CMS-PAS-SMP-22-015

CMS-PAS-SMP-22-015
Measurement of energy correlators inside jets and determination of the strong coupling constant
CMS Collaboration
2 August 2023

Abstract: We measure the two-point and three-point energy correlator jet substructure observables (E2C and E3C), using LHC 13 TeV data collected by the CMS experiment. These measurements reveal in a straightforward way the two most important features of strong interactions, confinement and asymptotic freedom. The E2C and E3C distributions show a sharp transition from the falling scaling behavior characterizing the quantum interactions of quarks and gluons to an integer power law reflective of classical noninteracting hadrons. The ratio of E3C/E2C is directly proportional to the strong coupling constant $ \alpha_S $. The slopes of the ratio of the distribution of E3C and E2C are measured in multiple jet transverse momentum regions, consistent with the expected decrease of $ \alpha_S $ with increasing energy due to asymptotic freedom. Measurements of scaling behavior are compared to theoretical predictions with all-orders resummation at next-to-next-to-leading logarithmic accuracy matched to a fixed-order next-to-leading order calculation, yielding an $ \alpha_S (m_{\mathrm{Z}}) $ value of 0.1229$ ^{+0.0040}_{-0.0050} $. This is the most precise extraction of $ \alpha_S (m_{\mathrm{Z}}) $ using jet substructure observables to date.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to PRL. The superseded preliminary plots can be found here.

Figures	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Unfolded data distribution of E3C using jets in the $ p_{\mathrm{T}} $ range between 220 and 330 GeV. The error bars for unfolded data distribution account for the correlated nature of the input data. Experimental uncertainties are presented by error bands around data. Three distinct regions are observed, marking a clear transition from interacting quarks and gluons to noninteracting hadrons. The two boundaries are approximately 0.8 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and 20 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and are explained in detail in the text.
png pdf	Figure 2: Unfolded E2C (upper) and E3C (bottom) distributions in data compared to MC predictions. The data are unfolded using migration matrices from PYTHIA8 simulation (black). Error bars in data distributions are statistical uncertainties, while experimental systematic uncertainties are shown in grey bands. The predictions from different simulations are shown for comparison. Theoretical uncertainty of PYTHIA8 CP5(simple shower) is shown in the blue bands. The two boundaries are approximately 0.8 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and 20 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and are explained in detail in the texts.
png pdf	Figure 2-a: Unfolded E2C (upper) and E3C (bottom) distributions in data compared to MC predictions. The data are unfolded using migration matrices from PYTHIA8 simulation (black). Error bars in data distributions are statistical uncertainties, while experimental systematic uncertainties are shown in grey bands. The predictions from different simulations are shown for comparison. Theoretical uncertainty of PYTHIA8 CP5(simple shower) is shown in the blue bands. The two boundaries are approximately 0.8 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and 20 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and are explained in detail in the texts.
png pdf	Figure 2-b: Unfolded E2C (upper) and E3C (bottom) distributions in data compared to MC predictions. The data are unfolded using migration matrices from PYTHIA8 simulation (black). Error bars in data distributions are statistical uncertainties, while experimental systematic uncertainties are shown in grey bands. The predictions from different simulations are shown for comparison. Theoretical uncertainty of PYTHIA8 CP5(simple shower) is shown in the blue bands. The two boundaries are approximately 0.8 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and 20 GeV/$p_{\mathrm{T}}^{\mathrm{j}} $ and are explained in detail in the texts.
png pdf	Figure 3: Unfolded E3C/E2C distributions in data, compared to theoretical predictions in the perturbative region. The data are unfolded using migration matrices in PYTHIA8 simulation (black). Error bars in data distributions are statistical uncertainties, systematic experimental systematic uncertainties are shown in grey bands. Theoretical predictions are calculated with resummation at NNLL accuracy matched to a fixed-order calculation at NLO ($ \textrm{NNLL}_{\text{approx}} $) [45] and corrected to the hadron level using NP corrections. The average NP factors are obtained with PYTHIA8 and with HERWIG 7 and are applied bin by bin. The comparison between the data distributions and theoretical predictions are used to extract $ \alpha_S (m_{\mathrm{Z}}) $.
png pdf	Figure 4: The fitted slopes of the E3C/E2C data distributions as a function of jet $ p_{\mathrm{T}} $ are used to illustrate the dependency of $ \alpha_S $ on jet $ p_{\mathrm{T}} $. A clear decreasing trend with jet $ p_{\mathrm{T}} $ is seen, demonstrating that the strong coupling gets weaker at higher energy scales.

Summary

The measurement of the two-point and three-point energy correlators is presented in this work. A multidimensional unfolding of the jet $ p_{\mathrm{T}} $, and the angular distance and energy weight of the particle pair is performed to take into account the correlation between these variables. Comparisons to various parton shower simulations are also presented. These results provide a new means of studying QCD in collider experiments, and can help validate future higher-order implementations in parton showers. The distinctive phases of jet formation that are embedded in the energy correlators provide approaches to understand the time scale of hadron formation, which remains an open question in QCD [80]. The $ \alpha_S (m_{\mathrm{Z}}) $ value extracted from the ratio of the three-point and two-point correlators is 0.1229$ ^{+0.0040}_{-0.0050} $. This represents the most precise determination of $ \alpha_S $ using jet substructure techniques to date. The precision greatly advances the previous expectation of 10% due to the development of novel jet substructure observables and the availability of higher-order theoretical calculations.

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