CMS-FSQ-15-009 ; CERN-EP-2019-151 | ||
Bose-Einstein correlations of charged hadrons in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
CMS Collaboration | ||
20 October 2019 | ||
JHEP 03 (2020) 014 | ||
Abstract: Bose-Einstein correlations of charged hadrons are measured over a broad multiplicity range, from a few particles up to about 250 reconstructed charged hadrons in proton-proton collisions at $\sqrt{s} = $ 13 TeV. The results are based on data collected using the CMS detector at the LHC during runs with a special low-pileup configuration. Three analysis techniques with different degrees of dependence on simulations are used to remove the non-Bose-Einstein background from the correlation functions. All three methods give consistent results. The measured lengths of homogeneity are studied as functions of particle multiplicity as well as average pair transverse momentum and mass. The results are compared with data from both CMS and ATLAS at $\sqrt{s} = $ 7 TeV, as well as with theoretical predictions. | ||
Links: e-print arXiv:1910.08815 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; |
Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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Figures | |
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Figure 1:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios employing PYTHIA 6 (Z2* tune) in different bins of $N^\text {offline}_\text {trk}$ and $ {k_{\mathrm {T}}} $ with the respective Gaussian fit from Eq. (4). The following $ {q_\text {inv}} $ ranges are excluded from the fits: 0.2 $ < {q_\text {inv}} < $ 0.3, 0.4 $ < {q_\text {inv}} < $ 0.9, and 0.95 $ < {q_\text {inv}} < $ 1.2 GeV. Coulomb interactions are not included in the simulation. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 1-a:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios employing PYTHIA 6 (Z2* tune) in bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0.2 $ < {k_{\mathrm {T}}} \leq $ 0.3 GeV with the Gaussian fit from Eq. (4). The following $ {q_\text {inv}} $ ranges are excluded from the fits: 0.2 $ < {q_\text {inv}} < $ 0.3, 0.4 $ < {q_\text {inv}} < $ 0.9, and 0.95 $ < {q_\text {inv}} < $ 1.2 GeV. Coulomb interactions are not included in the simulation. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 1-b:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios employing PYTHIA 6 (Z2* tune) in bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0.5 $ < {k_{\mathrm {T}}} \leq $ 0.7 GeV with the Gaussian fit from Eq. (4). The following $ {q_\text {inv}} $ ranges are excluded from the fits: 0.2 $ < {q_\text {inv}} < $ 0.3, 0.4 $ < {q_\text {inv}} < $ 0.9, and 0.95 $ < {q_\text {inv}} < $ 1.2 GeV. Coulomb interactions are not included in the simulation. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 1-c:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios employing PYTHIA 6 (Z2* tune) in bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0 $ < {k_{\mathrm {T}}} \leq $ 1 GeV with the Gaussian fit from Eq. (4). The following $ {q_\text {inv}} $ ranges are excluded from the fits: 0.2 $ < {q_\text {inv}} < $ 0.3, 0.4 $ < {q_\text {inv}} < $ 0.9, and 0.95 $ < {q_\text {inv}} < $ 1.2 GeV. Coulomb interactions are not included in the simulation. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 1-d:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios employing PYTHIA 6 (Z2* tune) in bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0.2 $ < {k_{\mathrm {T}}} \leq $ 0.3 GeV with the Gaussian fit from Eq. (4). The following $ {q_\text {inv}} $ ranges are excluded from the fits: 0.2 $ < {q_\text {inv}} < $ 0.3, 0.4 $ < {q_\text {inv}} < $ 0.9, and 0.95 $ < {q_\text {inv}} < $ 1.2 GeV. Coulomb interactions are not included in the simulation. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 1-e:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios employing PYTHIA 6 (Z2* tune) in bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0.5 $ < {k_{\mathrm {T}}} \leq $ 0.7 GeV with the Gaussian fit from Eq. (4). The following $ {q_\text {inv}} $ ranges are excluded from the fits: 0.2 $ < {q_\text {inv}} < $ 0.3, 0.4 $ < {q_\text {inv}} < $ 0.9, and 0.95 $ < {q_\text {inv}} < $ 1.2 GeV. Coulomb interactions are not included in the simulation. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 1-f:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios employing PYTHIA 6 (Z2* tune) in bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0 $ < {k_{\mathrm {T}}} \leq $ 1 GeV with the Gaussian fit from Eq. (4). The following $ {q_\text {inv}} $ ranges are excluded from the fits: 0.2 $ < {q_\text {inv}} < $ 0.3, 0.4 $ < {q_\text {inv}} < $ 0.9, and 0.95 $ < {q_\text {inv}} < $ 1.2 GeV. Coulomb interactions are not included in the simulation. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 2:
