A Study of Quark Fragmentation using Kaons Produced in Association with Prompt Ds±/D± Mesons

Primary Authors: Niharika Ranjan, Matthew Jones

This web page provides a concise summary of the analysis.

Here is a link to the public note.


Introduction

Quark fragmentation is a non-perturbative process for which Monte Carlo event generators implement only phenomenological models that have been tuned to reproduce general properties of hadron production. Since the description of the fragmentation process is provided using phenomenological models, studying aspects of the non-perturbative process in data is important for validation of the models. Although a number of fragmentation studies have been conducted at LEP, the non-perturbative process has not been extensively studied at hadron colliders. In this analysis we probe the non-perturbative aspects of quark fragmentation by measuring the quark flavor fractions of charged particles produced in association with Ds± and D± mesons. Since QCD locally conserves quark flavor, this probes new details of the process by which quark anti-quark pairs are produced and subsequently form bound states in the fragmentation of a heavy quark jet.

Previous studies of heavy quark fragmentation at CDF have studied the production of kaons and pions around bottom mesons. These results showed that more fragmentation kaons are produced around Bs0 mesons as compared to B0 and B+. Although this observation is in qualitative agreement with the predictions of the string fragmentation model used in the PYTHIA event generator, a detailed study of charge-flavor correlations between kaons and the decay flavor of Bs0 mesons is not feasible because of the high Bs0 oscillation frequency. Instead, we perform an analysis to study kaon production around charm mesons, namely Ds± and D±. According to the naive fragmentation model, a kaon will be produced in the first fragmentation branch in association with a Ds± whereas, creation of a D± meson results in the production a pion in the first fragmentation branch as illustrated in figure below:

Hence, more opposite charge sign kaons are likely to be produced around Ds± as compared to D±. Another advantage is that there are no known strong decays that can produce charge correlations between Ds± mesons and kaons unlike D**0 → D+ π- decays (that result in charge correlation between D+ and π-) and Bs**0 → B+ K- decays (that result in charge correlation between B+ and K-). Consequently, any charge correlation observed between the fragmentation kaon and Ds± will be due to flavor conservation in the first fragmentation branch and not due to resonance decays.

In this study, we provide a comparison of various kinematical distributions of kaons produced around prompt Ds± and prompt D± that allows us to extract some information about the properties of the kaon that is more likely to be produced in the first fragmentation branch, which is generated only around prompt Ds±. We compare the results in data with predictions of the PYTHIA event generator that uses the string fragmentation model and the HERWIG event generator that uses the cluster fragmentation model.

Overview of the Analysis

Using a sample of events collected with CDF's all-hadronic heavy flavor trigger, we reconstruct Ds±/D± → φ π±, φ → K+ K- decays and analyze events that have invariant mass in the range 1.75 < m(KKπ) < 2.2 GeV. The trigger path requires a pair of oppositely charged tracks that are identified as being displaced with respect to the primary vertex (collision point) based on the pattern of associated hits in the silicon detector. Both tracks are required to have transverse momentum pT > 2.0 GeV and the sum of their transverse momentum has to be greater than 5.5 GeV. In addition, the trigger path includes requirements on the opening angle between the two tracks in the transverse plane and the decay length in the transverse plane. This event sample, obtained from 360 pb-1 of pp-bar collisions at √s = 1.96 TeV, contains about 260,000 Ds± and 140,000 D± candidates with transverse momentum in the range 7 < pT(KKπ) < 30 GeV.

The Ds±/D± mesons in the sample include the prompt D component that is produced due to hadronization of a charm quark and the secondary D component that is produced in B decays. In order to extract information pertaining to charm quark fragmentation, we are primarily interested in the prompt Ds±/D± component. Hence, an important step in the analysis is the separation of the prompt and secondary components in data. We use the impact parameter distribution of the reconstructed KKπ candidates to statistically separate the prompt and secondary D components in data.

After separating the two components, the next step in the analysis is to measure the kaon, pion and proton fractions around the various D components. This is done by applying particle identification techniques on a sample of tracks found in a cone of radius ΔR = 0.7 around the reconstructed KKπ candidates. We use two main particle identification techniques in the analysis, namely, the measurement of the specific ionization per unit track length (dE/dx) in the Central Outer Tracker (COT) and the time of flight of the particle measured in the Time-of-Flight (TOF) sub-detector.

Although we also measure the pion and proton fractions in the analysis, we are primarily interested in the measured kaon fraction since we want to study the charge correlation between Ds± and kaons produced in the fragmentation process. The distribution of the kaon fraction around prompt Ds±/D± components is measured as a function of various kinematic quantities, which is compared with the distribution obtained around prompt Ds±/D± mesons produced in cc-bar events generated using the PYTHIA and HERWIG Monte Carlo event generators.

