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 Monte Carlo simulation. 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 the Pythia Tune A 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 is defined as
This can be schematically visialised 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 (difference very small, smaller than statistical errors on data)
- p_b is the purity of the sample
Blessed Plots
Tagged Jets
The tagged jet shapes are computed in data as the average integrated jet shapes for all taged jets. These are shown in the figures below. The data is compared to the Pythia Tune A MC predictions. The agreement is found to be not very good.
The Pythia Tune A predictions are re-weighted in order to agree better with the data. The re-weighting is done by varying the fraction of b-quark jets which contain only a single b-quark inside the same jet cone (f1b). Decresing this f1b fraction by 20% (absolute) gives the best agreement between the data and the MC. The re-weighted MC samples are the ones which are used to obtain the tagging bias and hadron level correction to the b-jets.
The eps version of this plot is here.
These plots show the same information as before but taking the ratio of the Pythia Tune A predictions to the measured tagged jet shapes. The yellow bands show the data statistical errors. The error bars on the points are the MC statistical errors. This shows that the re-weighted MC agrees much better with the data than the default one.
The eps version of this plot is here.
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.
The final results for the b-jet purity as shown 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.
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 - 20%) 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 errors show 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. It seems, from Pythia Tune A studies, that it is more likely to tag jets containing two b-quarks inside the same jet cone than a single b-quark. This is shown in the figure below which compares the f1b fraction before and after tagging for the default Pythia Tune A.
The eps version of this plot is here.
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 errors show 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 -20%) 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 shown for each of the 4 pt bins below, black points, showing 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
- Variation of the single c-quark jet fraction: In order for the data to agree best with the MC, the f1b fraction needed to be decreased by about 20%. There could be similar effects to those affecting the b-jets on c-quark jets. The fraction of c-quark jets is not known to be well reproduced with LO Pythia Tune A. A variation of 20% (absolute) is thus applied to the single c-quark jet fraction. This affects the nonb-jet templates used for the purity extraction as well as the tagging biases on nonb-jets.
- 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 Pythia Tune A MC statistics, particularly for the calculation of the bias due to tagging on the nonb-jets, gives a considerable error to the measurement. This error is taken as a systematic error. Despite this error being large, the generation of more MC sample would not significantly reduce the total systematic error
The other, non-dominant sources of systematic uncertainties considered are:
- The jet energy scale uncertainty: a 3% variation is applied to the jet pt
- 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.
Results: Hadron Level b-quark Jet Shapes
The final, hadron level, integrated jet shapes are shown below for each of the 4 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). This is compared to the Pythia Tune A predictions for b-jets and for inclusive jets.
The eps version of this plot is here.
The same results are compared to the Pythia Tune A predictions for b-jets, single b-quark jets, double b-quark jets and the b-jets with the f1b fraction decreased by 20%, as used for the bias and hadron level corrections.
The eps version of this plot is here.
The ratio of the Pythia tune A predictions over the measured b-quark jet shapes is shown below. The yellow band shows the total errors on the measurement. The ratio is computed for single b-quark jets, double b-quark jets and well as inclusive b-quark jets and b-quark jets with a f1b fraction decreased by 20%. 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, showing both the total and the statistical errors, as well as the Pythia Tune A predictions for b-jets and inclusive jets. Also shown on this plot is a comparison to the previously published inclusive jet shape results which have a slightly different rapidity cut (0.1<|Y|<0.7) but the effect of removing the central rapidity region was not found to affect significantly the measured jet shapes.
The eps version of this plot is here.
Below the same data points are shown but compared to the Pythia Tune A prediction for b-jets, b-jets with a 20% lower f1b fraction, single b-quark jets and double b-quark jets.
The eps version of this plot is here.
Last modified: Sat May 27 17:40:37 CDT 2006