CMS-PAS-TOP-18-012

CMS-PAS-TOP-18-012
Measurement of the shape of the b quark fragmentation function using charmed mesons produced inside b jets from $\mathrm{t}\bar{\mathrm{t}}$ pair decays
CMS Collaboration
June 2021

Abstract: A determination of the shape parameter of the Lund-Bowler fragmentation function for b quarks is presented. The analysis uses charm mesons produced inside b jets from $\mathrm{t}\bar{\mathrm{t}}$ pair decays in a data sample collected by the CMS experiment at the LHC at $\sqrt{s}=$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb $^{-1}$ . Samples of D $^{0}$ and J/ $\psi$ mesons are reconstructed from the decays D $^{0} \to$ K $^{\pm} \pi^{\mp}$ and J/ $\psi \to \mu^{+}\mu^{-}$ using charged particle track information. The reconstructed mesons are used as proxies for their parent B hadrons. The corresponding $x_{b}$ distributions, where $x_{b}$ is the fraction of the total transverse momentum of the charged constituents of the jet carried by the charm meson, are fitted to extract the value of the fragmentation function shape parameter, $r_{b}$ . A value of $r_{b}=$ 0.858 $\pm$ 0.037 (stat) $\pm$ 0.031 (syst) is obtained. This is the first measurement of the b quark fragmentation function in $\mathrm{t}\bar{\mathrm{t}}$ events at the LHC, and significantly improves the experimental constraints on the shape of the function. From a comparison with results at the Z pole in e $^{+}$ e $^{-}$ data, no evidence for an environmental dependence of the fragmentation function is observed.
Links: CDS record (PDF) ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the combined background predictions from simulations of ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair + vector boson production ( ${\mathrm{t} {}\mathrm{\bar{t}}}$ +V, where V is a W or Z boson), single top production in the $t$ channel (t-ch) and $\mathrm{t} \mathrm{W}$ channel ( $\mathrm{t} \mathrm{W}$ ), W boson production (W), Drell-Yan pair production (DY), and $\mathrm{W} \mathrm{W}$ , $\mathrm{W} \mathrm{Z}$ , and $\mathrm{Z} \mathrm{Z}$ production (multiboson). The lower panels show the ratio of the data to the simulation. The shaded bands correspond to the total uncertainty in the simulation (statistical and systematic).
png pdf	Figure 1-a: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the combined background predictions from simulations of ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair + vector boson production ( ${\mathrm{t} {}\mathrm{\bar{t}}}$ +V, where V is a W or Z boson), single top production in the $t$ channel (t-ch) and $\mathrm{t} \mathrm{W}$ channel ( $\mathrm{t} \mathrm{W}$ ), W boson production (W), Drell-Yan pair production (DY), and $\mathrm{W} \mathrm{W}$ , $\mathrm{W} \mathrm{Z}$ , and $\mathrm{Z} \mathrm{Z}$ production (multiboson). The lower panels show the ratio of the data to the simulation. The shaded bands correspond to the total uncertainty in the simulation (statistical and systematic).
png pdf	Figure 1-b: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the combined background predictions from simulations of ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair + vector boson production ( ${\mathrm{t} {}\mathrm{\bar{t}}}$ +V, where V is a W or Z boson), single top production in the $t$ channel (t-ch) and $\mathrm{t} \mathrm{W}$ channel ( $\mathrm{t} \mathrm{W}$ ), W boson production (W), Drell-Yan pair production (DY), and $\mathrm{W} \mathrm{W}$ , $\mathrm{W} \mathrm{Z}$ , and $\mathrm{Z} \mathrm{Z}$ production (multiboson). The lower panels show the ratio of the data to the simulation. The shaded bands correspond to the total uncertainty in the simulation (statistical and systematic).
png pdf	Figure 1-c: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the combined background predictions from simulations of ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair + vector boson production ( ${\mathrm{t} {}\mathrm{\bar{t}}}$ +V, where V is a W or Z boson), single top production in the $t$ channel (t-ch) and $\mathrm{t} \mathrm{W}$ channel ( $\mathrm{t} \mathrm{W}$ ), W boson production (W), Drell-Yan pair production (DY), and $\mathrm{W} \mathrm{W}$ , $\mathrm{W} \mathrm{Z}$ , and $\mathrm{Z} \mathrm{Z}$ production (multiboson). The lower panels show the ratio of the data to the simulation. The shaded bands correspond to the total uncertainty in the simulation (statistical and systematic).
png pdf	Figure 1-d: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the combined background predictions from simulations of ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair + vector boson production ( ${\mathrm{t} {}\mathrm{\bar{t}}}$ +V, where V is a W or Z boson), single top production in the $t$ channel (t-ch) and $\mathrm{t} \mathrm{W}$ channel ( $\mathrm{t} \mathrm{W}$ ), W boson production (W), Drell-Yan pair production (DY), and $\mathrm{W} \mathrm{W}$ , $\mathrm{W} \mathrm{Z}$ , and $\mathrm{Z} \mathrm{Z}$ production (multiboson). The lower panels show the ratio of the data to the simulation. The shaded bands correspond to the total uncertainty in the simulation (statistical and systematic).
png pdf	Figure 2: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the background predictions for charm and bottom jets from ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, single top production in the $t$ and $\mathrm{t} \mathrm{W}$ channels (t), W boson production (W), and Drell-Yan pair production (DY).
