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CMS-FSQ-13-004 ; CERN-EP-2021-173
Study of dijet events with large rapidity separation in proton-proton collisions at $\sqrt{s} = $ 2.76 TeV
JHEP 03 (2022) 189
Abstract: The cross sections for inclusive and Mueller-Navelet dijet production are measured as a function of the rapidity separation between the jets in proton-proton collisions at $\sqrt{s} = $ 2.76 TeV for jets with transverse momentum ${p_{\mathrm{T}}} > $ 35 GeV and rapidity $| y | < $ 4.7. Various dijet production cross section ratios are also measured. A veto on additional jets with ${p_{\mathrm{T}}} > $ 20 GeV is introduced to improve the sensitivity to the effects of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution. The measurement is compared with the predictions of various Monte Carlo models based on leading-order and next-to-leading-order calculations including the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi leading-logarithm (LL) parton shower as well as the LL BFKL resummation.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Summary of the systematic uncertainties on the cross sections $ {\mathrm {d} {\sigma ^{\text {incl}}} /\mathrm {d} {\Delta y}}$ (upper left) and $ {\mathrm {d} {\sigma ^{\mathrm {MN}}} /\mathrm {d} {\Delta y}}$ (upper right), as well as the ratios $ {R^{\text {incl}}} $ (middle left), $ {R^{\mathrm {MN}}} $ (middle right), $ {R^{\text {incl}}_{\text {veto}}} $ (lower left), and $ {R^{\mathrm {MN}}_{\text {veto}}} $ (lower right). The various contributions are indicated by the lines and the total uncertainty is shown with a band.

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Figure 1-a:
Summary of the systematic uncertainties on the $ {\mathrm {d} {\sigma ^{\text {incl}}} /\mathrm {d} {\Delta y}}$ cross section. The various contributions are indicated by the lines and the total uncertainty is shown with a band.

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Figure 1-b:
Summary of the systematic uncertainties on the $ {\mathrm {d} {\sigma ^{\mathrm {MN}}} /\mathrm {d} {\Delta y}}$ cross section. The various contributions are indicated by the lines and the total uncertainty is shown with a band.

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Figure 1-c:
Summary of the systematic uncertainties on the $ {R^{\text {incl}}} $ ratio. The various contributions are indicated by the lines and the total uncertainty is shown with a band.

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Figure 1-d:
Summary of the systematic uncertainties on the $ {R^{\mathrm {MN}}} $ ratio. The various contributions are indicated by the lines and the total uncertainty is shown with a band.

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Figure 1-e:
Summary of the systematic uncertainties on the $ {R^{\text {incl}}_{\text {veto}}} $ ratio. The various contributions are indicated by the lines and the total uncertainty is shown with a band.

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Figure 1-f:
Summary of the systematic uncertainties on the $ {R^{\mathrm {MN}}_{\text {veto}}}$ ratio. The various contributions are indicated by the lines and the total uncertainty is shown with a band.

