CMS-SMP-22-015

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	Summary	References	CMS Publications

Figures
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	Figure A5: The $\chi^2$ values determined from the fit of the measured data, as a function of $\alpha_\mathrm{S} (m_\mathrm{Z})$ .
png pdf	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.
png pdf	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.
png pdf	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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