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| CMS-BPH-15-003 ; CERN-EP-2019-186 | ||
| Study of $\mathrm{J}/\psi$ meson production from jet fragmentation in pp collisions at $\sqrt{s} = $ 8 TeV | ||
| CMS Collaboration | ||
| 3 October 2019 | ||
| Phys. Lett. B 804 (2020) 135409 | ||
| Abstract: A study of the production of prompt $\mathrm{J}/\psi$ mesons as fragmentation products of jets in proton-proton collisions at $\sqrt{s} = $ 8 TeV is presented. The analysis is based on data corresponding to an integrated luminosity of 19.1 fb$^{-1}$ collected with the CMS detector at the LHC. For events with at least one observed jet, the angular separation between the $\mathrm{J}/\psi$ meson and the jet is used to test whether the $\mathrm{J}/\psi$ meson is a jet fragment. The analysis shows that most prompt $\mathrm{J}/\psi$ mesons with energy above 15 GeV and rapidity $|y| < $ 1 are fragments of jets with pseudorapidity $|{\eta_{\text{jet}}}| < $ 1. The differential distributions of the jet fragmentation probability as a function of jet energy for a fixed $\mathrm{J}/\psi$ energy fraction are compared to a theoretical model using the fragmenting jet function approach. The data agree best with fragmenting jet function calculations that use a long-distance matrix element parameter set in which prompt $\mathrm{J}/\psi$ mesons are unpolarized. This technique demonstrates a new way to test predictions for prompt $\mathrm{J}/\psi$ production using nonrelativistic quantum chromodynamics. | ||
| Links: e-print arXiv:1910.01686 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The distributions of (left) $ {\Delta R}$ for one-jet events and (right) $ {\Delta R}_1$ vs. $ {\Delta R}_2$ for two-jet events. |
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Figure 1-a:
The distribution of $ {\Delta R}$ for one-jet events. |
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Figure 1-b:
The distribution of $ {\Delta R}_1$ vs. $ {\Delta R}_2$ for two-jet events. |
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Figure 2:
Comparison of $\Xi (E_{\text {jet}}; \ 0.425)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BCKL (left) and the BK (right) LDME parameter sets. The curves show the detailed energy dependence of the predictions. |
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Figure 2-a:
Comparison of $\Xi (E_{\text {jet}}; \ 0.425)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BCKL LDME parameter set. The curves show the detailed energy dependence of the predictions. |
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Figure 2-b:
Comparison of $\Xi (E_{\text {jet}}; \ 0.425)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BK LDME parameter set. The curves show the detailed energy dependence of the predictions. |
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Figure 3:
Comparison of $\Xi (E_{\text {jet}}; \ 0.525)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BCKL (left) and the BK (right) LDME parameter sets. The curves show the detailed energy dependence of the predictions. |
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Figure 3-a:
Comparison of $\Xi (E_{\text {jet}}; \ 0.525)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BCKL LDME parameter set. The curves show the detailed energy dependence of the predictions. |
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Figure 3-b:
Comparison of $\Xi (E_{\text {jet}}; \ 0.525)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BK LDME parameter set. The curves show the detailed energy dependence of the predictions. |
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Figure 4:
Comparison of $\Xi (E_{\text {jet}}; \ 0.625)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BCKL (left) and the BK (right) LDME parameter sets. The curves show the detailed energy dependence of the predictions. |
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Figure 4-a:
Comparison of $\Xi (E_{\text {jet}}; \ 0.625)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BCKL LDME parameter set. The curves show the detailed energy dependence of the predictions. |
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Figure 4-b:
Comparison of $\Xi (E_{\text {jet}}; \ 0.625)$ versus $E_{\text {jet}}$ from data with the FJF predictions from each of the four NRQCD terms, using the BK LDME parameter set. The curves show the detailed energy dependence of the predictions. |
| Tables | |
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Table 1:
