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| CMS-SMP-16-011 ; CERN-EP-2017-061 | ||
| Measurement of the triple-differential dijet cross section in proton-proton collisions at $ \sqrt{s} = $ 8 TeV and constraints on parton distribution functions | ||
| CMS Collaboration | ||
| 7 May 2017 | ||
| Eur. Phys. J. C 77 (2017) 746 | ||
| Abstract: A measurement is presented of the triple-differential dijet cross section at a centre-of-mass energy of 8 TeV using 19.7 fb$^{-1}$ of data collected with the CMS detector in proton-proton collisions at the LHC. The cross section is measured as a function of the average transverse momentum, half the rapidity separation, and the boost of the two leading jets in the event. The cross section is corrected for detector effects and compared to calculations in perturbative quantum chromodynamics at next-to-leading order accuracy, complemented with electroweak and nonperturbative corrections. New constraints on parton distribution functions are obtained and the inferred value of the strong coupling constant is $\alpha_S(M_\text{Z}) = $ 0.1199 $\pm$ 0.0015 (exp) $_{-0.0020}^{+0.0031}$ (theo), where $M_\text{Z}$ is the mass of the Z boson. | ||
| Links: e-print arXiv:1705.02628 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Illustration of the dijet event topologies in the ${y^{*}}$ and ${y_{\mathrm {b}}}$ kinematic plane. The dijet system can be classified as a same-side or opposite-side jet event according to the boost of the two leading jets, thereby providing insight into the parton kinematics. |
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Figure 2:
Relative contributions of all subprocesses to the total cross section at NLO as a function of $ {p_{\mathrm {T,avg}}} $ in the various ${y^{*}}$ and $ {y_{\mathrm {b}}} $ bins. The subprocess contributions are grouped into seven categories according to the type of the incoming partons. The calculations have been performed with NLOJet++. The notation implies the sum over initial-state parton flavors as well as interchanged quarks and antiquarks. |
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Figure 2-a:
Relative contributions of all subprocesses to the total cross section at NLO as a function of $ {p_{\mathrm {T,avg}}} $ in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 0 $ \leq {y^{*}} < $ 1) bin. The subprocess contributions are grouped into seven categories according to the type of the incoming partons. The calculations have been performed with NLOJet++. The notation implies the sum over initial-state parton flavors as well as interchanged quarks and antiquarks. |
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Figure 2-b:
Relative contributions of all subprocesses to the total cross section at NLO as a function of $ {p_{\mathrm {T,avg}}} $ in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 1 $ \leq {y^{*}} < $ 2) bin. The subprocess contributions are grouped into seven categories according to the type of the incoming partons. The calculations have been performed with NLOJet++. The notation implies the sum over initial-state parton flavors as well as interchanged quarks and antiquarks. |
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Figure 2-c:
Relative contributions of all subprocesses to the total cross section at NLO as a function of $ {p_{\mathrm {T,avg}}} $ in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 2 $ \leq {y^{*}} < $ 3) bin. The subprocess contributions are grouped into seven categories according to the type of the incoming partons. The calculations have been performed with NLOJet++. The notation implies the sum over initial-state parton flavors as well as interchanged quarks and antiquarks. |
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Figure 2-d:
Relative contributions of all subprocesses to the total cross section at NLO as a function of $ {p_{\mathrm {T,avg}}} $ in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 0 $ \leq {y^{*}} < $ 1) bin. The subprocess contributions are grouped into seven categories according to the type of the incoming partons. The calculations have been performed with NLOJet++. The notation implies the sum over initial-state parton flavors as well as interchanged quarks and antiquarks. |
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Figure 2-e:
Relative contributions of all subprocesses to the total cross section at NLO as a function of $ {p_{\mathrm {T,avg}}} $ in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 1 $ \leq {y^{*}} < $ 2) bin. The subprocess contributions are grouped into seven categories according to the type of the incoming partons. The calculations have been performed with NLOJet++. The notation implies the sum over initial-state parton flavors as well as interchanged quarks and antiquarks. |
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Figure 2-f:
Relative contributions of all subprocesses to the total cross section at NLO as a function of $ {p_{\mathrm {T,avg}}} $ in the (2 $ \leq {{y_{\mathrm {b}}}} < $ 3, 0 $ \leq {y^{*}} < $ 1) bin. The subprocess contributions are grouped into seven categories according to the type of the incoming partons. The calculations have been performed with NLOJet++. The notation implies the sum over initial-state parton flavors as well as interchanged quarks and antiquarks. |
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Figure 3:
Overview of all experimental uncertainties affecting the cross section measurement in six bins of $ {y_{\mathrm {b}}} $ and ${y^{*}}$. The error bars indicate the statistical uncertainty after unfolding. The different lines show the uncertainties resulting from jet energy corrections, jet energy resolution, integrated luminosity, non-Gaussian tails in the resolution, and from residual effects included in the uncorrelated uncertainty. The total uncertainty is obtained by adding all uncertainties in quadrature. |
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Figure 3-a:
Overview of all experimental uncertainties affecting the cross section measurement in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 0 $ \leq {y^{*}} < $ 1) bin. The error bars indicate the statistical uncertainty after unfolding. The different lines show the uncertainties resulting from jet energy corrections, jet energy resolution, integrated luminosity, non-Gaussian tails in the resolution, and from residual effects included in the uncorrelated uncertainty. The total uncertainty is obtained by adding all uncertainties in quadrature. |
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Figure 3-b:
Overview of all experimental uncertainties affecting the cross section measurement in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 1 $ \leq {y^{*}} < $ 2) bin. The error bars indicate the statistical uncertainty after unfolding. The different lines show the uncertainties resulting from jet energy corrections, jet energy resolution, integrated luminosity, non-Gaussian tails in the resolution, and from residual effects included in the uncorrelated uncertainty. The total uncertainty is obtained by adding all uncertainties in quadrature. |
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Figure 3-c:
Overview of all experimental uncertainties affecting the cross section measurement in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 2 $ \leq {y^{*}} < $ 3) bin. The error bars indicate the statistical uncertainty after unfolding. The different lines show the uncertainties resulting from jet energy corrections, jet energy resolution, integrated luminosity, non-Gaussian tails in the resolution, and from residual effects included in the uncorrelated uncertainty. The total uncertainty is obtained by adding all uncertainties in quadrature. |
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Figure 3-d:
Overview of all experimental uncertainties affecting the cross section measurement in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 0 $ \leq {y^{*}} < $ 1) bin. The error bars indicate the statistical uncertainty after unfolding. The different lines show the uncertainties resulting from jet energy corrections, jet energy resolution, integrated luminosity, non-Gaussian tails in the resolution, and from residual effects included in the uncorrelated uncertainty. The total uncertainty is obtained by adding all uncertainties in quadrature. |
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Figure 3-e:
Overview of all experimental uncertainties affecting the cross section measurement in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 1 $ \leq {y^{*}} < $ 2) bin. The error bars indicate the statistical uncertainty after unfolding. The different lines show the uncertainties resulting from jet energy corrections, jet energy resolution, integrated luminosity, non-Gaussian tails in the resolution, and from residual effects included in the uncorrelated uncertainty. The total uncertainty is obtained by adding all uncertainties in quadrature. |
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Figure 3-f:
Overview of all experimental uncertainties affecting the cross section measurement in the (2 $ \leq {{y_{\mathrm {b}}}} < $ 3, 0 $ \leq {y^{*}} < $ 1) bin. The error bars indicate the statistical uncertainty after unfolding. The different lines show the uncertainties resulting from jet energy corrections, jet energy resolution, integrated luminosity, non-Gaussian tails in the resolution, and from residual effects included in the uncorrelated uncertainty. The total uncertainty is obtained by adding all uncertainties in quadrature. |
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Figure 4:
Overview of the theoretical correction factors. For each of the six analysis bins the NLO QCD (top left), the electroweak (top right), and the NP correction factor (bottom) are shown as a function of $ {p_{\mathrm {T,avg}}} $. The NLO QCD correction has been derived with the same NLO PDF in numerator and denominator and is included in the NLO prediction by NLOJet++. |
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Figure 4-a:
Overview of the theoretical correction factors. For each of the six analysis bins the NLO QCD correction factor is shown as a function of $ {p_{\mathrm {T,avg}}} $. The NLO QCD correction has been derived with the same NLO PDF in numerator and denominator and is included in the NLO prediction by NLOJet++. |
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Figure 4-b:
Overview of the theoretical correction factors. For each of the six analysis bins the electroweak correction factor is shown as a function of $ {p_{\mathrm {T,avg}}} $. The NLO QCD correction has been derived with the same NLO PDF in numerator and denominator and is included in the NLO prediction by NLOJet++. |
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Figure 4-c:
Overview of the theoretical correction factors. For each of the six analysis bins the NP correction factor is shown as a function of $ {p_{\mathrm {T,avg}}} $. The NLO QCD correction has been derived with the same NLO PDF in numerator and denominator and is included in the NLO prediction by NLOJet++. |
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Figure 5:
Overview of the theoretical uncertainties. The scale uncertainty dominates in the low- $ {p_{\mathrm {T,avg}}} $ region. At high $ {p_{\mathrm {T,avg}}} $, and especially in the boosted region, the PDFs become the dominant source of uncertainty. |
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Figure 5-a:
Overview of the theoretical uncertainties in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 0 $ \leq {y^{*}} < $ 1) bin. The scale uncertainty dominates in the low- $ {p_{\mathrm {T,avg}}} $ region. At high $ {p_{\mathrm {T,avg}}} $, and especially in the boosted region, the PDFs become the dominant source of uncertainty. |
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Figure 5-b:
Overview of the theoretical uncertainties in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 1 $ \leq {y^{*}} < $ 2) bin. The scale uncertainty dominates in the low- $ {p_{\mathrm {T,avg}}} $ region. At high $ {p_{\mathrm {T,avg}}} $, and especially in the boosted region, the PDFs become the dominant source of uncertainty. |
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Figure 5-c:
Overview of the theoretical uncertainties in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 2 $ \leq {y^{*}} < $ 3) bin. The scale uncertainty dominates in the low- $ {p_{\mathrm {T,avg}}} $ region. At high $ {p_{\mathrm {T,avg}}} $, and especially in the boosted region, the PDFs become the dominant source of uncertainty. |
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Figure 5-d:
Overview of the theoretical uncertainties in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 0 $ \leq {y^{*}} < $ 1) bin. The scale uncertainty dominates in the low- $ {p_{\mathrm {T,avg}}} $ region. At high $ {p_{\mathrm {T,avg}}} $, and especially in the boosted region, the PDFs become the dominant source of uncertainty. |
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Figure 5-e:
Overview of the theoretical uncertainties in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 1 $ \leq {y^{*}} < $ 2) bin. The scale uncertainty dominates in the low- $ {p_{\mathrm {T,avg}}} $ region. At high $ {p_{\mathrm {T,avg}}} $, and especially in the boosted region, the PDFs become the dominant source of uncertainty. |
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Figure 5-f:
Overview of the theoretical uncertainties in the (2 $ \leq {{y_{\mathrm {b}}}} < $ 3, 0 $ \leq {y^{*}} < $ 1) bin. The scale uncertainty dominates in the low- $ {p_{\mathrm {T,avg}}} $ region. At high $ {p_{\mathrm {T,avg}}} $, and especially in the boosted region, the PDFs become the dominant source of uncertainty. |
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Figure 6:
The triple-differential dijet cross section in six bins of ${y^{*}}$ and $ {y_{\mathrm {b}}} $. The data are indicated by different markers for each bin. The theoretical predictions, obtained with NLOJet++ and NNPDF3.0, and complemented with EW and NP corrections, are depicted by solid lines. Apart from the boosted region, the data are well described by the predictions at NLO accuracy over many orders of magnitude. |
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Figure 7:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added; the solid and dashed lines give the ratios calculated with the predictions for different PDF sets. |
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Figure 7-a:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 0 $ \leq {y^{*}} < $ 1) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added; the solid and dashed lines give the ratios calculated with the predictions for different PDF sets. |
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Figure 7-b:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 1 $ \leq {y^{*}} < $ 2) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added; the solid and dashed lines give the ratios calculated with the predictions for different PDF sets. |
