CMS-PAS-SMP-24-007

CMS-PAS-SMP-24-007
The strong coupling constant and its running from inclusive jet production at CMS
CMS Collaboration
8 October 2024

Abstract: A comprehensive analysis at next-to-next-to-leading order (NNLO) accuracy in quantum chromodynamics (QCD) is presented. It uses double-differential cross section measurements of inclusive jet production from the CMS Collaboration at centre-of-mass energies of 2.76, 7, 8, and 13 TeV. The result is a simultaneous determination of the value of the strong coupling constant at the mass of the Z boson $ \alpha_{\mathrm{s}}(M_{\mathrm{Z}}) $ together with the parton distribution functions of the proton. The value $ \alpha_{\mathrm{s}}(M_{\mathrm{Z}}) = $ 0.1176 $ ^{+0.0014}_{-0.0016} $ is obtained. By using the measurements in different intervals of jet transverse momenta, the running of the strong coupling is probed for energy scales between 100 and 1600 GeV.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Cross sections of inclusive jet production in pp collisions as measured by CMS (black markers) at $ \sqrt{s} $ of 2.76, 7, 8 and 13 TeV, using the anti-$ k_{\mathrm{T}} $ clustering algorithm with $ R= $ 0.7, as a function of individual jet $ p_{\mathrm{T}} $ in bins of absolute rapidity $ \|y\| $. Shown is the total uncertainty of every data point (vertical bar). The data are divided by the NNLO LC QCD prediction corrected by the NP and EW effects. The PDFs obtained in this note are used. The total theory uncertainty (shaded band) includes the PDF and scale variation uncertainty.
png pdf	Figure 2: The fractional Hessian uncertainties in the u-valence $ u_v $ (upper left), d-valence $ \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 factorisation scale $ Q^{2}=m_{\mathrm{t}}^{2} $. The results of the HERA+CMS fit (blue hatched area) are compared to the results of the HERA-only fit using $ \alpha_\mathrm{S}(m_{\mathrm{Z}})= $ 0.118 (orange hatched area). The uncertainties are given at 68% CL.
png pdf	Figure 3: Ratios of different global PDF sets at NNLO, in particular CT18 [32], NNPDF4 [33], MSHT20 [34], and HERAPDF20 [13] to the result of the present study. The u-valence $ \mathrm{u}_v $ (upper left), d-valence $ \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 factorisation scale $ Q^{2} = m_{\mathrm{t}}^{2} $. The Hessian PDF uncertainties at 68% CL are shown.
png pdf	Figure 4: The value of $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ obtained in this analysis (red marker), compared to a selection of recent results obtained by using different methods (black markers) with their uncertainties (horizontal error bars). Also, the PDG world average is shown (shaded band).
png pdf	Figure 5: Values of $ \alpha_\mathrm{S} $ as a function of the renormalization scale, obtained in the present QCD analysis at NNLO. The results (black markers) are shown with their total uncertainties (vertical error bars). For comparison, the RGE at five loops is shown using the current world-average value $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) = $ 0.1180 $ \pm $ 0.0009 [39] (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 considered in this study. The columns show the $ \sqrt{s} $, the integrated luminosity, the number of measured data points, the ranges of individual jet $ p_{\mathrm{T}} $ and $ \|y\| $, and the reference.
png pdf	Table 2: The values of $ \chi^2 $ per number of degrees of freedom, $ N_\mathrm{dof} $, as obtained in the fit to HERA and CMS jet data. The partial $ \chi^2 $ is reported for each of the individual datasets considered, together with the contribution to the $ \chi^2 $ from correlated uncertainty sources.
png pdf	Table 3: The extracted $ \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 in the minimal subtraction scheme 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) in quantum chromodynamics (QCD). The analysis includes electroweak effects at next-to-leading order and non-perturbative corrections. The CMS measurements of inclusive jet production at $ \sqrt{s} = $ 2.76, 7, 8 and 13 TeV, using the anti-$ k_{\mathrm{T}} $ clustering algorithm with a distance parameter of $ R= $ 0.7, are used together with the combined deep inelastic scattering (DIS) cross sections from HERA. The simultaneous extraction of $ \alpha_\mathrm{S}(m_{\mathrm{Z}}) $ and the PDFs mitigates a possible bias from their correlations. By using the CMS jet data in the fit, the precision of PDFs is significantly improved and 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 measurement from jet cross sections, to date. Furthermore, by extracting the value of $ \alpha_\mathrm{S} $ in different bins of jet $ p_{\mathrm{T}} $, the running of $ \alpha_\mathrm{S} $ is tested at NNLO in QCD up to scales of 1.6 TeV. The observed running of $ \alpha_\mathrm{S} $ is in agreement with the prediction of the QCD renormalization group equation.

