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| CMS-PAS-SMP-22-005 | ||
| Measurement of azimuthal correlations among jets and determination of the strong coupling in pp collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 26 August 2023 | ||
| Abstract: A measurement is presented of the ratio observable $ R_{\Delta\phi}(p_\mathrm{T}) $ that provides a measure of the azimuthal correlations among jets with large transverse momentum $ p_\mathrm{T} $. The $ R_{\Delta\phi}(p_\mathrm{T}) $ variable is defined as the ratio of the number of neighbouring jets in events with a 3-jet topology, enforced through an azimuthal angular separation of 2$ \pi$/3 $ < \Delta\phi < $ 7$\pi$/8, over the number of inclusive jets within the same jet $ p_\mathrm{T} $ bin. The $ R_{\Delta\phi}(p_\mathrm{T}) $ variable is measured over the $ p_\mathrm{T} \approx$ 360-3200 GeV range based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 134 fb$ ^{-1} $. The results are compared to predictions from Monte Carlo event generator simulations that include parton showers, hadronisation, and multiparton interactions. Fixed-order predictions of perturbative quantum chromodynamics (pQCD) at next-to-leading-order (NLO) accuracy obtained with the NNPDF3.1 NLO parton densities, corrected for nonperturbative and electroweak effects, are also compared to the measurement. Within uncertainties, data and theory are in agreement. From this comparison, the strong coupling constant at the Z boson mass scale is determined to be $ \alpha_S(M_{\mathrm{Z}})= $ 0.1177 $ \pm $ 0.0013 (exp) $ _{-0.0073}^{+0.0116} $ (th) $ = $ 0.1177$_{-0.0074}^{+0.0117} $, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of $ \alpha_S(Q) $ in the TeV region shows no deviation from the expected pQCD behaviour. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to . The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
Probability matrix for the $ N(p_{\mathrm{T}},n) $ distribution built using PYTHIA 8 simulated events. The horizontal axis corresponds to the generator-level jet $ p_{\mathrm{T}} $, and the vertical axis to the reconstructed-level jet $ p_{\mathrm{T}} $. The 4$ \times $4 structure of the matrix corresponds to the bins of neighbouring jets $ n $ (labeled in the uppermost row and rightmost column), and indicates migrations among those bins. The horizontal and vertical axes of each cell correspond to the $ p_{\mathrm{T}} $ of the jets, and each cell indicates the migrations among the jet $ p_{\mathrm{T}} $ bins. The colour range covers from 10$^{-6} $ to 1, and indicates the probability of migrations from a (generator) particle-level bin to the corresponding (reconstructed) detector-level bin. |
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Figure 2:
Bin-to-bin correlation matrix for the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ distribution at particle level, where the value 1 ($-$1) corresponds to fully (anti) correlated bins. For illustration purposes, only bins with (anti) correlations larger (smaller) than 0.05 ($-$0.05) are shown also as text. |
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Figure 3:
The $ R_{\Delta\phi}(p_{\mathrm{T}}) $ observable as a function of $ p_{\mathrm{T}} $, compared to MC generator predictions at LO (left) and at NLO (right) accuracy. The LO predictions are obtained with PYTHIA 8 tune CUETP8M1, PYTHIA 8 tune CUETP8M2, and HERWIG++ tune UE-EE-5-CTEQ6L1 MC event generators. The NLO predictions are obtained with POWHEG interfaced to each of the aforementioned MC event generators. The data are represented with black markers and the MC predictions with coloured lines. The lower panel of each plot shows the ratio between MC predictions and data. |
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Figure 4:
Theoretical predictions for the numerator (left) and denominator (right) of the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ ratio, Eq. (1), obtained using the NNPDF31_NLO PDF set. The coloured bands represent the LO and NLO scale uncertainties derived with a six-point variation of $ \mu_r $ and $ \mu_f $ from the central reference value. The lower panels show the ratios to the respective LO predictions. |
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Figure 5:
Nonperturbative correction factors for the numerator (upper left) and denominator (upper right) of the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ ratio, Eq. (1), using PYTHIA 8 with tunes CUETP8M1 and CUETP8M2, HERWIG++ with tune UE-EE-5-CTEQ6L1 and POWHEG interfaced to each of them. The lower plot shows the NP correction factors (blue line) for $ R_{\Delta\phi}(p_{\mathrm{T}}) $ and their uncertainties. |
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Figure 6:
Electroweak corrections for the numerator (blue) and denominator (green) of Eq. (1), and for the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ ratio itself (red). The solid lines correspond to the additive combination of NLO EW corrections to the QCD process (NLO QCD$ \,+\, $EW), and the markers represent the multiplicative combination (NLO QCD$ \,\times\, $EW). |
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Figure 7:
The $ R_{\Delta\phi}(p_{\mathrm{T}}) $ observable as a function of $ p_{\mathrm{T}} $, compared to fixed-order theoretical calculations at NLO accuracy using the ABMP16nlo (top left), CT18nlo (top right), MSHT20nlo (lower left), and NNPDF31nlo (lower right) PDF sets. The data are indicated with blue markers, the theoretical prediction for default $ \alpha_S(M_{\mathrm{Z}}) $ for each PDF set with black solid lines, the scale uncertainties with red bands, and the PDF uncertainties with green bands. The lower panel of each plot shows the ratio between data and theoretical predictions. |
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Figure 8:
Sensitivity of the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ ratio to the strong coupling constant $ \alpha_S(M_{\mathrm{Z}}) $. In each plot, the lines represent fixed-order NLO theoretical calculations obtained with ABMP16 (upper left), CT18 (upper right), MSHT20 (lower left) and NNPDF3.1 (lower right) PDF sets. Solid green (red) lines indicate maximum (minimum) values, and dashed black lines intermediate values of $ \alpha_S(M_{\mathrm{Z}}) $ for each PDF set. |
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Figure 9:
Minimisation of the $ \chi^2 $ between experimental measurements and theoretical predictions for the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ ratio, with respect to $ \alpha_S(M_{\mathrm{Z}}) $ for ABMP16, CT18, MSHT20, and NNPDF3.1 NLO PDF sets. In this plot, only experimental uncertainties are included in the covariance matrix. The minimum value of $ \alpha_S(M_{\mathrm{Z}}) $ found for each PDF set is indicated with a dashed line and corresponds to the central result. The experimental uncertainty is estimated from the $ \alpha_S(M_{\mathrm{Z}}) $ values for which the $ \chi^2 $ is increased by one unit with respect to the minimum value. |
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Figure 10:
Determination of $ \alpha_S(M_{\mathrm{Z}}) $ from the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ ratio with the NNPDF3.1 PDF set (red), in comparison with previous NLO determinations of $ \alpha_S(M_{\mathrm{Z}}) $ from inclusive jet (magenta), dijet (green), and multijet (blue) measurements. The world-average $ \alpha_S(M_{\mathrm{Z}}) $ value is represented by the vertical dashed black line and its uncertainty by the yellow band. |
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Figure 11:
Running of the strong coupling constant $ \alpha_S(Q) $ (dashed line) evolved using the current world-average value $ \alpha_S(M_{\mathrm{Z}}) = $ 0.1179 $ \pm $ 0.0009 [5] together with its associated total uncertainty (yellow band). The four new extractions from the present analysis (Table 5) are shown as filled red circles, compared with results from the H1 [77,78,74], ZEUS [79], D0 [11,12], CMS [14,16,17,20], and ATLAS [19,18] experiments. All the experimental results shown in this figure are based on fixed-order predictions at NLO accuracy in pQCD. |
| Tables | |
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Table 1:
The different HLT $ p_{\mathrm{T}} $ thresholds used in the measurement and the corresponding integrated luminosities for 2016, 2017 and 2018 respectively. |
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Table 2:
Values of the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ observable in different $ p_{\mathrm{T}} $ intervals, and associated experimental uncertainties. |
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Table 3:
Default and range of $ \alpha_S(M_{\mathrm{Z}}) $ values used in the different PDF sets. |
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Table 4:
Results for $ \alpha_S(M_{\mathrm{Z}}) $, associated uncertainties, and goodness-of-fit per degree of freedom, obtained from the measured $ R_{\Delta\phi}(p_{\mathrm{T}}) $ distribution compared to theoretical predictions using different PDF sets. |
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Table 5:
Determinaed values of $ \alpha_S(M_{\mathrm{Z}}) $ and $ \alpha_S(Q) $ values in four different jet $ p_{\mathrm{T}} $ fitting subregions corresponding to an average scale $ \langle Q \rangle $. |
| Summary |
| A measurement of the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ ratio, sensitive to azimuthal correlations in multijet events, has been presented using proton-proton collision data collected by the CMS experiment at a centre-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 134 fb$ ^{-1} $. The experimental data are compared to predictions from Monte Carlo (MC) event generators, PYTHIA 8 with tunes CUETP8M1 and CUETP8M2, HERWIG++ with tune UE-EE-5-CTEQ6L1, and POWHEG interfaced to each one of them. Data-MC deviations are observed in all cases, except for PYTHIA 8 tune CUETP8M2, which gives a good overall description of the measurement. The measurement is also compared to fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy using NLOJET++ package within the FASTNLO framework. Those predictions are extracted for four different NLO parton distribution function (PDF) sets, ABMP16, CT18, MSHT20, and NNPDF3.1. Corrections for nonperturbative effects are evaluated using all the aforementioned MC event generators, and are applied to the fixed-order predictions. The latter are additionally corrected for electroweak effects that become important at large jet transverse momenta. Generally, the fixed-order predictions are in agreement with the data in the phase space of this analysis, and they provide a good description of the measurement for all PDF sets. Based on a comparison of experimental measurement of the $ R_{\Delta\phi}(p_{\mathrm{T}}) $ distribution and the theoretical predictions, the strong coupling constant at the scale of the Z boson mass is determined to be: $ \alpha_S(M_{\mathrm{Z}}) = $ 0.1177 $_{-0.0068}^{+0.0114}$ (scale) $ \pm $ 0.0013 (exp) $ \pm $ 0.0011 (NP) $ \pm$ 0.0010 (PDF) $ \pm $ 0.0003 (EW) $ \pm$ 0.0020 (PDF choice) $ = $ 0.1177$_{-0.0074}^{+0.0117} $, using calculations based on the NNPDF3.1 NLO PDF set. Alternative $ \alpha_S(M_{\mathrm{Z}}) $ results using other PDF sets are found to be compatible among each other, as well as with the central result and the current world average, $ \alpha_S(M_{\mathrm{Z}}) = $ 0.1179 $ \pm $ 0.0009. The dominant uncertainty for this measurement originates from the scale dependence of the fixed order predictions (NLO in pQCD), and is expected to be reduced by a factor of three with the future inclusion of fixed-order pQCD predictions at next-to-NLO accuracy. The evolution of $ \alpha_S(Q) $ has also been tested up to $ \approx $ 2 TeV, for scales chosen as the jet transverse momentum in the different intervals considered, $ \langle Q \rangle =p_{\mathrm{T}} $, and no deviation from the expected pQCD running of the strong coupling is observed. |
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