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Figure 7-c:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 2 $ \leq {y^{*}} < $ 3) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added; the solid and dashed lines give the ratios calculated with the predictions for different PDF sets. |
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Figure 7-d:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 0 $ \leq {y^{*}} < $ 1) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added; the solid and dashed lines give the ratios calculated with the predictions for different PDF sets. |
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Figure 7-e:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 1 $ \leq {y^{*}} < $ 2) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added; the solid and dashed lines give the ratios calculated with the predictions for different PDF sets. |
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Figure 7-f:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (2 $ \leq {{y_{\mathrm {b}}}} < $ 3, 0 $ \leq {y^{*}} < $ 1) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added; the solid and dashed lines give the ratios calculated with the predictions for different PDF sets. |
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Figure 8:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added. The predictions of the NLO MC event generators POWHEG+PYTHIA-8 and HERWIG-7 are depicted by solid and dashed lines, respectively. |
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Figure 8-a:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 0 $ \leq {y^{*}} < $ 1) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added. The predictions of the NLO MC event generators POWHEG+PYTHIA-8 and HERWIG-7 are depicted by solid and dashed lines, respectively. |
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Figure 8-b:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 1 $ \leq {y^{*}} < $ 2) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added. The predictions of the NLO MC event generators POWHEG+PYTHIA-8 and HERWIG-7 are depicted by solid and dashed lines, respectively. |
png pdf |
Figure 8-c:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (0 $ \leq {{y_{\mathrm {b}}}} < $ 1, 2 $ \leq {y^{*}} < $ 3) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added. The predictions of the NLO MC event generators POWHEG+PYTHIA-8 and HERWIG-7 are depicted by solid and dashed lines, respectively. |
png pdf |
Figure 8-d:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 0 $ \leq {y^{*}} < $ 1) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added. The predictions of the NLO MC event generators POWHEG+PYTHIA-8 and HERWIG-7 are depicted by solid and dashed lines, respectively. |
png pdf |
Figure 8-e:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (1 $ \leq {{y_{\mathrm {b}}}} < $ 2, 1 $ \leq {y^{*}} < $ 2) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added. The predictions of the NLO MC event generators POWHEG+PYTHIA-8 and HERWIG-7 are depicted by solid and dashed lines, respectively. |
png pdf |
Figure 8-f:
Ratio of the triple-differential dijet cross section to the NLOJet++ prediction using the NNPDF3.0 set in the (2 $ \leq {{y_{\mathrm {b}}}} < $ 3, 0 $ \leq {y^{*}} < $ 1) bin. The data points including statistical uncertainties are indicated by markers, the systematic experimental uncertainty is represented by the hatched band. The solid band shows the PDF, scale, and NP uncertainties quadratically added. The predictions of the NLO MC event generators POWHEG+PYTHIA-8 and HERWIG-7 are depicted by solid and dashed lines, respectively. |
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Figure 9:
The gluon (top left), sea quark (top right), dvalence quark (bottom left), and uvalence quark (bottom right) PDFs as a function of $x$ as derived from HERA inclusive DIS data alone (hatched band) and in combination with CMS dijet data (solid band). The PDFs are shown at the scale $Q^2 = 10^{4}$ GeV$ ^2 $ with their total uncertainties. |
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Figure 9-a:
The gluon PDF as a function of $x$ as derived from HERA inclusive DIS data alone (hatched band) and in combination with CMS dijet data (solid band). The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$ ^2$ with their total uncertainties. |
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Figure 9-b:
The sea quark PDFs as a function of $x$ as derived from HERA inclusive DIS data alone (hatched band) and in combination with CMS dijet data (solid band). The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$ ^2$ with their total uncertainties. |
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Figure 9-c:
The d-valence quark PDF as a function of $x$ as derived from HERA inclusive DIS data alone (hatched band) and in combination with CMS dijet data (solid band). The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$ ^2$ with their total uncertainties. |