Separating prompt and secondary Ds±/D± components

A prompt Ds±/D± meson that is created via hadronization of a charm quark will be produced at the primary vertex and should ideally have zero impact parameter with respect to the primary vertex. However, due to finite resolution of the detector the impact parameter distribution of the prompt component will be a Gaussian distribution with the width of the Gaussian being equal to the detector resolution. On the other hand, a secondary Ds±/D± meson that is produced in B decays will be boosted and can have non zero impact parameter (d0) with respect to the primary vertex as illustrated:

This difference in the inherent shape of the impact parameter distribution of the two components measured with respect to the primary vertex can be used for separating the prompt and secondary Ds±/D± components. In the analysis, we statistically separate the prompt and secondary D components by using the invariant mass distribution and the impact parameter distributions of the reconstructed KKπ candidates in a likelihood fit. The invariant mass distribution is used to separate the Ds± and D± signal from the combinatorial background. The Ds± and D± signal peak is described using a double Gaussian function. The shape of the wide bump in the invariant mass distribution that occurs around 2.02 GeV is obtained using Monte Carlo samples of mis-reconstructed D+ → K-π+π+ decays. A fourth order polynomial is used to describe the shape of the background component in the invariant mass distribution. The likelihood fit is performed in ranges of transverse momentum of the KKπ candidate. The invariant mass projections obtained from the fit are shown below in the plot below:

The impact parameter distribution is used to separate the prompt and secondary components in the Ds± and D± signal. The shape of the prompt D component in the impact parameter distribution is described using a double Gaussian function. In order to describe the shape of the secondary component, we extract the impact parameter distribution of secondary Ds±/D± mesons using Monte Carlo samples of B decays. The template that describes the distribution of impact parameter for secondary Ds±/D± obtained from Monte Carlo is convoluted with the prompt resolution function. The shape of the background component in the impact parameter distribution is obtained empirically. We compare the impact parameter distribution in the background sideband regions in the invariant mass distribution and find that the background impact parameter is independent of mass. Hence, we use the same function to describe the impact parameter of the background component in the sideband regions and under the Ds±/D± signal peaks, i.e. in the entire mass range [1.75,2.2] GeV. The impact parameter projections obtained from the likelihood fit, plotted in the Ds±/D± signal region defined within ±3σ from the Ds±/D± signal peak are shown below:

We observe similar level of agreement between data and fit projections in the other transverse momentum pT(KKπ) ranges in which the likelihood fit is performed.

Measurement of the kaon fraction around prompt Ds±/D± mesons

In the analysis, we select the maximum-pT track in a cone of radius ΔR = 0.7 around a KKπ candidate based on the hypothesis that the maximum-pT is more likely to be correlated with the production of a heavy meson in the fragmentation process. In addition, by studying PYTHIA samples, we find that the kinematic properties of the maximum-pT track in the cone are not affected by the underlying event activity. Using the sample of maximum-pT tracks, we measure the kaon fraction around the prompt Ds±/D± component by performing a multidimensional likelihood fit using four distributions: the invariant mass and impact parameter distributions of the KKπ candidates; and the Time-of-Flight (TOF) and dE/dx distributions of the maximum-pT track found in the cone around the reconstructed KKπ candidates.

The parameterization of the TOF distribution is obtained by studying a sample of soft pions πs from D* → D0 πs decays. The parameterization of the dE/dx distribution is obtained using a sample of generic tracks found in a cone of radius ΔR = 0.7 around reconstructed D* → D0 πs decays. Since the data sample used for the dE/dx study is not a pure sample of pions or kaons, we use the TOF distribution of the tracks found in the cone around reconstructed D* as additional information to identify the particles in the generic sample. We choose a sample of generic tracks instead of trigger tracks to calibrate the dE/dx distribution since they are produced in the same environment as the tracks found in a cone around Ds±/D± candidates used in our fragmentation study.

The underlying principle of the multidimensional fitting procedure is as follows: Given the invariant mass and impact parameter of a KKπ candidate, we can use the probability density functions describing the shape of the various components in the KKπ invariant mass and impact parameter distributions to calculate the likelihood that a given KKπ candidate is a prompt Ds±/D± meson, a secondary Ds±/D± meson or part of the background component. Using the probability density functions for the TOF and dE/dx distributions, we can calculate the likelihood that a track found in the cone around a reconstructed KKπ candidate is a kaon, pion or proton. Although we measure particle fractions around the various D components (i.e. prompt, secondary and background) separately in the fitting procedure, we are mainly interested in the kaon fraction around the prompt Ds±/D± component for a direct comparison with predictions of the Monte Carlo event generators.

Sources of systematic uncertainties

We study the following sources of systematic uncertainty in the measured kaon fraction:

(1) The effect of kaons decaying in flight: Kaons produced in pp-bar collisions can sometimes decay before traversing the CDF tracking system completely. Some of the kaons that decay in flight are either not reconstructed or mis-reconstructed. We account for this effect by studying the distribution of the fraction of generated kaons that are not reconstructed as a function of transverse momentum using Monte Carlo samples.