Relations between same-sign ($++,-$) and opposite-sign ($+-$) fit parameters from Eq. (4), as a function of $ {k_{\mathrm {T}}} $ and $N^\text {offline}_\text {trk}$ for events in MB (i.e., higher $\sigma _{\text {B}}^{-1}$ and lower $\text {log}_{10}\text {B}$) and HM (i.e., lower $\sigma _{\text {B}}^{-1}$ and higher $\text {log}_{10}\text {B}$) ranges. The fit values found for the parameters corresponding to the peak's width (left) and the amplitude (right) of the same-sign and opposite-sign correlations are shown. For a given $ {k_{\mathrm {T}}} $ range, each point represents an $N^\text {offline}_\text {trk}$ bin. The line in the left plot is a linear fit to all the data. The error bars represent statistical uncertainties. |
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Figure 2-a:
Relations between same-sign ($++,-$) and opposite-sign ($+-$) fit parameters from Eq. (4), as a function of $ {k_{\mathrm {T}}} $ and $N^\text {offline}_\text {trk}$ for events in MB (i.e., higher $\sigma _{\text {B}}^{-1}$ and lower $\text {log}_{10}\text {B}$) and HM (i.e., lower $\sigma _{\text {B}}^{-1}$ and higher $\text {log}_{10}\text {B}$) ranges. The fit values found for the parameters corresponding to the peak's width of the same-sign and opposite-sign correlations are shown. For a given $ {k_{\mathrm {T}}} $ range, each point represents an $N^\text {offline}_\text {trk}$ bin. The line is a linear fit to all the data. The error bars represent statistical uncertainties. |
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Figure 2-b:
Relations between same-sign ($++,-$) and opposite-sign ($+-$) fit parameters from Eq. (4), as a function of $ {k_{\mathrm {T}}} $ and $N^\text {offline}_\text {trk}$ for events in MB (i.e., higher $\sigma _{\text {B}}^{-1}$ and lower $\text {log}_{10}\text {B}$) and HM (i.e., lower $\sigma _{\text {B}}^{-1}$ and higher $\text {log}_{10}\text {B}$) ranges. The fit values found for the parameters corresponding to the peak's amplitude of the same-sign and opposite-sign correlations are shown. For a given $ {k_{\mathrm {T}}} $ range, each point represents an $N^\text {offline}_\text {trk}$ bin. The error bars represent statistical uncertainties. |
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Figure 3:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios in data for different bins of $N^\text {offline}_\text {trk}$ and $ {k_{\mathrm {T}}} $, with their respective fits. The label "(Exp. $\times $ Gauss.) fit'' refers to the same-sign data and is given by Eq. (7). The label "Gaussian fit'' corresponds to Eq. (4) applied to opposite-sign data and "Background'' is the component of Eq. (7) that is found from the Gaussian fit using Eqs. (5) and (6) to convert the fit parameters. Coulomb corrections are accounted for using the Gamow factor. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 3-a:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios in data for bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0.2 $ < {k_{\mathrm {T}}} \leq $ 0.3 GeV, with fit. The label "(Exp. $\times $ Gauss.) fit'' refers to the same-sign data and is given by Eq. (7). The label "Gaussian fit'' corresponds to Eq. (4) applied to opposite-sign data and "Background'' is the component of Eq. (7) that is found from the Gaussian fit using Eqs. (5) and (6) to convert the fit parameters. Coulomb corrections are accounted for using the Gamow factor. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 3-b:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios in data for bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0.5 $ < {k_{\mathrm {T}}} \leq $ 0.7 GeV, with fit. The label "(Exp. $\times $ Gauss.) fit'' refers to the same-sign data and is given by Eq. (7). The label "Gaussian fit'' corresponds to Eq. (4) applied to opposite-sign data and "Background'' is the component of Eq. (7) that is found from the Gaussian fit using Eqs. (5) and (6) to convert the fit parameters. Coulomb corrections are accounted for using the Gamow factor. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 3-c:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios in data for bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0 $ < {k_{\mathrm {T}}} \leq $ 1 GeV, with fit. The label "(Exp. $\times $ Gauss.) fit'' refers to the same-sign data and is given by Eq. (7). The label "Gaussian fit'' corresponds to Eq. (4) applied to opposite-sign data and "Background'' is the component of Eq. (7) that is found from the Gaussian fit using Eqs. (5) and (6) to convert the fit parameters. Coulomb corrections are accounted for using the Gamow factor. