic uncertainties, the measured b-quark jet shapes are significantly different from those expected from Pythia Tune A and Herwig Monte Carlo simulations. This difference seems to be in part explained by the fact that the fraction of b-quark jets that originate from flavour creation (where a single b-quark is expected inside the same jet cone) over those that originate from gluon splitting (where two b-quarks are expected to be inside the same jet cone) is slightly different in Monte Carlo predictions than in data. This measurement can help in the tuning of the fraction of gluon splitting to flavour creation b-quark jets in the Monte Carlo simulation. This tuning is particularly important for the extrapolation up to LHC energies where many searches will involve b-quark jets.
[jet shape definition]
[b-quark jet definition]
[event selection]
[analysis methodology]
[blessed plots]
Integrated jet shape definition
The integrated jet shape is defined as the fraction jet pt which is inside a cone of size r around the jet axis (where the normalisation is carried out over the total jet pt inside a cone of size R, the jet cone size, this removes from the calculation the towers which are further away from the jet axis than the jet cone radius).
The distance between the jet axis and an object of interest (such as the edge of the jet cone, in this case R=0.7) is defined as the opening angle in (Y,phi)-space:
This can be schematically visualised by
and mathematically expressed as
The limit as the cone tends to the jet cone radius is expressed as
b-quark jet definition
In this analysis. A b-quark jet is defined to be a jet which contains at least one b-quark inside a cone of size 0.7 (equal to the jet cone radius) around the jet axis.
This includes both b-jets from hard scattered processes involving b-quarks as well as b-jets originating from a hard-scattered gluon which splits into a b bbar pair (in which case both b-quarks are most of the time inside the same jet cone).
The fraction of b-jets which contain only a single b-quark inside the jet cone is called here the single b-quark jet fraction, f1b.
Event selection
The 4 different datasets used are: Jet20, Jet50, Jet70 and Jet100. These samples are only used when their trigger efficiency is above 99%.
Events are selected with one and only one primary vertex with |Zvtx|<50 cm and a cut on the missing Et significance which varies as a function of the jet energy (3.5,5.0,6.0,7.0 for the Jet20, Jet50,Jet70 and Jet100 samples).
The jets used for this analysis are central jets (|Y|<0.7), reconstructed using the MidPoint cone algorithm with a cone size of 0.7 and a splitting/merging fraction of 75%. The jets are corrected back to hadron level using b-jet specific corrections, the same as used for the b-jet cross section measurement. This analysis uses jets in the pt range from 52 to 300 GeV/c.
The jets are tagged using the SecVtx tagging algorithm. This algorithm attempts to reconstruct displaced vertices from tracks which are within a cone of size 0.4 around the jet axis. A cut is applied on the projection along the jet axis of the distance between the primary and secondary vertices (L2D).
Analysis Method
The basis of this measurement lies in the possibility of enhancing the b-quark jet content of jet samples by requiring the jets to be identified as having a displaced vertex inside the jet cone. Such jets are called tagged. This enhances the b-quark jet fraction from about 5% before tagging to 20-40% after tagging, depending on the transverse momentum of the jets.
Because the b-quark purity of the jets is still relatively low, it is necessary to extract the shapes of b-quark jets in a statistical manner from the jet shapes both before and after tagging. The other parameters that enter into the unfolding equation used to extract the b-quark jet shapes are the b-jet purities, the biases due to the tagging requirement both for b- and nonb-jets and the hadron level corrections. The last of these terms corrects the measured b-jet shapes back to the shapes expected at hadron level which makes comparisons with theoretical models and other experimental results possible.
The measured jet shape after tagging is a combination of the jet shapes from b-quark jets and from nonb-quark jets.