For $z_1 =$ 0.425, the $\chi ^2$ value and the associated $p$-value (in parentheses) for 7 degrees of freedom from the comparison of the data and the prediction for each FJF term, using the BCKL and BK LDME parameter sets. |
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Table 2:
For $z_1 =$ 0.525, the $\chi ^2$ value and the associated $p$-value (in parentheses) for 7 degrees of freedom from the comparison of the data and the prediction for each FJF term, using the BCKL and BK LDME parameter sets. |
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Table 3:
For $z_1 =$ 0.625, the $\chi ^2$ value and the associated $p$-value (in parentheses) for 7 degrees of freedom from the comparison of the data and the prediction for each FJF term, using the BCKL and BK LDME parameter sets. |
| Summary |
|
The first analysis has been presented comparing data for prompt $\mathrm{J}/\psi$ mesons produced as fragments of central gluonic jets with a theoretical analysis based on the fragmenting jet function (FJF) approach. The term prompt means that the $\mathrm{J}/\psi$ meson is consistent with originating from the primary vertex. In the FJF model, the jet fragments into a $\mathrm{c}\mathrm{\bar{c}}$ system in an angular momentum state and quark color configuration $^{2S+1}L_{J}^{n}$ plus other hadrons. Here, $S$, $L$, and $J$ are the spin, orbital, and total angular momentum quantum numbers of the $\mathrm{c}\mathrm{\bar{c}}$ system and $n$ indicates a color-singlet ($n$ = 1) or color-octet ($n$ = 8) configuration. The FJF analysis uses the nonrelativistic quantum chromodynamics (NRQCD) approach to compute the cross section for the formation of a $\mathrm{J}/\psi$ meson from the $\mathrm{c}\mathrm{\bar{c}}$ system for four specific $S$, $J$, $L$, and $n$ configurations: $^{1}S_{0}^{8}$, $^3S_{1}^{8}$, $^{3}S_{1}^{1}$, and $^3P_{J}^{8}$. The data were collected by the CMS Collaboration in proton-proton collisions at $\sqrt{s} = $ 8 TeV, corresponding to an integrated luminosity of 19.1 fb$^{-1}$ . The kinematic selections for the analysis are $E_{\mathrm{J}/\psi} > $ 15 GeV, $|{y_{\mathrm{J}/\psi}}| < $ 1, ${p_{\mathrm{T}}}^{\text{jet}} > $ 25 GeV, and $|{\eta_{\text{jet}}}| < $ 1. The agreement between the data and the FJF predictions over a wide range of $z$, where $z$ is the $\mathrm{J}/\psi$ meson fraction of the jet energy, supports the FJF model predictions for gluon jet fragmentation into $\mathrm{J}/\psi$ mesons. For three specific $z$ ranges, 0.40-0.45, 0.50-0.55, and 0.60-0.65, the $^{3}S_{1}^{8}$ and $^3P_{J}^{8}$ FJF terms do not match the fragmentation data for either the Bodwin, Chung, Kim, and Lee (BCKL) [32] or Butenschoen and Kniehl (BK) [33] long-distance matrix element (LDME) parameter sets, indicating that these terms are not the main contributors to $\mathrm{J}/\psi$ meson production by jet fragmentation. Only the nonrelativistic quantum chromodynamics (NRQCD) $^{1}S_{0}^{8}$ term, using the BCKL LDME parameters, matches the data for jet fragmentation to $\mathrm{J}/\psi$ mesons for all three $z$ ranges. The dominance of this term, which has all angular momenta equal to zero in the $\mathrm{c}\mathrm{\bar{c}}$ rest frame, would explain the experimental measurements [6,7] of small $\mathrm{J}/\psi$ meson polarization for ${p_{\mathrm{T}}}^{\mathrm{J}/\psi} > 12$ GeV. For $z > 0.5$, the NRQCD $^{3}S_{1}^{1}$ term, using the BK LDME parameters, has almost the same jet energy dependence as the BCKL $^{1}S_{0}^{8}$ term and could play the dominant role in jet fragmentation to $\mathrm{J}/\psi$ mesons. However, the $^{3}S_{1}^{1}$ NRQCD term implies a significant $\mathrm{J}/\psi$ meson polarization for $z > $ 0.5, corresponding to 16 $ < {p_{\mathrm{T}}}^{\mathrm{J}/\psi} < $ 34 GeV, in contradiction with experimental results. When a jet is observed in an event, the fraction of $\mathrm{J}/\psi$ mesons from jet fragmentation is (94.2 $\pm$ 0.1)%, averaged over one- and two-jet events. Using a simple model to estimate the fraction of $\mathrm{J}/\psi$ mesons that are fragments of jets that fail the analysis ${p_{\mathrm{T}}}^{\text{jet}}$ requirement, jet fragmentation is found to be the source of (85 $\pm$ 3 (stat) $\pm$ 7 (syst))% of the $\mathrm{J}/\psi$ mesons produced in the kinematic region probed in this study. This analysis shows that jet fragmentation accounts for almost all prompt $\mathrm{J}/\psi$ mesons produced at large ${p_{\mathrm{T}}}^{\mathrm{J}/\psi}$ and is consistent with being dominated by the $^{1}S_{0}^{8}$ FJF term using the BCKL parameter set, thus explaining the small $\mathrm{J}/\psi$ meson polarization for ${p_{\mathrm{T}}}^{\mathrm{J}/\psi} > $ 12 GeV. |
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