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 3-d:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios in data for bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0.2 $ < {k_{\mathrm {T}}} \leq $ 0.3 GeV, with fit. The label "(Exp. $\times $ Gauss.) fit'' refers to the same-sign data and is given by Eq. (7). The label "Gaussian fit'' corresponds to Eq. (4) applied to opposite-sign data and "Background'' is the component of Eq. (7) that is found from the Gaussian fit using Eqs. (5) and (6) to convert the fit parameters. Coulomb corrections are accounted for using the Gamow factor. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 3-e:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios in data for bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0.5 $ < {k_{\mathrm {T}}} \leq $ 0.7 GeV, with fit. The label "(Exp. $\times $ Gauss.) fit'' refers to the same-sign data and is given by Eq. (7). The label "Gaussian fit'' corresponds to Eq. (4) applied to opposite-sign data and "Background'' is the component of Eq. (7) that is found from the Gaussian fit using Eqs. (5) and (6) to convert the fit parameters. Coulomb corrections are accounted for using the Gamow factor. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 3-f:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios in data for bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0 $ < {k_{\mathrm {T}}} \leq $ 1 GeV, with fit. The label "(Exp. $\times $ Gauss.) fit'' refers to the same-sign data and is given by Eq. (7). The label "Gaussian fit'' corresponds to Eq. (4) applied to opposite-sign data and "Background'' is the component of Eq. (7) that is found from the Gaussian fit using Eqs. (5) and (6) to convert the fit parameters. Coulomb corrections are accounted for using the Gamow factor. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 4:
Results for $ {R_\text {inv}} $ (left) and $\lambda $ (right) from the three methods as a function of multiplicity (upper) and $ {k_{\mathrm {T}}} $ (lower). In the upper plots, statistical and systematic uncertainties are represented by internal and external error bars, respectively. In the lower plots, statistical and systematic uncertainties are shown as error bars and open boxes, respectively. |
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Figure 4-a:
Result for $ {R_\text {inv}} $ from the three methods as a function of multiplicity. Statistical and systematic uncertainties are represented by internal and external error bars, respectively. |
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Figure 4-b:
Result for $\lambda $ from the three methods as a function of $ {k_{\mathrm {T}}} $. Statistical and systematic uncertainties are represented by internal and external error bars, respectively. |
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Figure 4-c:
Result for $ {R_\text {inv}} $ from the three methods as a function of multiplicity. Statistical and systematic uncertainties are shown as error bars and open boxes, respectively. |
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Figure 4-d:
Result for $\lambda $ from the three methods as a function of $ {k_{\mathrm {T}}} $. Statistical and systematic uncertainties are shown as error bars and open boxes, respectively. |
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Figure 5:
The $ {R_\text {inv}} $ fit parameters as a function of particle-level multiplicities using the HCS method in pp collisions at 13 TeV compared to results for pp collisions at 7 TeV from CMS (left) and ATLAS (right). Both the ordinate and abscissa for the CMS data in the right plot have been adjusted for compatibility with the ATLAS analysis procedure, as explained in the text. The error bars in the CMS [5] case represent systematic uncertainties (statistical uncertainties are smaller than the marker size) and in the ATLAS [15] case, statistical and systematic uncertainties added in quadrature. |
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Figure 5-a:
The $ {R_\text {inv}} $ fit parameters as a function of particle-level multiplicities using the HCS method in pp collisions at 13 TeV compared to results for pp collisions at 7 TeV from CMS. The error bars represent systematic uncertainties (statistical uncertainties are smaller than the marker size). |
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Figure 5-b:
The $ {R_\text {inv}} $ fit parameters as a function of particle-level multiplicities using the HCS method in pp collisions at 13 TeV compared to results for pp collisions at 7 TeV from ATLAS. Both the ordinate and abscissa for the CMS data have been adjusted for compatibility with the ATLAS analysis procedure, as explained in the text. In the ATLAS [15] case, statistical and systematic uncertainties added in quadrature. |
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Figure 6:
Comparison of $ {R_\text {inv}} $ obtained with the HCS method with theoretical expectations. Values of $ {R_\text {inv}} $ as a function of $< N_\text {tracks}> ^{1/3}$ (left) are shown with a linear fit to illustrate the expectation from hydrodynamics. Values of $ {R_\text {inv}} $ are compared with predictions from the CGC as a function of $< {\mathrm {d}}N_\text {tracks}/ {\mathrm {d}}\eta > ^{1/3}$ (right). The dot-dashed blue line is the result of the parameterization in Eq. (8). The linear plus constant function (dashed black lines) for $< {\mathrm {d}}N_\text {tracks}/ {\mathrm {d}}\eta > ^{1/3}$ is shown to illustrate the qualitative behavior suggested by the CGC (the matching point of the two lines is the result of a fit). Only statistical uncertainties are considered. |
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Figure 6-a:
Comparison of $ {R_\text {inv}} $ obtained with the HCS method with theoretical expectations. Values of $ {R_\text {inv}} $ as a function of $< N_\text {tracks}> ^{1/3}$ are shown with a linear fit to illustrate the expectation from hydrodynamics. |
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Figure 6-b:
Comparison of $ {R_\text {inv}} $ obtained with the HCS method with theoretical expectations. Values of $ {R_\text {inv}} $ are compared with predictions from the CGC as a function of $< {\mathrm {d}}N_\text {tracks}/ {\mathrm {d}}\eta > ^{1/3}$. The dot-dashed blue line is the result of the parameterization in Eq. (8). The linear plus constant function (dashed black lines) for $< {\mathrm {d}}N_\text {tracks}/ {\mathrm {d}}\eta > ^{1/3}$ is shown to illustrate the qualitative behavior suggested by the CGC (the matching point of the two lines is the result of a fit). Only statistical uncertainties are considered. |
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Figure 7:
The distribution $1/R_{\text {inv}}^2$ as a function of $ {m_{\mathrm {T}}} $ for the HCS method. Results corresponding to the MB range (0 $ \le N_\text {trk}^\text {offline} \le $ 79) and to the HM one (80 $ \le N_\text {trk}^\text {offline} \le $ 250) are shown (left). Results are also shown in more differential bins of multiplicity (right). Statistical uncertainties are represented by the error bars, systematic uncertainties related to the HCS method are shown as open boxes, and the relative uncertainties from the intramethods variation are represented by the shaded bands. Only statistical uncertainties are considered in all the fits. |
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Figure 7-a:
The distribution $1/R_{\text {inv}}^2$ as a function of $ {m_{\mathrm {T}}} $ for the HCS method. Results corresponding to the MB range (0 $ \le N_\text {trk}^\text {offline} \le $ 79) and to the HM one (80 $ \le N_\text {trk}^\text {offline} \le $ 250) are shown. Statistical uncertainties are represented by the error bars, systematic uncertainties related to the HCS method are shown as open boxes, and the relative uncertainties from the intramethods variation are represented by the shaded bands. Only statistical uncertainties are considered in all the fits. |
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Figure 7-b:
The distribution $1/R_{\text {inv}}^2$ as a function of $ {m_{\mathrm {T}}} $ for the HCS method. Results are shown in bins of multiplicity. Statistical uncertainties are represented by the error bars, systematic uncertainties related to the HCS method are shown as open boxes, and the relative uncertainties from the intramethods variation are represented by the shaded bands. Only statistical uncertainties are considered in all the fits. |
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Figure 8:
Illustration of the steps in the double ratio method. The single ratio in data is constructed (left), followed by a similar procedure with simulated events (PYTHIA 6, Z2* tune). The ratio of the two curves on the left defines the double ratio (right). The reference sample is obtained with the $\eta $-mixing procedure. All results correspond to integrated values in $N^\text {offline}_\text {trk}$ and $ {k_{\mathrm {T}}} $. |
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Figure 8-a:
Illustration of the steps in the double ratio method. The single ratio in data is constructed, followed by a similar procedure with simulated events (PYTHIA 6, Z2* tune). The reference sample is obtained with the $\eta $-mixing procedure. All results correspond to integrated values in $N^\text {offline}_\text {trk}$ and $ {k_{\mathrm {T}}} $. |
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Figure 8-b:
Illustration of the steps in the double ratio method. The ratio of the two curves in Fig. 8-a defines the double ratio. The reference sample is obtained with the $\eta $-mixing procedure. All results correspond to integrated values in $N^\text {offline}_\text {trk}$ and $ {k_{\mathrm {T}}} $. |