The final b-quark jet shape unfolding equation is given by:
where
- C_had(r) is the hadron level correction factor
- b^b(r) is the bias due to tagging on b-jets
- b^nonb(r) is the bias due to tagging on nonb-jets
- Psi^nonb(r) is approximated to the inclusive jet shape (in the Monte Carlo, the differences between the non-b and the inclusive jet shapes are found to be negligible, smaller than statistical errors on the inclusive jet shape as obtained from the data)
- p_b is the purity of the sample
Blessed Plots
Re-weighting of Monte Carlo with a increased fraction of gluon splitting
The measurement of b-jet shapes is somewhat sensitive to the fraction of b-jets that contain two b-quarks inside the same jet cone (these jets are mostly from gluon splitting). The Monte Carlo (MC) samples used for the unfolding of the measured shapes are Leading Order (LO) predictions which are tuned on data for underlying event, hadronisation, etc. These predictions only contain gluon splitting to b bbar pairs as part of the fragmentation and not in the matrix element. A comparison between Pythia Tune A and Next to Leading Order (NLO) calculations for the fraction of jets containing two b-quarks inside the same jet cone (bbar fraction, i.e. 1-f1b) for two different hadronisation and factorisation scales is shown in the figure below. This fraction is plotted as a function of jet pt and shows that the NLO predictions are systematically higher.
The maximum difference observed between data and MC is of the order of 0.2. It was deemed important that the MC samples used to unfold the b-jet shapes were re-weighted in order to take into account a larger gluon splitting fraction than expected at LO. The samples are thus re-weighted by decreasing f_1b (the fraction of b-jets that contain only a single b-quark) by 0.2 before the bias terms and hadron level corrections are calculated. A decrease of 0.2 is used for each of the fractions: detector level inclusive, detector level tagged and hadron level.
The predictions for the f_1b fraction are shown below for Pythia Tune A and Herwig at detector level for all b-jets and only the tagged b-jets.
The eps version of this plot is here.
Tagged Jets
The tagged jet shapes are computed in data as the average integrated jet shapes for all tagged jets.
Inclusive Jets
The nonb-jet shapes can be approximated by using the jet shapes for all jets. The fraction of b-jets in the inclusive jet sample is only of the order of a few percent and it was shown that this approximation does not affect the outcome of the measurement.
Purity
The b-jet purity is extracted in the same way as for the b-jet cross-section analysis. The distribution of the secondary vertex masses (total mass of all tracks associated with the displaced vertex) for b-jets is not centrered on the b-jet mass because the tracking does not see neutral particles. Nevertheless the distributions of the secondary vertex mass (Msecvtx) are significantly different for b-jets than for nonb-jets. Distributions are obtained from Pythia Tune A for both b-jets and nonb-jets for each pt bin (templates).
The templates for the second pt bin are shown below:
The eps version of this plot is here.
The data is then fitted to these templates using an unbinned chi2 fit (using the root function: TFractionFitter). The fraction of b-jets is obtained. The fit is shown in the above plot. The data, shown as black points, is compared to the fit, shown as a red line. The fit is very stable with respect to a change in the bin size and the fit range.
Below is a plot comparing the templates obtained for b-jets and nonb-jets from Pythia Tune A and Herwig MC. This shows that both MC samples give very similar templates.
The eps version of this plot is here.
The final results for the b-jet purity are reported below for the four pt bins considered, showing only the statistical errors on the data. These values are in good agreement with the previously obtained results. This plot shows the purity extracted from fits to Pythia Tune A templates as well as those obtained from Herwig templates. The use of Herwig MC samples in the unfolding procedure is used as an evaluation of the systematic error associated with the use of a particular set of models to describe the fragmentation, hadronisation and underlying event.
The eps version of this plot is here.
Tagging Bias on b-jets
The bias due to tagging is computed, from the re-weighted Pythia Tune A MC (using f1b - 0.2) as the ratio of the tagged over the inclusive jet shapes for b-jets:
The maximum bias due to tagging on b-jet is of the order of 8%.
The tagging biases on b-jet are shown in the following plots for the 4 pt bins, the reported errors are the MC statistical errors. Also shown, are the tagging biases for single b-quark jet shapes and double b-quark jet shapes.
The eps version of this plot is here.
It is not necessary that the biases for the b-jets are between those for the single and the double b-quark jet shapes because of the different single b-quark jet fraction before and after tagging.
Tagging Bias on nonb-jets
The bias due to tagging on nonb-jets is computed from Pythia Tune A MC as the ratio of the tagged over the inclusive jet shapes for nonb-jets
The maximum bias due to tagging on nonb-jet is of the order of 17%.
The tagging biases on nonb-jet are shown in the following plots for the 4 pt bins, the reported errors are the MC statistical errors. Also shown, are the tagging biases for c-quark jet shapes and gluon+light-quark jet shapes.