(2) Statistical error in the KKπ invariant mass and impact parameter PDFs: We use the KKπ invariant mass and impact parameter to statistically separate the prompt and secondary D components. The parameters in these probability distribution functions are obtained using a likelihood fitting procedure and have statistical errors. We estimate the systematic error that results by propagating the statistical uncertainty in the parameters of the mass and impact parameter PDFs.

(3) Statistical error in the calibration of particle identification variables: We use the TOF and dE/dx information for identifying kaons, pions and protons; and the parameterization of these distributions is obtained using calibration samples. We estimate the systematic error that results by propagating the statistical uncertainty in the calibration of the particle identification variables.

(4) Bias induced due to mis-identification of particle types: The kaon fraction can be biased due to mis-identification of the pion and proton components in the sample. We estimate the magnitude of the bias by studying pure kaon and pure pion samples; and find that the bias is smaller at lower momentum regime compared to higher momentum where we have poorer separation power between kaons and protons.

The results of the systematic studies indicate that the most significant source of error in the measured kaon fraction results from the bias induced due to mis-identification of particle types (see tables listed at the bottom of this page).

Results and comparison with Monte Carlo event generators

We measure the kaon fraction around prompt Ds±/D± mesons in the opposite sign and same sign charge combinations. In the opposite sign combination, the track in the cone and the D candidate are oppositely charged. In this case, we expect the kaon production to be enhanced around prompt Ds± compared to prompt D± since formation of a prompt Ds± meson requires conservation of strangeness in the first fragmentation branch. In the same sign combination, the track in the cone and the D candidate have the same sign charge. In this combination, we expect the kaon production be similar around both Ds±/D± mesons since same sign kaons are likely to be produced in later branches of the fragmentation process.

In addition to the two charge combinations, the distribution of the measured kaon fraction in data is compared with predictions of the PYTHIA and HERWIG Monte Carlo event generators as a function of the following kinematic variables:
1) Transverse momentum (pT) of the maximum-pT track found in a cone of radius Δ R = 0.7 around the reconstructed KKπ candidates
2) Invariant mass (mDK) of the maximum-pT track (using the kaon mass hypothesis) and the D candidate
3) Difference in rapidity (Δy) between the maximum-pT track and the D meson along the direction of the D momentum axis

pT distribution: The plot below shows the distribution of the measured kaon fraction around prompt Ds±/D± mesons in ranges of transverse momentum of the track. Comparing the top left and top right plots we can see that kaon production around prompt Ds± is enhanced compared to prompt D± in the opposite sign combination. The bottom two plots indicate that kaon production in the same sign combination is similar around prompt Ds± and prompt D±. The results indicate that the pT distribution for early fragmentation kaons produced around prompt Ds± mesons (top left plot) is in better qualitative agreement with the predictions of the fragmentation models, whereas the models underestimate the fraction of generic kaons that are produced in the later fragmentation branches (bottom two plots).

mDK distribution : The plot below shows the distribution of the measured kaon fraction around prompt Ds±/D± mesons in ranges of D-kaon invariant mass. Comparing the top left and top right plots we can see that kaon production around prompt Ds± is enhanced compared to prompt D± in the opposite sign combination. The bottom two plots indicate that kaon production in the same sign combination is similar around prompt Ds± and prompt D±. The results indicate that the mDK distribution for early fragmentation kaons produced around prompt Ds± mesons (top left plot) is overestimated by the fragmentation models, compared to the distribution for generic kaons produced later in the fragmentation process, for which the models are in better agreement with the data (bottom two plots).

Δy distribution : The plot below shows the distribution of the measured kaon fraction around prompt Ds±/D± mesons in ranges of rapidity difference between the track and the D candidate along the D momentum axis. Comparing the top left and top right plots we can see that kaon production around prompt Ds± is enhanced compared to prompt D± in the opposite sign combination. The bottom two plots indicate that kaon production in the same sign combination is similar around prompt Ds± and prompt D±. The distribution in opposite sign combination peaks near Δy = 0, which indicates that early fragmentation kaons produced around prompt Ds± have similar rapidity in the direction of the Ds± momentum. The results indicate that the Δy distribution for early fragmentation kaons produced around prompt Ds± mesons (top left plot) is overestimated by the fragmentation models, whereas the predictions of the models are in better agreement with the results for generic kaons that are produced in later fragmentation branches (bottom two plots).

Summary

We compare various kinematic distribution of the measured kaon fraction around prompt Ds±/D± mesons with predictions of the string fragmentation model used in the PYTHIA event generator and the cluster fragmentation model used in the HERWIG event generator. The results of the comparative study indicate that the pT distribution for early fragmentation kaons produced around prompt Ds± is in better qualitative agreement with predictions of fragmentation models, compared to generic kaons that are produced in later fragmentation branches, for which the models underestimate the fraction of kaons. Conversely, the mDK and Δy distributions indicate that the fragmentation models overestimate the fraction of kaons produced in early stages of the fragmentation process compared to the fraction of generic kaons that are produced in later branches, for which the predictions of the models are in better qualitative agreement with the distribution in data.


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