CMS-SMP-24-007

CMS-SMP-24-007 ; CERN-EP-2024-293
Determination of the strong coupling and its running from measurements of inclusive jet production
CMS Collaboration
21 December 2024
Submitted to Phys. Lett. B
Abstract: The value of the strong coupling $ \alpha_\mathrm{S} $ is determined in a comprehensive analysis at next-to-next-to-leading order accuracy in quantum chromodynamics. The analysis uses double-differential cross section measurements from the CMS Collaboration at the CERN LHC of inclusive jet production in proton-proton collisions at centre-of-mass energies of 2.76, 7, 8, and 13 TeV, combined with inclusive deep-inelastic data from HERA. The value $ \alpha_\mathrm{S}(m_{\mathrm{Z}})= $ 0.1176$^{+0.0014}_{-0.0016} $ is obtained at the scale of the Z boson mass. By using the measurements in different intervals of jet transverse momentum, the running of $ \alpha_\mathrm{S} $ is probed for energies between 100 and 1600 GeV.
Links: e-print arXiv:2412.16665 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Cross section ratios between data and theory for inclusive jet production in pp collisions as measured by CMS at $ \sqrt{s} $ of 2.76, 8, 7, and 13 TeV, using the anti-$ k_{\mathrm{T}} $ clustering algorithm with $ R= $ 0.7, as functions of individual jet $ p_{\mathrm{T}} $ in intervals of absolute rapidity $ \|y\| $. Shown is the total uncertainty of every data point (vertical bar). Predictions correspond to the NNLO LC QCD calculations corrected for NP and EW effects. The PDFs obtained in this work are used. The total theory uncertainty (red shaded band) includes the PDF and scale variation uncertainties.
png pdf	Figure 2: The fit uncertainties in the valence u quark ($ \mathrm{ u_V } $) (upper left), valence d quark ($ \mathrm{ d_V } $) (upper right), gluon $ \mathrm{g} $ (lower left), and sea quark $ \Sigma $ (lower right) distributions, shown as a function of $ x $ at the factorization scale $ Q^2=m_{\mathrm{t}}^2 $. The results of the HERA+CMS fit (blue shaded area) are compared with the results of the HERA-only fit (orange shaded area). In the HERA-only fit, due to poor sensitivity of the DIS data to $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $, its value is fixed to that of the HERA+CMS fit. The uncertainties are given at 68% CL.
png pdf	Figure 3: Ratios of different global PDF sets at NNLO, namely HERAPDF20 [13], CT18 [46], NNPDF4 [45], and MSHT20 [47], to the result of the present study. The valence u quark ($ \mathrm{ u_V } $) (upper left), valence d quark ($ \mathrm{ d_V } $) (upper right), gluon $ \mathrm{g} $ (lower left), and sea quark $ \Sigma $ (lower right) distributions are shown as functions of $ x $ at the factorization scale $ Q^2=m_{\mathrm{t}}^2 $. The Hessian PDF uncertainties at 68% CL are shown, where the width of the band represents the uncertainty in the numerator by keeping the denominator constant.
png pdf	Figure 4: The value of $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ obtained in this analysis (red marker), compared with all CMS results obtained at NNLO by using different methods (black markers) with their total uncertainties (horizontal error bars). The PDG world average (dashed line) together with its uncertainty (shaded band) is also shown.
png pdf	Figure 5: Values of $ \alpha_\mathrm{S} $ as extracted from different jet transverse momentum ranges in the present QCD analysis at NNLO, each translated to a single scale $ \langle Q\rangle $, as indicated in Table 3. The results (black markers) are shown with their total uncertainties (vertical error bars). For comparison, the RGE at 5 loops is shown using the current world-average value $ \alpha_\mathrm{S}(m_{\mathrm{Z}})= $ 0.1180 $ \pm $ 0.0009 [48] (red line) together with its associated total uncertainty (shaded band).
png pdf	Figure 6: Sketch of the treatment of JES sources of uncertainty among the measurements at different $ \sqrt{s} $. A filled black box indicates that the corresponding two uncertainty sources are treated as correlated.

Tables
png pdf	Table 1: The CMS inclusive jet measurements used in this analysis. The columns show the centre-of-mass energy, the integrated luminosity, the number of measured data points, the ranges of individual jet $ p_{\mathrm{T}} $ and $ \|y\| $, and the reference to the corresponding publication.
png pdf	Table 2: The values of $ \chi^2 $ per $ N_{\mathrm{p}} $ for each individual data set as obtained in the fit to HERA and CMS jet data, together with the contribution to the $ \chi^2 $ from correlated uncertainty sources. In the last line, the total $ \chi^2 $ per number of degrees of freedom, $ N_{\mathrm{dof}} $, is reported.
png pdf	Table 3: The determined $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ and the corresponding $ \alpha_\mathrm{S}(Q) $ values for each $ p_{\mathrm{T}} $ range with their total uncertainties. For $ \alpha_\mathrm{S}(Q) $, the individual uncertainty contributions (fit, scale, model, parametrization) are listed.

Summary

The value of the strong coupling constant at the scale of the mass of the Z boson, $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $, is extracted together with the parton distribution functions (PDFs) of the proton in an analysis at next-to-next-to-leading order (NNLO) accuracy in quantum chromodynamics (QCD). The simultaneous extraction of $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ and PDFs mitigates a possible bias from their correlations. The analysis includes electroweak effects at next-to-leading order and nonperturbative corrections. The CMS measurements of inclusive jet production in proton-proton collisions at $ \sqrt{s}= $ 2.76, 7, 8, and 13 TeV, using the anti-$ k_{\mathrm{T}} $ clustering algorithm with a distance parameter of 0.7, are used together with the inclusive deep inelastic scattering cross sections from HERA. The correlations among the systematic uncertainties of each individual jet cross section measurement, as well as across all centre-of-mass energies, are reevaluated. These correlations should be included in future global QCD analyses of these data. By using the CMS jet data in the fit, the value of $ \alpha_\mathrm{S}(m_{\mathrm{Z}})= $ 0.1176$^{+0.0014}_{-0.0016} $ is obtained, in good agreement with the world average. It is the most precise result for $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ from jet cross sections to date. At the same time, this analysis demonstrates that improved PDFs can be extracted by using these data. Furthermore, by extracting the value of $ \alpha_\mathrm{S} $ in different intervals of jet $ p_{\mathrm{T}} $, the running of $ \alpha_\mathrm{S} $ is tested at NNLO in QCD up to energy scales of 1.6 TeV. The observed running of $ \alpha_\mathrm{S} $ is in agreement with the prediction of the QCD renormalization group equation.

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