References
1	CMS Collaboration	Measurement of the inclusive jet cross section in pp collisions at $ \sqrt{s} = $ 2.76 TeV	EPJC 76 (2016) 265	CMS-SMP-14-017 1512.06212
2	CMS Collaboration	Measurements of differential jet cross sections in proton-proton collisions at $ \sqrt{s}= $ 7 TeV with the CMS detector	PRD 87 (2013) 112002	CMS-QCD-11-004 1212.6660
3	CMS Collaboration	Constraints on parton distribution functions and extraction of the strong coupling constant from the inclusive jet cross section in pp collisions at $ \sqrt{s} = $ 7 TeV	EPJC 75 (2015) 288	CMS-SMP-12-028 1410.6765
4	CMS Collaboration	Measurement and QCD analysis of double-differential inclusive jet cross sections in pp collisions at $ \sqrt{s}= $ 8 TeV and cross section ratios to 2.76 and 7 TeV	JHEP 03 (2017) 156	CMS-SMP-14-001 1609.05331
5	CMS Collaboration	Measurement and QCD analysis of double-differential inclusive jet cross sections in proton-proton collisions at $ \sqrt{s} = $ 13 TeV	JHEP 02 (2022) 142	CMS-SMP-20-011 2111.10431
6	CMS Collaboration	Measurement of the double-differential inclusive jet cross section in proton-proton collisions at $ \sqrt{s} $ = 5.02 TeV	Submitted to JHEP, 2024	CMS-SMP-21-009 2401.11355
7	ATLAS Collaboration	Measurement of inclusive jet and dijet cross sections in proton-proton collisions at 7 TeV centre-of-mass energy with the ATLAS detector	EPJC 71 (2011) 1512	1009.5908
8	ATLAS Collaboration	Measurement of inclusive jet and dijet production in $ pp $ collisions at $ \sqrt{s}= $ 7 TeV using the ATLAS detector	PRD 86 (2012) 014022	1112.6297
9	ATLAS Collaboration	Measurement of the inclusive jet cross section in $ pp $ collisions at $ \sqrt{s}= $ 2.76 TeV and comparison to the inclusive jet cross section at $ \sqrt{s}= $ 7 TeV using the ATLAS detector	EPJC 73 (2013) 2509	1304.4739
10	ATLAS Collaboration	Measurement of the inclusive jet cross-section in proton-proton collisions at $ \sqrt{s}= $ 7 TeV using 4.5 fb$ ^{-1} $ of data with the ATLAS detector	JHEP 02 (2015) 153	1410.8857
11	ATLAS Collaboration	Measurement of the inclusive jet cross-sections in proton-proton collisions at $ \sqrt{s}= $ 8 TeV with the ATLAS detector	JHEP 09 (2017) 020	1706.03192
12	ATLAS Collaboration	Measurement of inclusive jet and dijet cross-sections in proton-proton collisions at $ \sqrt{s}= $ 13 TeV with the ATLAS detector	JHEP 05 (2018) 195	1711.02692
13	H1 and ZEUS Collaborations	Combination of measurements of inclusive deep inelastic $ {\mathrm{e}^\pm\mathrm{p}} $ scattering cross sections and QCD analysis of HERA data	EPJC 75 (2015) 580	1506.06042
14	S. Forte and Z. Kassabov	Why $ \alpha _s $ cannot be determined from hadronic processes without simultaneously determining the parton distributions	EPJC 80 (2020) 182	2001.04986
15	M. Cacciari, G. P. Salam, and G. Soyez	The anti-$ k_{\mathrm{T}} $ jet clustering algorithm	JHEP 04 (2008) 063	0802.1189
16	M. Cacciari, G. P. Salam, and G. Soyez	FastJet User Manual	EPJC 72 (2012) 1896	1111.6097
17	CMS Collaboration	Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV	JINST 12 (2017) P02014	CMS-JME-13-004 1607.03663
