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CMS-SMP-19-006 ; CERN-EP-2020-229
Hard color-singlet exchange in dijet events in proton-proton collisions at $\sqrt{s} = $ 13 TeV
Phys. Rev. D 104 (2021) 032009
Abstract: Events where the two leading jets are separated by a pseudorapidity interval devoid of particle activity, known as jet-gap-jet events, are studied in proton-proton collisions at $\sqrt{s} = $ 13 TeV. The signature is expected from hard color-singlet exchange. Each of the highest transverse momentum (${p_{\mathrm{T}}}$) jets must have ${p_{\mathrm{T}}}^\text{jet} > $ 40 GeV and pseudorapidity 1.4 $ < |{\eta^\text{jet}}| < $ 4.7, with $\eta^\text{jet1} \eta^\text{jet2} < $ 0, where jet1 and jet2 are the leading and subleading jets in ${p_{\mathrm{T}}}$, respectively. The analysis is based on data collected by the CMS and TOTEM experiments during a low luminosity, high-$\beta^*$ run at the CERN LHC in 2015, with an integrated luminosity of 0.66 pb$^{-1}$. Events with a low number of charged particles with ${p_{\mathrm{T}}} > $ 0.2 GeV in the interval $|{\eta}| < $ 1 between the jets are observed in excess of calculations that assume only color-exchange. The fraction of events produced via color-singlet exchange, $f_\text{CSE}$, is measured as a function of ${p_{\mathrm{T}}}^\text{jet2}$, the pseudorapidity difference between the two leading jets, and the azimuthal angular separation between the two leading jets. The fraction $f_\text{CSE}$ has values of 0.6-1.0%. The results are compared with previous measurements and with predictions from perturbative quantum chromodynamics. In addition, the first study of jet-gap-jet events detected in association with an intact proton using a subsample of events with an integrated luminosity of 0.40 pb$^{-1}$ is presented. The intact protons are detected with the Roman pot detectors of the TOTEM experiment. The $f_\text{CSE}$ in this sample is 2.91 $\pm$ 0.70 (stat) $^{+ 1.02}_{- 0.94}$(syst) times larger than that for inclusive dijet production in dijets with similar kinematics.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
(Left) Schematic diagram of a jet-gap-jet event by hard color-singlet exchange in pp collisions. The lines following the protons represent the proton breakup. (Right) Jet-gap-jet event signature in the $\eta $-$\phi $ plane. The filled circles represent final-state particles. The shaded rectangular area between the jets denotes the interval $ {| \eta |} < $ 1 devoid of charged particles.

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Figure 1-a:
Schematic diagram of a jet-gap-jet event by hard color-singlet exchange in pp collisions. The lines following the protons represent the proton breakup.

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Figure 1-b:
Jet-gap-jet event signature in the $\eta $-$\phi $ plane. The filled circles represent final-state particles. The shaded rectangular area between the jets denotes the interval $ {| \eta |} < $ 1 devoid of charged particles.

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Figure 2:
(Left) Schematic diagram of a jet-gap-jet event by hard color-singlet exchange with an intact proton in pp collisions. The jet-gap-jet is reconstructed in the CMS detector, while the intact proton is detected with one of the forward proton spectrometers of the TOTEM experiment. (Right) Proton-gap-jet-gap-jet event signature in the $\eta $-$\phi $ plane. The filled circles represent final-state particles. The shaded rectangular areas denote the central gap region $ {| \eta |} < $ 1 devoid of charged particles and the forward gap that is inferred from the forward proton detection.

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Figure 2-a:
Schematic diagram of a jet-gap-jet event by hard color-singlet exchange with an intact proton in pp collisions. The jet-gap-jet is reconstructed in the CMS detector, while the intact proton is detected with one of the forward proton spectrometers of the TOTEM experiment.

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Figure 2-b:
Proton-gap-jet-gap-jet event signature in the $\eta $-$\phi $ plane. The filled circles represent final-state particles. The shaded rectangular areas denote the central gap region $ {| \eta |} < $ 1 devoid of charged particles and the forward gap that is inferred from the forward proton detection.

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Figure 3:
Profile schematic of the CMS-TOTEM detector configuration during the 2015 run. The horizontal dashed line represents the beamline. The CMS detector is denoted by the filled circle in the center. The intact proton(s) are transported via the accelerator magnetic fields (violet light rectangles), eventually passing through the silicon detectors housed in the Roman pots (black dark rectangles) of the TOTEM experiment. Sectors 45 and 56 are located in the positive and negative $\eta $ regions in the CMS coordinate system, respectively.