The eps version of this plot is here.
Hadron Level Corrections to b-jets
The hadron level corrections, needed to obtain a detector independent measurement, are computed from the re-weighted Pythia Tune A MC (using f1b -0.2) as the ratio of the hadron level over the detector level b-jet shapes. At hadron level the jet shapes are computed using all the final state hadrons inside the jet cone.
The hadron level corrections to b-jet are reported below for each of the 4 pt bins, where the errors correspond to the MC statistical errors. The hadron level corrections to single b-quark jets and double b-quark jets are also shown.
The eps version of this plot is here.
Systematics
The dominant sources of systematic uncertainties are
- The whole analysis is re-done but using tracks instead of calorimeter towers in order to compute the measured jet shapes. The tagging biases and well as the hadron level corrections need to be re-calculated. The difference between the hadron level b-quark jet shapes computed with tracks and with calorimeter towers is taken as a systematic uncertainty on the measurement. This investigates how well the calorimeter response to low energy particles is modelled.
- The difference in the hadron level b-jet shapes unfolded using Pythia Tune A, as the default, and Herwig. The gives an estimate of the effect of using different fragmentation, hadronisation and underlying event models.
- Variation of the single b-quark jet fraction from decreased by 0.2 and decreased by 0.5 with respect to the default predictions.
- The effect of decreasing the single c-quark jet content by 0.2 is investigated. This has an effect on the nonb-jet templates used for the purity extraction as well as the tagging biases on nonb-jets.
- The jet energy scale uncertainty: a 3% variation is applied to the jet pt.
The other, non-dominant sources of systematic uncertainties considered are:
- A variation by 5 cm of the primary vertex Z-position cut
- A variation of 15% (relative) on the missing Et significance cut
- The difference in the hadron level b-quark jet shapes computed using only calorimeter towers above a pt threshold of 0.5 GeV/c and those computed using the default cut at 0.1 GeV/c
- Possible effects associated with the simulation of the b-tagging algorithm were investigated and found to be very small.
The total error on the measurement for each point in pt and in r/R is shown in the figure below. Also reported are the five dominant sources of systematic uncertainty and the contribution from the statistical error.
The eps version of this plot is here.
Results: Hadron Level b-quark Jet Shapes
The final, hadron level, integrated jet shapes are shown below for each of the four pt bins. The data is shown with both the total and the statistical errors (the statistical errors are most of the time smaller than the points). The data is compared to the Pythia Tune A and Herwig predictions for b-jets and for inclusive jets as well as for b-jets with a single b-quark fraction reduced by 0.2.
The eps version of this plot is here.
The same results are compared to the Pythia Tune A and Herwig predictions for b-jets, single b-quark jets, double b-quark jets and the b-jets with the f1b fraction decreased by 0.2, as used for the bias and hadron level corrections.
The eps version of this plot is here.
The ratios of the MC predictions over the measured b-quark jet shapes are shown below. The yellow band stands for the total errors on the measurement. The ratio is computed for single b-quark jets, double b-quark jets as well as inclusive b-quark jets and b-quark jets with a f1b fraction decreased by 0.2. This shows that the agreement between data and MC is significantly improved by decreasing the f1b fraction but that the agreement is still not perfect.
The eps version of this plot is here.
The evolution, as a function of jet pt, of the momentum fraction outside a cone of fixed radius (0.2 in this case) gives a good indication of the evolution of the parton flavour of the jets. The plot below shows the evolution of this fraction as a function of the transverse momentum of the jets for b-jets. The measurements are compared to the Pythia Tune A and Herwig predictions for b-jets, b-jets with a f1b fraction decreased by 0.2 and inclusive jets. Also reported on this plot are the previously published inclusive jet shape results (those were obtained with a slightly different rapidity cut, 0.1<|Y|<0.7, but this was found not to affect significantly the jet shapes).
The eps version of this plot is here.
Below the same data points are shown but compared to the Pythia Tune A and Herwig predictions for b-jets, b-jets with a f1b fraction decreased by 0.2, single b-quark jets and double b-quark jets.
The eps version of this plot is here.
Last modified: October 25th 2006