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| CMS-SMP-22-015 ; CERN-EP-2024-010 | ||
| Measurement of energy correlators inside jets and determination of the strong coupling $ \alpha_\mathrm{S} (m_\mathrm{Z}) $ | ||
| CMS Collaboration | ||
| 21 February 2024 | ||
| Phys. Rev. Lett. 133 (2024) 071903 | ||
| Abstract: Energy correlators that describe energy-weighted distances between two or three particles in a jet are measured using an event sample of $ \sqrt{s} = $ 13 TeV proton-proton collisions collected by the CMS experiment and corresponding to an integrated luminosity of 36.3 fb$ ^{-1} $. The measured distributions reveal two key features of the strong interaction: confinement and asymptotic freedom. By comparing the ratio of the two measured distributions with theoretical calculations that resum collinear emissions at approximate next-to-next-to-leading logarithmic accuracy matched to a next-to-leading order calculation, the strong coupling is determined at the Z boson mass: $ \alpha_\mathrm{S} (m_\mathrm{Z}) = $ 0.1229 $ ^{+0.0040}_{-0.0050} $, the most precise $ \alpha_\mathrm{S} (m_\mathrm{Z}) $ value obtained using jet substructure observables. | ||
| Links: e-print arXiv:2402.13864 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Measured (unfolded) E2C distributions, compared with three MC predictions in the jet $ p_{\mathrm{T}} $ regions mentioned in the legends. The lower panels show the ratios to the PYTHIA8 CP5 ($ p_{\mathrm{T}} $-ordered showers) reference. The data statistical and systematic uncertainties are shown by vertical bars and hatched boxes, respectively; the PYTHIA8 uncertainty is shown by the blue band. The three $ x_\text{L} $ regions are described in the text. |
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Figure 2:
Measured E3C/E2C ratio (left) and their ratio to predictions (right) in the perturbative $ x_\text{L} $ region, in the jet $ p_{\mathrm{T}} $ regions mentioned in the legends. The $ \text{NLO}+\text{NNLL}_\text{approx} $ theoretical predictions [19] are corrected to hadron-level and normalized to the measured data. The statistical and experimental systematic uncertainties are shown with error bars and boxes, respectively. |
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Figure 3:
Fitted slopes of the measured E3C/E2C ratios, in the eight jet $ p_{\mathrm{T}} $ regions, compared to the corresponding theoretical predictions for three different $ \alpha_\mathrm{S} $ values. |
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Figure A1:
Measured (unfolded) E2C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A1-a:
Measured (unfolded) E2C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A1-b:
Measured (unfolded) E2C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A2:
Measured (unfolded) E3C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A2-a:
Measured (unfolded) E3C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A2-b:
Measured (unfolded) E3C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A3:
Ratio of the unfolded E3C and E2C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A3-a:
Ratio of the unfolded E3C and E2C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A3-b:
Ratio of the unfolded E3C and E2C distributions compared with the PYTHIA8 CP5 prediction (upper) and all the MC predictions (lower) in the eight $ p_{\mathrm{T}} $ regions. Statistical and experimental systematic uncertainties are shown with error bars and hatched bands, respectively. The theory uncertainty in the PYTHIA8 CP5 prediction is shown with the blue bands. |
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Figure A4:
Ratio of the unfolded E3C and E2C distributions in the eight $ p_{\mathrm{T}} $ regions. The $ \text{NLO}+\text{NNLL}_\text{approx} $ theoretical predictions [19] and the corresponding uncertainties are corrected to hadron-level and normalized to the measured data. The statistical and experimental systematic uncertainties are shown with error bars and boxes, respectively. |
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Figure A5:
The $ \chi^2 $ values determined from the fit of the measured data, as a function of $ \alpha_\mathrm{S} (m_\mathrm{Z}) $. |
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Figure A6:
The statistical correlation matrix of the bins of the unfolded E2C distribution. The bin number $ n $ in this figure is defined by $ n=22 i_{p_{\mathrm{T}}} + i_{x_\text{L}} $, where $ i_{p_{\mathrm{T}}} $ and $ i_{x_\text{L}} $ are the indices of the $ p_{\mathrm{T}} $ and $ x_\text{L} $ bins. In total there are ten $ p_{\mathrm{T}} $ bins, the eight presented in the analysis plus the overflow and underflow bins. The number of $ x_\text{L} $ bins per $ p_{\mathrm{T}} $ region is 22. |
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Figure A7:
The statistical correlation matrix of the bins of the unfolded E3C distribution. The bin number $ n $ in this figure is defined by $ n=22 i_{p_{\mathrm{T}}} + i_{x_\text{L}} $, where $ i_{p_{\mathrm{T}}} $ and $ i_{x_\text{L}} $ are the indices of the $ p_{\mathrm{T}} $ and $ x_\text{L} $ bins. In total there are ten $ p_{\mathrm{T}} $ bins, the eight presented in the analysis plus the overflow and underflow bins. The number of $ x_\text{L} $ bins per $ p_{\mathrm{T}} $ region is 22. |
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Figure A8:
The statistical correlation matrix of the bins of the unfolded E3C/E2C distribution. The bin number $ n $ in this figure is defined by $ n=22 i_{p_{\mathrm{T}}} + i_{x_\text{L}} $, where $ i_{p_{\mathrm{T}}} $ and $ i_{x_\text{L}} $ are the indices of the $ p_{\mathrm{T}} $ and $ x_\text{L} $ bins. In total there are ten $ p_{\mathrm{T}} $ bins, the eight presented in the analysis plus the overflow and underflow bins. The number of $ x_\text{L} $ bins per $ p_{\mathrm{T}} $ region is 22. |
| Summary |
| In summary, the E2C and E3C (two- and three-particle energy correlators) jet substructure observables, have been measured using a sample of proton-proton collisions at $ \sqrt{s} = $ 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 36.3 fb$ ^{-1} $. A multidimensional unfolding has been performed, of the jet $ p_{\mathrm{T}} $, of the (largest) distance between particles in a pair or a triplet, $ x_\text{L} $, and of the product of their energy weights, to compare the data with samples of events simulated with different parton showering algorithms and hadronization models. The results provide a high-precision measurement of jet properties described by QCD and can help validate future higher-order corrections in parton shower algorithms. The strong coupling at the Z boson mass, $ \alpha_\mathrm{S} (m_\mathrm{Z}) $, is extracted by comparing the measured E3C/E2C ratio with calculations at approximate next-to-next-to-leading logarithmic accuracy matched to a next-to-leading order: $ \alpha_\mathrm{S} (m_\mathrm{Z}) = $ 0.1229 $ ^{+0.0040}_{-0.0050} $. This is the most precise determination of $ \alpha_\mathrm{S} $ using jet substructure techniques. The result benefits greatly from the development of novel jet substructure observables, which reduce the sensitivity to the quark-gluon composition, and from the availability of high-precision theoretical calculations. |
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