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Figure 9:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios are shown in different $N^\text {offline}_\text {trk}$ and $ {k_{\mathrm {T}}} $ bins, together with the full fits (continuous curves) given in Eqs. (10) and (13), for minimum-bias (upper row) and HM (lower row) events. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 9-a:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios are shown in bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0.2 $ < {k_{\mathrm {T}}} \leq $ 0.3 GeV, together with the full fit (continuous curve) given in Eqs. (10) and (13), for minimum-bias events. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 9-b:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios are shown in bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0.5 $ < {k_{\mathrm {T}}} \leq $ 0.7 GeV, together with the full fit (continuous curve) given in Eqs. (10) and (13), for minimum-bias events. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 9-c:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios are shown in bin 19 $ \leq N^\text {offline}_\text {trk} \leq $ 21 and 0 $ < {k_{\mathrm {T}}} \leq $ 1 GeV, together with the full fit (continuous curve) given in Eqs. (10) and (13), for minimum-bias events. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 9-d:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios are shown in bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0.2 $ < {k_{\mathrm {T}}} \leq $ 0.3 GeV, together with the full fit (continuous curve) given in Eqs. (10) and (13), for HM events. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 9-e:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios are shown in bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0.5 $ < {k_{\mathrm {T}}} \leq $ 0.7 GeV, together with the full fit (continuous curve) given in Eqs. (10) and (13), for HM events. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 9-f:
The same-sign ($++,-$) and opposite-sign ($+-$) single ratios are shown in bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109 and 0 $ < {k_{\mathrm {T}}} \leq $ 1 GeV, together with the full fit (continuous curve) given in Eqs. (10) and (13), for HM events. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 10:
Correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in six multiplicity bins. The results are zoomed along the vertical axis. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 10-a:
Correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 0 $ \leq N^\text {offline}_\text {trk} \leq $ 4. The results are zoomed along the vertical axis. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 10-b:
Correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 10 $ \leq N^\text {offline}_\text {trk} \leq $ 12. The results are zoomed along the vertical axis. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 10-c:
Correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 31 $ \leq N^\text {offline}_\text {trk} \leq $ 33. The results are zoomed along the vertical axis. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 10-d:
Correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 80 $ \leq N^\text {offline}_\text {trk} \leq $ 84. The results are zoomed along the vertical axis. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 10-e:
Correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109. The results are zoomed along the vertical axis. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 10-f:
Correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 130 $ \leq N^\text {offline}_\text {trk} \leq $ 250. The results are zoomed along the vertical axis. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Figure 11:
The depth of the anticorrelation $\Delta $ is shown as a function of multiplicity (left) for $ {k_{\mathrm {T}}} $-integrated values. The fit parameter $\Delta $ is also shown in finer bins of $N_\text {tracks}$ and $ {k_{\mathrm {T}}} $ (right). The statistical uncertainties are represented by the error bars, while the systematic ones are represented by the open boxes. |
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Figure 11-a:
The depth of the anticorrelation $\Delta $ is shown as a function of multiplicity for $ {k_{\mathrm {T}}} $-integrated values. The statistical uncertainties are represented by the error bars, while the systematic ones are represented by the open boxes. |
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Figure 11-b:
The fit parameter $\Delta $ is shown in fine bins of $N_\text {tracks}$ and $ {k_{\mathrm {T}}} $. The statistical uncertainties are represented by the error bars, while the systematic ones are represented by the open boxes. |
Tables | |
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Table 1:
Total systematic uncertainties in different $ {k_{\mathrm {T}}} $ bins for the hybrid cluster subtraction technique. The ranges in the uncertainties indicate the minimum and maximum values found for all multiplicity bins. |