png pdf	Figure 2-a: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the background predictions for charm and bottom jets from ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, single top production in the $t$ and $\mathrm{t} \mathrm{W}$ channels (t), W boson production (W), and Drell-Yan pair production (DY).
png pdf	Figure 2-b: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the background predictions for charm and bottom jets from ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, single top production in the $t$ and $\mathrm{t} \mathrm{W}$ channels (t), W boson production (W), and Drell-Yan pair production (DY).
png pdf	Figure 2-c: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the background predictions for charm and bottom jets from ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, single top production in the $t$ and $\mathrm{t} \mathrm{W}$ channels (t), W boson production (W), and Drell-Yan pair production (DY).
png pdf	Figure 2-d: Invariant mass distributions for the initial samples of $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower left) meson candidates. The data are compared to the background predictions for charm and bottom jets from ${\mathrm{t} {}\mathrm{\bar{t}}}$ pair production, single top production in the $t$ and $\mathrm{t} \mathrm{W}$ channels (t), W boson production (W), and Drell-Yan pair production (DY).
png pdf	Figure 3: Fragmentation proxy distributions for the background-subtracted samples for $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower) meson candidates. The proxy for the $\mathrm{J}/\psi$ and ${\mathrm{D^0}}$ events is defined as the ratio of the meson ${p_{\mathrm {T}}}$ over the ${p_{\mathrm {T}}}$ of all of the charged particles in the jet, ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . For the ${{\mathrm{D^0}} _{\mu}}$ sample this is changed to the ( ${p_{\mathrm {T}}}$ of the combined meson and tag $\mu$ system) / ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . The shaded bands show the result of the combined fit to the data, where the width of the band is the combined statistical and systematic uncertainty.
png pdf	Figure 3-a: Fragmentation proxy distributions for the background-subtracted samples for $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower) meson candidates. The proxy for the $\mathrm{J}/\psi$ and ${\mathrm{D^0}}$ events is defined as the ratio of the meson ${p_{\mathrm {T}}}$ over the ${p_{\mathrm {T}}}$ of all of the charged particles in the jet, ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . For the ${{\mathrm{D^0}} _{\mu}}$ sample this is changed to the ( ${p_{\mathrm {T}}}$ of the combined meson and tag $\mu$ system) / ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . The shaded bands show the result of the combined fit to the data, where the width of the band is the combined statistical and systematic uncertainty.
png pdf	Figure 3-b: Fragmentation proxy distributions for the background-subtracted samples for $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower) meson candidates. The proxy for the $\mathrm{J}/\psi$ and ${\mathrm{D^0}}$ events is defined as the ratio of the meson ${p_{\mathrm {T}}}$ over the ${p_{\mathrm {T}}}$ of all of the charged particles in the jet, ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . For the ${{\mathrm{D^0}} _{\mu}}$ sample this is changed to the ( ${p_{\mathrm {T}}}$ of the combined meson and tag $\mu$ system) / ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . The shaded bands show the result of the combined fit to the data, where the width of the band is the combined statistical and systematic uncertainty.
png pdf	Figure 3-c: Fragmentation proxy distributions for the background-subtracted samples for $\mathrm{J}/\psi$ (upper left), untagged ${\mathrm{D^0}}$ (upper right), and flavor-tagged ${{\mathrm{D^0}} _{\mu}}$ (lower) meson candidates. The proxy for the $\mathrm{J}/\psi$ and ${\mathrm{D^0}}$ events is defined as the ratio of the meson ${p_{\mathrm {T}}}$ over the ${p_{\mathrm {T}}}$ of all of the charged particles in the jet, ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . For the ${{\mathrm{D^0}} _{\mu}}$ sample this is changed to the ( ${p_{\mathrm {T}}}$ of the combined meson and tag $\mu$ system) / ${\Sigma {{p_{\mathrm {T}}} ^{\text {ch}}}}$ . The shaded bands show the result of the combined fit to the data, where the width of the band is the combined statistical and systematic uncertainty.
png pdf	Figure 4: The Lund-Bowler fragmentation function for b quarks plotted as a function of ${x_{\mathrm{b}}}$ . The left panel shows the comparison of the result from this analysis (green), the result obtained from the data at the Z pole (light blue), and the current default function from PYTHIA 8 (black line). The right panel shows the value of the the fitted functions divided by the PYTHIA 8 calculation.
png pdf	Figure 4-a: The Lund-Bowler fragmentation function for b quarks plotted as a function of ${x_{\mathrm{b}}}$ . The left panel shows the comparison of the result from this analysis (green), the result obtained from the data at the Z pole (light blue), and the current default function from PYTHIA 8 (black line). The right panel shows the value of the the fitted functions divided by the PYTHIA 8 calculation.
png pdf	Figure 4-b: The Lund-Bowler fragmentation function for b quarks plotted as a function of ${x_{\mathrm{b}}}$ . The left panel shows the comparison of the result from this analysis (green), the result obtained from the data at the Z pole (light blue), and the current default function from PYTHIA 8 (black line). The right panel shows the value of the the fitted functions divided by the PYTHIA 8 calculation.

