CMS-PAS-SMP-16-008 | ||
Determination of the strong coupling constant from the measurement of inclusive multijet event cross sections in pp collisions at $\sqrt{s} = $ 8 TeV | ||
CMS Collaboration | ||
February 2017 | ||
Abstract: A measurement of inclusive multijet event cross sections is presented from proton-proton collisions recorded at $\sqrt{s} = $ 8 TeV with the CMS detector and corresponding to an integrated luminosity of 19.7 fb$^{-1}$. Jets are reconstructed with the anti-k$_t$ clustering algorithm for a jet size parameter $ R = $ 0.7 in a phase space region ranging up to jet transverse momenta $p_\mathrm{T}$ of 2.0 TeV and an absolute rapidity of $|y|= $ 2.5. The inclusive 2-jet and 3-jet event cross sections are measured as a function of the average $p_\mathrm{T}$ of the two leading jets. The data are well described by predictions at next-to-leading order in perturbative quantum chromodynamics and additionally are compared to several Monte Carlo event generators. The strong coupling constant at the scale of the Z boson mass is inferred from a fit of the ratio of the 3-jet over 2-jet event cross section giving $\alpha_s(M_{\mathrm{Z}}) = $ 0.1150 $\pm$ 0.0010 (exp) $\pm$ 0.0013 (PDF) $\pm$ 0.0015 (NP) $^{+0.0050}_{-0.0000}$ (scale). | ||
Links: CDS record (PDF) ; inSPIRE record ; CADI line (restricted) ; |
Figures | |
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Figure 1:
Response matrices derived using a Toy MC procedure for the inclusive 2-jet (left) and 3-jet event samples (right). |
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Figure 1-a:
Response matrices derived using a Toy MC procedure for the inclusive 2-jet (left) and 3-jet event samples (right). |
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Figure 1-b:
Response matrices derived using a Toy MC procedure for the inclusive 2-jet (left) and 3-jet event samples (right). |
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Figure 2:
Overview of all experimental uncertainties affecting the inclusive 2-jet (top left) and 3-jet event cross sections (top right) and their ratio ${R_{32}}$ (bottom). The error bars indicate the statistical uncertainty after unfolding. The colored lines represent the systematic uncertainties resulting from JEC, the luminosity, residual effects, and the unfolding including JER effects. Uncertainties due to luminosity and residual effects are cancelled completely in the ratio. The total experimental uncertainty, indicated by dashed black lines, is calculated by adding in quadrature all the sources of uncertainty. |
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Figure 2-a:
Overview of all experimental uncertainties affecting the inclusive 2-jet (top left) and 3-jet event cross sections (top right) and their ratio ${R_{32}}$ (bottom). The error bars indicate the statistical uncertainty after unfolding. The colored lines represent the systematic uncertainties resulting from JEC, the luminosity, residual effects, and the unfolding including JER effects. Uncertainties due to luminosity and residual effects are cancelled completely in the ratio. The total experimental uncertainty, indicated by dashed black lines, is calculated by adding in quadrature all the sources of uncertainty. |
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Figure 2-b:
Overview of all experimental uncertainties affecting the inclusive 2-jet (top left) and 3-jet event cross sections (top right) and their ratio ${R_{32}}$ (bottom). The error bars indicate the statistical uncertainty after unfolding. The colored lines represent the systematic uncertainties resulting from JEC, the luminosity, residual effects, and the unfolding including JER effects. Uncertainties due to luminosity and residual effects are cancelled completely in the ratio. The total experimental uncertainty, indicated by dashed black lines, is calculated by adding in quadrature all the sources of uncertainty. |
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Figure 2-c:
Overview of all experimental uncertainties affecting the inclusive 2-jet (top left) and 3-jet event cross sections (top right) and their ratio ${R_{32}}$ (bottom). The error bars indicate the statistical uncertainty after unfolding. The colored lines represent the systematic uncertainties resulting from JEC, the luminosity, residual effects, and the unfolding including JER effects. Uncertainties due to luminosity and residual effects are cancelled completely in the ratio. The total experimental uncertainty, indicated by dashed black lines, is calculated by adding in quadrature all the sources of uncertainty. |
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Figure 3:
Fits to the nonperturbative corrections obtained for inclusive 2-jet (top left) and 3-jet (top right) event cross sections and their ratio ${R_{32}}$ (bottom) as a function of ${H_{\mathrm {T,2}}/2} $ within $|y|< $ 2.5 for the three investigated MC event generators. |
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Figure 3-a:
Fits to the nonperturbative corrections obtained for inclusive 2-jet (top left) and 3-jet (top right) event cross sections and their ratio ${R_{32}}$ (bottom) as a function of ${H_{\mathrm {T,2}}/2} $ within $|y|< $ 2.5 for the three investigated MC event generators. |
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Figure 3-b:
Fits to the nonperturbative corrections obtained for inclusive 2-jet (top left) and 3-jet (top right) event cross sections and their ratio ${R_{32}}$ (bottom) as a function of ${H_{\mathrm {T,2}}/2} $ within $|y|< $ 2.5 for the three investigated MC event generators. |
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Figure 3-c:
Fits to the nonperturbative corrections obtained for inclusive 2-jet (top left) and 3-jet (top right) event cross sections and their ratio ${R_{32}}$ (bottom) as a function of ${H_{\mathrm {T,2}}/2} $ within $|y|< $ 2.5 for the three investigated MC event generators. |
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Figure 4:
Overview of theoretical uncertainties affecting the cross section prediction for inclusive 2-jet (top left) and 3-jet events (top right) and their ratio ${R_{32}}$ (bottom), using the CT10 PDF set. The total uncertainty is calculated by adding in quadrature the individual sources of uncertainty. The statistical uncertainties of the NLO computations are too small to be visible and are not shown. |
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Figure 4-a:
Overview of theoretical uncertainties affecting the cross section prediction for inclusive 2-jet (top left) and 3-jet events (top right) and their ratio ${R_{32}}$ (bottom), using the CT10 PDF set. The total uncertainty is calculated by adding in quadrature the individual sources of uncertainty. The statistical uncertainties of the NLO computations are too small to be visible and are not shown. |
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Figure 4-b:
Overview of theoretical uncertainties affecting the cross section prediction for inclusive 2-jet (top left) and 3-jet events (top right) and their ratio ${R_{32}}$ (bottom), using the CT10 PDF set. The total uncertainty is calculated by adding in quadrature the individual sources of uncertainty. The statistical uncertainties of the NLO computations are too small to be visible and are not shown. |
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Figure 4-c:
Overview of theoretical uncertainties affecting the cross section prediction for inclusive 2-jet (top left) and 3-jet events (top right) and their ratio ${R_{32}}$ (bottom), using the CT10 PDF set. The total uncertainty is calculated by adding in quadrature the individual sources of uncertainty. The statistical uncertainties of the NLO computations are too small to be visible and are not shown. |
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Figure 5:
Comparison of the inclusive 2-jet and 3-jet event cross sections as a function of ${H_{\mathrm {T,2}}/2}$ to theoretical predictions. On the (left), the data (points) are shown together with NLOJet++ predictions (line) using the CT10 PDF set, corrected for NP and EWK (2-jet) or only NP effects (3-jet). On the (right), the data (points) are compared to predictions from MadGraph5+PYTHIA6 with tune ${\mathrm {Z2}^\star } $ (line), corrected for EWK effects in the 2-jet case. The error bars correspond to the total uncertainty, for which the statistical and systematic uncertainties are added in quadrature. |
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Figure 5-a:
Comparison of the inclusive 2-jet and 3-jet event cross sections as a function of ${H_{\mathrm {T,2}}/2}$ to theoretical predictions. On the (left), the data (points) are shown together with NLOJet++ predictions (line) using the CT10 PDF set, corrected for NP and EWK (2-jet) or only NP effects (3-jet). On the (right), the data (points) are compared to predictions from MadGraph5+PYTHIA6 with tune ${\mathrm {Z2}^\star } $ (line), corrected for EWK effects in the 2-jet case. The error bars correspond to the total uncertainty, for which the statistical and systematic uncertainties are added in quadrature. |
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Figure 5-b:
Comparison of the inclusive 2-jet and 3-jet event cross sections as a function of ${H_{\mathrm {T,2}}/2}$ to theoretical predictions. On the (left), the data (points) are shown together with NLOJet++ predictions (line) using the CT10 PDF set, corrected for NP and EWK (2-jet) or only NP effects (3-jet). On the (right), the data (points) are compared to predictions from MadGraph5+PYTHIA6 with tune ${\mathrm {Z2}^\star } $ (line), corrected for EWK effects in the 2-jet case. The error bars correspond to the total uncertainty, for which the statistical and systematic uncertainties are added in quadrature. |