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Table 2:
Values of the fit parameters from Eqs. (11) and (12), describing the cluster contribution in the data OS correlation function. The estimated uncertainty in the parameters is about 10%. |
Summary |
A Bose-Einstein correlation measurement is reported using data collected with the CMS detector at the LHC in proton-proton collisions at $\sqrt{s} = $ 13 TeV, covering a broad range of charged particle multiplicity, from a few particles up to 250 reconstructed charged hadrons. Three analysis methods, each with a different dependence on Monte Carlo simulations, are used to generate correlation functions, which are found to give consistent results. One dimensional studies of the radius fit parameter, $R_{\text{inv}}$, and the intercept parameter, $\lambda$, have been carried out for both inclusive events and high multiplicity events selected using a dedicated online trigger. For multiplicities in the range 0 $ < N_{\text{trk}}^{\text{offline}} < $ 250 and average pair transverse momentum 0 $ < {k_{\mathrm{T}}} < $ 1 GeV, values of the radius fit parameter and intercept are in the ranges 0.8 $ < R_{\text{inv}} < $ 3.0 fm and 0.5 $ < \lambda < $ 1.0, respectively. Over most of the multiplicity range studied, the value of $R_{\text{inv}}$ increases with increasing event multiplicities and is proportional to $ < N_{\text{tracks}} > ^{1/3} $, a trend which is predicted by hydrodynamical calculations. For events with more than ${\sim}$ 100 charged particles, the observed dependence of $R_{\text{inv}}$ suggests a possible saturation, with the lengths of homogeneity also consistent with a constant value. Comparisons of the multiplicity dependence are made with predictions of the color glass condensate effective theory, by means of a parameterization of the radius of the system formed in pp collisions. The values of the radius parameters in the model are much lower than those in the data, although the general shape of the dependence on multiplicity is similar in both cases. The radius fit parameter $R_{\text{inv}}$ is also observed to decrease with increasing ${k_{\mathrm{T}}}$, a behavior that is consistent with emission from a system that is expanding prior to its decoupling. Inspired by hydrodynamic models, the dependence of $R_{\text{inv}}^{-2}$ on the average pair transverse mass was investigated and the two are observed to be proportional, a behavior similar to that seen in nucleus-nucleus collisions. The proportionality constant between $R_{\text{inv}}^{-2}$ and transverse mass can be related to the flow parameter of a Hubble-type expansion of the system. For pp collisions at 13 TeV, this expansion is slower for larger event multiplicity, a dependence that was also found in nucleus-nucleus collisions. Therefore, the present analysis reveals additional similarities between the systems produced in high multiplicity pp collisions and those found using data for larger initial systems. These results may provide additional constraints on future attempts using hydrodynamical models and/or the color glass condensate framework to explain the entire range of similarities between pp and heavy ion interactions. |
Additional Figures | |
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Additional Figure 1:
Unzoomed correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bins. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Additional Figure 1-a:
Unzoomed correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 0 $ \leq N^\text {offline}_\text {trk} \leq $ 4. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Additional Figure 1-b:
Unzoomed correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 10 $ \leq N^\text {offline}_\text {trk} \leq $ 12. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Additional Figure 1-c:
Unzoomed correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 31 $ \leq N^\text {offline}_\text {trk} \leq $ 33. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Additional Figure 1-d:
Unzoomed correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 80 $ \leq N^\text {offline}_\text {trk} \leq $ 84. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
png pdf |
Additional Figure 1-e:
Unzoomed correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 105 $ \leq N^\text {offline}_\text {trk} \leq $ 109. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
png pdf |
Additional Figure 1-f:
Unzoomed correlation functions from the double ratio technique, integrated in the range 0 $ < {k_{\mathrm {T}}} < $ 1 GeV, in multiplicity bin 130 $ \leq N^\text {offline}_\text {trk} \leq $ 250. The error bars represent statistical uncertainties and in most cases are smaller than the marker size. |
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Compact Muon Solenoid LHC, CERN |