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Figure 9-d:
The u-valence quark PDF as a function of $x$ as derived from HERA inclusive DIS data alone (hatched band) and in combination with CMS dijet data (solid band). The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$ ^2$ with their total uncertainties. |
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Figure 10:
The gluon PDF as a function of $x$ as derived from HERA inclusive DIS data alone (hatched band) and in combination with CMS dijet data (solid band). The PDF and its total uncertainty are shown at the starting scale $Q^2 = $ 1.9 GeV$^2$ of the PDF evolution. |
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Figure 11:
The gluon (top left), sea quark (top right), dvalence quark (bottom left), and uvalence quark (bottom right) PDFs as a function of $x$ as derived from a fit of HERA inclusive DIS data in combination with CMS inclusive jet data (solid band) and CMS dijet data (hatched band) at 8 TeV. The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$^2$ with their total uncertainties. |
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Figure 11-a:
The gluon PDF as a function of $x$ as derived from a fit of HERA inclusive DIS data in combination with CMS inclusive jet data (solid band) and CMS dijet data (hatched band) at 8 TeV. The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$^2$ with their total uncertainties. |
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Figure 11-b:
The sea quark PDF as a function of $x$ as derived from a fit of HERA inclusive DIS data in combination with CMS inclusive jet data (solid band) and CMS dijet data (hatched band) at 8 TeV. The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$^2$ with their total uncertainties. |
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Figure 11-c:
The d-valence quark PDF as a function of $x$ as derived from a fit of HERA inclusive DIS data in combination with CMS inclusive jet data (solid band) and CMS dijet data (hatched band) at 8 TeV. The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$^2$ with their total uncertainties. |
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Figure 11-d:
The u-valence quark PDF as a function of $x$ as derived from a fit of HERA inclusive DIS data in combination with CMS inclusive jet data (solid band) and CMS dijet data (hatched band) at 8 TeV. The PDFs are shown at the scale $Q^2 = 10^{4} $ GeV$^2$ with their total uncertainties. |
| Tables | |
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Table 1:
List of single-jet trigger thresholds used in the analysis. |
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Table 2:
The partial ${\chi ^2}$ ($ {\chi ^2_\text {p}} $) for each data set in the HERA DIS (middle section) or the combined fit including the CMS triple-differential dijet data (right section) are shown. The bottom two lines show the total ${\chi ^2}$ and ${\chi ^2/n_\text {dof}} $. The difference between the sum of all ${\chi ^2_\text {p}}$ and the total ${\chi ^2}$ for the combined fit is attributed to the nuisance parameters. |
| Summary |
|
A measurement of the triple-differential dijet cross section is presented for $ \sqrt{s} = $ 8 TeV. The data are found to be well described by NLO predictions corrected for nonperturbative and electroweak effects, except for highly boosted event topologies that suffer from large uncertainties in parton distribution functions (PDFs). The precise data constrain the PDFs, especially in the highly boosted regime that probes the highest fractions $x$ of the proton momentum carried by a parton. The impact of the data on the PDFs is demonstrated by performing a simultaneous fit to cross sections of deep-inelastic scattering obtained by the HERA experiments and the dijet cross section measured in this analysis. When including the dijet data, an increased gluon PDF at high $x$ is obtained and the overall uncertainties of the PDFs, especially those of the gluon distribution, are significantly reduced. In contrast to a fit that uses inclusive jet data, this measurement carries more information on the valence-quark content of the proton such that a more flexible parameterisation is needed to describe the low-$x$ behaviour of the u and d valence quark PDFs. This higher sensitivity is accompanied by slightly larger uncertainties in the valence quark distributions as a consequence of the greater flexibility in the parameterisation of the PDFs. In a simultaneous fit the strong coupling constant $\alpha_S(M_\text{Z})$ is extracted together with the PDFs. The value obtained at the mass of the Z boson is and is in agreement with previous measurements at the LHC by CMS [54, 62, 70-72] and ATLAS [73], and with the world average value of $\alpha_S(M_\text{Z}) = $ 0.1181 $\pm$ 0.0011 [74]. The dominant uncertainty is theoretical in nature and is expected to be reduced significantly in the future using pQCD predictions at next-to-next-to-leading order [75]. |
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