Tables
png pdf	Table 1: Systematic uncertainties in ${r_{\mathrm{b}}}$ from the background subtraction procedure for the different processes producing c and b jets. Entries for which the uncertainty is less than 0.001 are denoted by "---''.
png pdf	Table 2: Systematic uncertainties in ${r_{\mathrm{b}}}$ from the modeling of the ${x_{\mathrm{b}}}$ shape in PYTHIA 8.
png pdf	Table 3: Sources of systematic uncertainty in ${r_{\mathrm{b}}}$ and their estimated values.

Summary

A determination of the shape parameter of the Lund-Bowler fragmentation function for b quarks has been presented. The analysis uses charm mesons produced inside b jets from

$\mathrm{t\bar{t}}$ production and is based on 35.9 fb

$^{-1}$ of data recorded by the CMS experiment at

$\sqrt{s} =$ 13 TeV during 2016. Samples of

${\mathrm{D^0}}$ and

$\mathrm{J}/\psi$ meson candidates are reconstructed from the decays

${\mathrm{D^0}} \to \mathrm{K^{\pm}} \pi^{\mp}$ and

$\mathrm{J}/\psi \to \mu^{+}\mu^{-}$ using charged particle track information. The mesons are used as proxies for their parent b quarks and the corresponding

${x_{\mathrm{b}}}$ distributions, where

${x_{\mathrm{b}}}$ is the fraction of the combined transverse momentum of the charged constituents of the jet carried by the charm meson, are fitted to extract the value of the shape parameter

${r_{\mathrm{b}}}$ . A value of

${{{r_{\mathrm{b}}}}} =$ 0.858

$\pm$ 0.037 (stat)

$\pm$ 0.031 (syst) is obtained. This is the first measurement of the b quark fragmentation function in the

$\mathrm{t\bar{t}}$ environment, and it significantly improves the experimental precision on the shape of the fragmentation function. From a comparison with results obtained from

$\mathrm{e^{+}}\mathrm{e^{-}}$ data at the Z pole, no evidence is observed for an environmental dependence of the shape of the fragmentation function.

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