18	CMS Collaboration	Determination of jet energy calibration and transverse momentum resolution in CMS	JINST 6 (2011) P11002	CMS-JME-10-011 1107.4277
19	J. Currie, E. W. N. Glover, and J. Pires	Next-to-next-to leading order QCD predictions for single jet inclusive production at the LHC	PRL 118 (2017) 072002	1611.01460
20	X. Chen et al.	NNLO QCD corrections in full colour for jet production observables at the LHC	JHEP 09 (2022) 025	2204.10173
21	J. Currie et al.	Infrared sensitivity of single jet inclusive production at hadron colliders	JHEP 10 (2018) 155	1807.03692
22	D. Britzger et al.	NNLO interpolation grids for jet production at the LHC	EPJC 82 (2022) 930	2207.13735
23	S. Dittmaier, A. Huss, and C. Speckner	Weak radiative corrections to dijet production at hadron colliders	JHEP 11 (2012) 095	1210.0438
24	M. Botje	QCDNUM: Fast QCD evolution and convolution	Comput. Phys. Commun. 182 (2011) 490	1005.1481
25	R. S. Thorne and R. G. Roberts	Ordered analysis of heavy flavor production in deep inelastic scattering	PRD 57 (1998) 6871	hep-ph/9709442
26	R. S. Thorne	Variable-flavor number scheme for NNLO	PRD 73 (2006) 054019	hep-ph/0601245
27	R. S. Thorne	Effect of changes of variable flavor number scheme on parton distribution functions and predicted cross sections	PRD 86 (2012) 074017	1201.6180
28	S. Alekhin et al.	HERAFitter	EPJC 75 (2015) 304	1410.4412
29	xFitter Developers' Team Collaboration	xFitter 2.0.0: An Open Source QCD Fit Framework	PoS DIS 203, 2018 link	1709.01151
30	F. James and M. Roos	Minuit: a system for function minimization and analysis of the parameter errors and correlations	Comput. Phys. Commun. 10 (1975) 343
31	J. Pumplin et al.	Uncertainties of predictions from parton distribution functions. II. The Hessian method	PRD 65 (2001) 014013	hep-ph/0101032
32	T.-J. Hou et al.	New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC	PRD 103 (2021) 014013	1912.10053
33	NNPDF Collaboration	The path to proton structure at 1\% accuracy	EPJC 82 (2022) 428	2109.02653
34	S. Bailey et al.	Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs	EPJC 81 (2021) 341	2012.04684
35	CMS Collaboration	Measurement of multidifferential cross sections for dijet production in proton-proton collisions at $ \sqrt{s} $ = 13 TeV	12, . . Submitted to the European Physical Journal C, 2023	CMS-SMP-21-008 2312.16669
36	ATLAS Collaboration	A precise determination of the strong-coupling constant from the recoil of $ Z $ bosons with the ATLAS experiment at $ \sqrt{s} = $ 8 TeV	9, . . Submitted to Nature Phys., 2023	2309.12986
37	ATLAS Collaboration	Determination of the strong coupling constant from transverse energy-energy correlations in multijet events at $ \sqrt{s} = $ 13 TeV with the ATLAS detector	JHEP 07 (2023) 085	2301.09351
38	S. Camarda, G. Ferrera, and M. Schott	Determination of the strong-coupling constant from the Z-boson transverse-momentum distribution	EPJC 84 (2024) 39	2203.05394
39	Particle Data Group Collaboration	Review of particle physics	PRD 110 (2024) 030001
40	Flavour Lattice Averaging Group (FLAG) Collaboration	FLAG review 2021	EPJC 82 (2022) 869	2111.09849
41	F. Herren and M. Steinhauser	Version 3 of RunDec and CRunDec	Comput. Phys. Commun. 224 (2018) 333	1703.03751