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Figure 2:
Differential cross section $ {\mathrm {d} {\sigma ^{\text {incl}}} /\mathrm {d} {\Delta y}}$ for inclusive dijet production. The upper and lower rows present the comparison with different MC models. The plots on the left present the cross sections and those on the right the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 2-a:
Differential cross section $ {\mathrm {d} {\sigma ^{\text {incl}}} /\mathrm {d} {\Delta y}}$ for inclusive dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 2-b:
Differential cross section $ {\mathrm {d} {\sigma ^{\text {incl}}} /\mathrm {d} {\Delta y}}$ for inclusive dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 2-c:
Differential cross section $ {\mathrm {d} {\sigma ^{\text {incl}}} /\mathrm {d} {\Delta y}}$ for inclusive dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 2-d:
Differential cross section $ {\mathrm {d} {\sigma ^{\text {incl}}} /\mathrm {d} {\Delta y}}$ for inclusive dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 3:
Differential cross section $ {\mathrm {d} {\sigma ^{\mathrm {MN}}} /\mathrm {d} {\Delta y}}$ for MN dijet production. The upper and lower rows present the comparison with different MC models. The plots on the left present the cross sections and those on the right the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 3-a:
Differential cross section $ {\mathrm {d} {\sigma ^{\mathrm {MN}}} /\mathrm {d} {\Delta y}}$ for MN dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 3-b:
Differential cross section $ {\mathrm {d} {\sigma ^{\mathrm {MN}}} /\mathrm {d} {\Delta y}}$ for MN dijet production, compared with different MC models. The plots presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 3-c:
Differential cross section $ {\mathrm {d} {\sigma ^{\mathrm {MN}}} /\mathrm {d} {\Delta y}}$ for MN dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 3-d:
Differential cross section $ {\mathrm {d} {\sigma ^{\mathrm {MN}}} /\mathrm {d} {\Delta y}}$ for MN dijet production, compared with different MC models. The plots presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 4:
Ratio ${R^{\text {incl}}}$ of the cross sections for inclusive to "exclusive" dijet production. The upper and lower rows present the comparison with different MC models. The plots on the left present the ratio ${R^{\text {incl}}}$ and those on the right the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 4-a:
Ratio ${R^{\text {incl}}}$ of the cross sections for inclusive to "exclusive" dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 4-b:
Ratio ${R^{\text {incl}}}$ of the cross sections for inclusive to "exclusive" dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 4-c:
Ratio ${R^{\text {incl}}}$ of the cross sections for inclusive to "exclusive" dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 4-d:
Ratio ${R^{\text {incl}}}$ of the cross sections for inclusive to "exclusive" dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 5:
Ratio ${R^{\text {incl}}_{\text {veto}}}$ of the cross sections for inclusive to "exclusive" with veto dijet production. The upper and lower rows present the comparison with different MC models. The plots on the left present the ratio ${R^{\text {incl}}_{\text {veto}}}$ and those on the right the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 5-a:
Ratio ${R^{\text {incl}}_{\text {veto}}}$ of the cross sections for inclusive to "exclusive" with veto dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 5-b:
Ratio ${R^{\text {incl}}_{\text {veto}}}$ of the cross sections for inclusive to "exclusive" with veto dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 5-c:
Ratio ${R^{\text {incl}}_{\text {veto}}}$ of the cross sections for inclusive to "exclusive" with veto dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 5-d:
Ratio ${R^{\text {incl}}_{\text {veto}}}$ of the cross sections for inclusive to "exclusive" with veto dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 6:
Ratio ${R^{\mathrm {MN}}}$ of the cross sections for MN to "exclusive" dijet production. The upper and lower rows present the comparison with different MC models. The plots on the left present the ratio ${R^{\mathrm {MN}}}$ and those on the right the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 6-a:
Ratio ${R^{\mathrm {MN}}}$ of the cross sections for MN to "exclusive" dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 6-b:
Ratio ${R^{\mathrm {MN}}}$ of the cross sections for MN to "exclusive" dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 6-c:
Ratio ${R^{\mathrm {MN}}}$ of the cross sections for MN to "exclusive" dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 6-d:
Ratio ${R^{\mathrm {MN}}}$ of the cross sections for MN to "exclusive" dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 7:
Ratio ${R^{\mathrm {MN}}_{\text {veto}}}$ of the cross sections for MN to "exclusive" with veto dijet production. The upper and lower rows present the comparison with different MC models. The plots on the left present the ratio ${R^{\mathrm {MN}}_{\text {veto}}}$ and those on the right the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 7-a:
Ratio ${R^{\mathrm {MN}}_{\text {veto}}}$ of the cross sections for MN to "exclusive" with veto dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 7-b:
Ratio ${R^{\mathrm {MN}}_{\text {veto}}}$ of the cross sections for MN to "exclusive" with veto dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 7-c:
Ratio ${R^{\mathrm {MN}}_{\text {veto}}}$ of the cross sections for MN to "exclusive" with veto dijet production, compared with different MC models. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 7-d:
Ratio ${R^{\mathrm {MN}}_{\text {veto}}}$ of the cross sections for MN to "exclusive" with veto dijet production, compared with different MC models. The plot presents the ratio of theory to data. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 8:
Ratios ${R^{\text {incl}}}$ (left) and ${R^{\mathrm {MN}}}$ (right) of the cross sections for inclusive (left) and MN (right) and "exclusive" dijet production, measured at 2.76 TeV and 7 TeV [21] collision energies. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 8-a:
Ratio ${R^{\text {incl}}}$ of the cross sections for inclusive and "exclusive" dijet production, measured at 2.76 TeV and 7 TeV [21] collision energies. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.

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Figure 8-b:
Ratio ${R^{\mathrm {MN}}}$ of the cross sections for MN and "exclusive" dijet production, measured at 2.76 TeV and 7 TeV [21] collision energies. The systematic uncertainties are indicated by the shaded bands and the statistical uncertainties by the vertical bars.
Tables

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Table 1:
Event definitions for cross section measurements.
Summary
A study of dijet events with large rapidity separation ${\Delta y}$ between the jets has been performed using proton-proton collision data at $\sqrt{s} = $ 2.76 TeV, collected by the CMS experiment in 2013 with an integrated luminosity of 5.4 pb$^{-1}$. The cross sections for Mueller-Navelet and inclusive dijet event production, as well as their ratios to "exclusive", and "exclusive" with veto, dijet event production, are measured up to ${\Delta y} \leq $ 8.0 between the jets.

None of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP)-based Monte Carlo generators using leading-order (LO) or next-to-LO (NLO) calculations can provide a complete description of all measured cross sections and their ratios. The dijet ratio with extra jet veto cannot be described by the LO or NLO DGLAP-based generators. To compare the present results with the Balitsky-Fadin-Kuraev-Lipatov approach, calculations at the next-to-leading-logarithm level are needed.

The present results at $\sqrt{s} = $ 2.76 TeV can be used along with data at higher energies to reveal possible effects beyond the DGLAP approach to make more definite conclusions. Tabulated results are provided in the HEPData record for this analysis [53].
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