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Figure 6:
Ratio of data over theory using the CT10 PDF set for inclusive 2-jet (top left) and inclusive 3-jet event cross sections (top right) and their ratio $ {R_{32}} $ (bottom). For comparison predictions employing two other PDF sets are also shown. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. The shaded band around unity represents the total uncertainty of the theory. |
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Figure 6-a:
Ratio of data over theory using the CT10 PDF set for inclusive 2-jet (top left) and inclusive 3-jet event cross sections (top right) and their ratio $ {R_{32}} $ (bottom). For comparison predictions employing two other PDF sets are also shown. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. The shaded band around unity represents the total uncertainty of the theory. |
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Figure 6-b:
Ratio of data over theory using the CT10 PDF set for inclusive 2-jet (top left) and inclusive 3-jet event cross sections (top right) and their ratio $ {R_{32}} $ (bottom). For comparison predictions employing two other PDF sets are also shown. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. The shaded band around unity represents the total uncertainty of the theory. |
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Figure 6-c:
Ratio of data over theory using the CT10 PDF set for inclusive 2-jet (top left) and inclusive 3-jet event cross sections (top right) and their ratio $ {R_{32}} $ (bottom). For comparison predictions employing two other PDF sets are also shown. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. The shaded band around unity represents the total uncertainty of the theory. |
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Figure 7:
Ratio of data over the prediction from POWHEG+PYTHIA8 with tune CUETS1. For comparison the alternative tune CUETM1 of POWHEG+PYTHIA8 , the tree-level multi-leg improved prediction by MadGraph5+PYTHIA6 with tune $ {\mathrm {Z2}^\star } $ , and the LO MC predictions from PYTHIA6 tune $ {\mathrm {Z2}^\star } $ are shown as well. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. EWK corrections have been accounted for in this comparison in the 2-jet case. |
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Figure 7-a:
Ratio of data over the prediction from POWHEG+PYTHIA8 with tune CUETS1. For comparison the alternative tune CUETM1 of POWHEG+PYTHIA8 , the tree-level multi-leg improved prediction by MadGraph5+PYTHIA6 with tune $ {\mathrm {Z2}^\star } $ , and the LO MC predictions from PYTHIA6 tune $ {\mathrm {Z2}^\star } $ are shown as well. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. EWK corrections have been accounted for in this comparison in the 2-jet case. |
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Figure 7-b:
Ratio of data over the prediction from POWHEG+PYTHIA8 with tune CUETS1. For comparison the alternative tune CUETM1 of POWHEG+PYTHIA8 , the tree-level multi-leg improved prediction by MadGraph5+PYTHIA6 with tune $ {\mathrm {Z2}^\star } $ , and the LO MC predictions from PYTHIA6 tune $ {\mathrm {Z2}^\star } $ are shown as well. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. EWK corrections have been accounted for in this comparison in the 2-jet case. |
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Figure 7-c:
Ratio of data over the prediction from POWHEG+PYTHIA8 with tune CUETS1. For comparison the alternative tune CUETM1 of POWHEG+PYTHIA8 , the tree-level multi-leg improved prediction by MadGraph5+PYTHIA6 with tune $ {\mathrm {Z2}^\star } $ , and the LO MC predictions from PYTHIA6 tune $ {\mathrm {Z2}^\star } $ are shown as well. The error bars correspond to the statistical uncertainty of the data and the shaded rectangles to the total experimental systematic uncertainty. EWK corrections have been accounted for in this comparison in the 2-jet case. |
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Figure 8:
Cross section ratio $ {R_{32}} $ as a function of $ {H_{\mathrm {T,2}}/2} $ calculated from data (solid circles) in comparison to that from NLO pQCD (lines). The error bars correspond to the total experimental uncertainty derived as quadratic sum from all uncertainty sources. The NLO predictions using the CT10 NLO PDF set corrected with NP corrections are shown for a series of values assumed for $ {\alpha _s(M_{\mathrm{Z}})} $ (dashed lines) together with the central prediction (solid line) where $ {\alpha _s(M_{\mathrm{Z}})} =0.118$. The assumption on $ {\alpha _s(M_{\mathrm{Z}})} $ is varied in steps of 0.001 in the range of 0.112-0.127. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 9:
Ratio of measured 2-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 9-a:
Ratio of measured 2-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 9-b:
Ratio of measured 2-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 9-c:
Ratio of measured 2-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 9-d:
Ratio of measured 2-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 9-e:
Ratio of measured 2-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 10:
Ratio of measured 3-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 10-a:
Ratio of measured 3-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 10-b:
Ratio of measured 3-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 10-c:
Ratio of measured 3-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 10-d:
Ratio of measured 3-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 10-e:
Ratio of measured 3-jet inclusive event cross section (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table {tab:chap2:nlopdfsets}. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 11:
Ratio of measured $ {R_{32}} $ ratio (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table 2. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 11-a:
Ratio of measured $ {R_{32}} $ ratio (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table 2. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 11-b:
Ratio of measured $ {R_{32}} $ ratio (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table 2. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 11-c:
Ratio of measured $ {R_{32}} $ ratio (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table 2. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 11-d:
Ratio of measured $ {R_{32}} $ ratio (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table 2. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 11-e:
Ratio of measured $ {R_{32}} $ ratio (data points) over NLO theory times NP corrections for various PDF sets at their respective default value for $ {\alpha _s(M_{\mathrm{Z}})} $ (black solid line at unity). The error bars correspond to the total experimental uncertainty. The NLO predictions have been derived with the CT10 (top left), the CT14 (top right), the MSTW2008 (middle left), the MMHT2014 (middle right) and the NNPDF2.3 PDF sets (bottom) for the series of assumptions on $ {\alpha _s(M_{\mathrm{Z}})} $ available for the respective PDF set as specified in Table 2. For brevity, the relative factor of NP between data and theory has been indicated as ``Data/NP'' in the legend. |
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Figure 12:
The running $ {\alpha _S(Q)} $ as a function of the scale $Q $ is shown as obtained by using the MSTW2008 NLO PDF set. The solid line and the uncertainty band are drawn by evolving the extracted $ {\alpha _s(M_{\mathrm{Z}})} $ values using the 2-loop 5-flavour renormalization group equations as implemented in RunDec [50,51]. The dashed line represents the evolution of the world average [52] and the black circles correspond to the $ {\alpha _S(Q)} $ determinations presented in Table 9. Results from other measurements of CMS [12,53,48,26,11], ATLAS [54], D0 [55,56], H1 [57,58], and ZEUS [59] are superimposed. |
Tables | |
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Table 1:
Trigger regions defined as ranges of the ${H_{\mathrm {T,2}}/2}$ for every single-jet trigger used in the inclusive multijet cross section measurement along with the effective integrated luminosities. |
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Table 2:
NLO PDF sets available via {LHAPDF6} for comparisons to data with various assumptions on the value of ${\alpha _s(M_{\mathrm{Z}})} $. Sets existing already in LHC Run1 (upper rows) and newer sets for Run2 (lower rows) are listed together with the corresponding number of flavours ${N_F} $, the assumed masses $M_{\mathrm{t}}$ and $M_{\mathrm{Z}}$ of the top quark and the $Z$ boson, respectively, the default values of ${\alpha _s(M_{\mathrm{Z}})} $, and the range in ${\alpha _s(M_{\mathrm{Z}})}$ variation available for fits. A $^*$ behind the ${\alpha _s(M_{\mathrm{Z}})}$ values signifies that the parameter was fixed, not fitted. |
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Table 3:
Determination of $ {\alpha _s(M_{\mathrm{Z}})} $ from the inclusive 2-jet and 3-jet event cross sections using five PDF sets at NLO. Only total uncertainties without scale variations are quoted. The results are obtained from a simultaneous fit to all 19 $ {H_{\mathrm {T,2}}/2} $ bins in the restricted range of 0.3 $ < {H_{\mathrm {T,2}}/2} < $ 1.0 TeV. |
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Table 4:
Determination of $ {\alpha _s(M_{\mathrm{Z}})} $ from the inclusive 2-jet and 3-jet event cross sections simultaneously and from their ratio $ {R_{32}} $ using five PDF sets at NLO. Only total uncertainties without scale variations are quoted. The results are obtained from a simultaneous fit to all 38 (19) $ {H_{\mathrm {T,2}}/2} $ bins in the restricted range of 0.3 $ < {H_{\mathrm {T,2}}/2} < $ 1.0 TeV. For comparison, correlations between the two cross sections are neglected in the simultaneous fit on the left, but fully taken into account in the ratio fit on the right. |
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Table 5:
Determination of $ {\alpha _s(M_{\mathrm{Z}})} $ from the inclusive 2-jet event cross section using five PDF sets at NLO with (right) and without (left) EWK corrections. Only total uncertainties without scale variations are quoted. The results are obtained from a simultaneous fit to all 29 $ {H_{\mathrm {T,2}}/2} $ bins in the range of 0.3 $ < {H_{\mathrm {T,2}}/2} < $ 1.68 TeV. |
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Table 6:
Determination of $ {\alpha _s(M_{\mathrm{Z}})} $ from the ratio $ {R_{32}} $ using the two most compatible PDF sets MSTW2008 and MMHT2014 at NLO. The results are obtained from a simultaneous fit to all 29 $ {H_{\mathrm {T,2}}/2} $ bins in the full range of 0.3 $ < {H_{\mathrm {T,2}}/2} < $ 1.68 TeV. |
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Table 7:
Fitted values of $ {\alpha _s(M_{\mathrm{Z}})} $ using $ {R_{32}} $ in the $ {H_{\mathrm {T,2}}/2} $ range from 0.3 up to 1.68 TeV at the central scale and for the six scale factor combinations for the two PDF sets MSTW2008 and MMHT2014. |
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Table 8:
Uncertainty composition for $ {\alpha _s(M_{\mathrm{Z}})} $ from the determination of ${\alpha _S}$ from the jet event rate $ {R_{32}} $ in bins of $ {H_{\mathrm {T,2}}/2} $ . The statistical uncertainty of the NLO computation is negligible in comparison to any of the other sources of uncertainty. Electroweak corrections, significant only at high $ {H_{\mathrm {T,2}}/2} $ , are assumed to cancel between the numerator and denominator. |
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Table 9:
Evolution of the strong coupling constant between the scale of the Z boson mass and the cross-section averaged $ {H_{\mathrm {T,2}}/2} $ scale $ < Q > $ for the separate determinations in each respective fit range. The evolution is performed for five flavours at 2-loop order with the RunDec program [50,51]. |
Summary |
A measurement of the inclusive 2-jet (3-jet) event cross sections has been presented in a range of 0.3 $ < H_{\mathrm{T},2}/2 < $ 2.0 TeV (0.3 $ < H_{\mathrm{T},2}/2 < $ 1.68 TeV) for the average $ p_{\mathrm{T}} $ of the two leading jets at central rapidity of $|y|< $ 2.5. The data sample has been collected from proton-proton collisions at 8 TeV centre-of-mass energy and corresponds to an integrated luminosity of 19.7 fb$^{-1}$. The data are found to be well described by calculations at NLO in pQCD complemented with NP corrections that are important at low $ H_{\mathrm{T},2} /2 $. The upwards trend seen in the 2- and 3-jet data at high $ H_{\mathrm{T},2} /2 $ in comparison to the prediction at NLO QCD, is explained by the onset of EWK corrections in the 2-jet case. For the 3-jet event cross section these correction have not yet been computed. In the 3-jet to 2-jet cross section ratio the EWK corrections are assumed to cancel. In fact, NLO QCD provides an adequate description of $R_{32}$ in the accessible range of $ H_{\mathrm{T},2} /2 $. In contrast, LO tree-level MC predictions exhibit significant deviations. Based on the observed agreement, the strong coupling constant is determined in a fit to the $R_{32}$ measurement to $ \ \ \ \ \alpha_s(M_{\mathrm{Z}}) = $ 0.1150 $\pm$ 0.0023 (exp) $\pm$ 0.0013 (PDF) $\pm$ 0.0015 (NP) $^{+0.0050}_{-0.0000}$ (scale) $ \ \ \ \ \phantom{\alpha_s(M_{\mathrm{Z}}) = } $ 0.1150 $\pm$ 0.0010 (all except scale) $^{+0.0050}_{-0.0000}$ (scale) using the MSTW2008 PDF set. Employing the MMHT2014 PDF set instead leads to very similar results. Equally compatible determinations of $\alpha_{s}(M_{\mathrm{Z}})$ are achieved with separate fits to the inclusive 2-jet and 3-jet event cross sections employing various PDF sets provided the range in HT,2/2 is restricted to 0.3 $ < H_{\mathrm{T},2} /2 < $ 1.0 TeV. The result for $\alpha_{s}(M_{\mathrm{Z}})$ is in agreement with previous determinations obtained by the ATLAS and CMS collaborations [11, 12, 26, 48, 53, 54] and with the world average value of $\alpha_{s}(M_{\mathrm{Z}}) = $ 0.1181 $\pm$ 0.0011 derived in Ref. [52]. |
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Compact Muon Solenoid LHC, CERN |