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Figure 4:
Distributions of the ratio of the subleading jet to leading jet transverse momenta $ {p_{\mathrm {T}}} ^\text {jet2}/ {p_{\mathrm {T}}} ^\text {jet1}$ (left panel), the azimuthal angular separation between the two leading jets $\Delta \phi _\text {jj}$ (right panel), and the number of additional jets $N_\text {extra-jets}$ with $ {p_{\mathrm {T}}} ^\text {extra-jet} > $ 15 GeV (lower panel), for jet-gap-jet candidates with $N_\text {tracks} = $ 0 in $ {| \eta |} < $ 1 (black circle) and color-exchange dijet candidates $N_\text {tracks} \geq $ 3 in $ {| \eta |} < $ 1 (red triangle). The vertical bars represent the statistical uncertainties, which are smaller than the marker for some data points. The horizontal bars represent the bin width. The distributions are normalized to unity.

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Figure 4-a:
Distribution of

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Figure 4-b:
Distribution of the azimuthal angular separation between the two leading jets $\Delta \phi _\text {jj}$, for jet-gap-jet candidates with $N_\text {tracks} = $ 0 in $ {| \eta |} < $ 1 (black circle) and color-exchange dijet candidates $N_\text {tracks} \geq $ 3 in $ {| \eta |} < $ 1 (red triangle). The vertical bars represent the statistical uncertainties, which are smaller than the marker for some data points. The horizontal bars represent the bin width. The distributions are normalized to unity.

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Figure 4-c:
Distribution of the number of additional jets $N_\text {extra-jets}$ with $ {p_{\mathrm {T}}} ^\text {extra-jet} > $ 15 GeV, for jet-gap-jet candidates with $N_\text {tracks} = $ 0 in $ {| \eta |} < $ 1 (black circle) and color-exchange dijet candidates $N_\text {tracks} \geq $ 3 in $ {| \eta |} < $ 1 (red triangle). The vertical bars represent the statistical uncertainties, which are smaller than the marker for some data points. The horizontal bars represent the bin width. The distributions are normalized to unity.

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Figure 5:
Charged particle multiplicity distribution $N_\text {tracks}$ in the $ {| \eta |} < $ 1 region for charged particle tracks with $ {p_{\mathrm {T}}} > $ 200 MeV for opposite side (OS) dijet events satisfying $\eta ^\text {jet1} \eta ^\text {jet2} < $ 0 with 40 $ < {p_{\mathrm {T}}} ^\text {jet2} < $ 50 GeV. Vertical bars, which represent statistical uncertainties, are smaller than the markers for most data points. Results from color-exchange dijet background estimation based on the same side (SS) dijet events and the negative binomial distribution (NBD) function fit are shown on the left and right panels, respectively. The NBD function is fit in the interval 3 $ \leq N_\text {tracks} \leq $ 35, and extrapolated to $N_\text {tracks} = $ 0. The dashed-line arrow represents the jet-gap-jet signal region used in the analysis, $N_\text {tracks} \leq $ 2. The fraction $f_\text {CSE}$ corresponds to the ratio of the excess of events at low multiplicities relative to the integrated number of events, as described in the text.

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Figure 5-a:
Charged particle multiplicity distribution $N_\text {tracks}$ in the $ {| \eta |} < $ 1 region for charged particle tracks with $ {p_{\mathrm {T}}} > $ 200 MeV for opposite side (OS) dijet events satisfying $\eta ^\text {jet1} \eta ^\text {jet2} < $ 0 with 40 $ < {p_{\mathrm {T}}} ^\text {jet2} < $ 50 GeV. Vertical bars, which represent statistical uncertainties, are smaller than the markers for most data points. Results from color-exchange dijet background estimation based on the same side (SS) dijet events are shown. The dashed-line arrow represents the jet-gap-jet signal region used in the analysis, $N_\text {tracks} \leq $ 2. The fraction $f_\text {CSE}$ corresponds to the ratio of the excess of events at low multiplicities relative to the integrated number of events, as described in the text.

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Figure 5-b:
Charged particle multiplicity distribution $N_\text {tracks}$ in the $ {| \eta |} < $ 1 region for charged particle tracks with $ {p_{\mathrm {T}}} > $ 200 MeV for opposite side (OS) dijet events satisfying $\eta ^\text {jet1} \eta ^\text {jet2} < $ 0 with 40 $ < {p_{\mathrm {T}}} ^\text {jet2} < $ 50 GeV. Vertical bars, which represent statistical uncertainties, are smaller than the markers for most data points. Results from color-exchange dijet background estimation based on the negative binomial distribution (NBD) function fit are shown. The NBD function is fit in the interval 3 $ \leq N_\text {tracks} \leq $ 35, and extrapolated to $N_\text {tracks} = $ 0. The dashed-line arrow represents the jet-gap-jet signal region used in the analysis, $N_\text {tracks} \leq $ 2. The fraction $f_\text {CSE}$ corresponds to the ratio of the excess of events at low multiplicities relative to the integrated number of events, as described in the text.

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Figure 6:
Distribution of $\xi _{\mathrm{p}} (\text {PF}) - \xi _{\mathrm{p}} (\text {RP})$ in sectors 45 (left) and 56 (right) in data, where $\xi _{\mathrm{p}} (\text {PF})$ and $\xi _{\mathrm{p}} (\text {RP})$ denote the fractional momentum loss of the proton reconstructed with the particle-flow (PF) candidates of CMS and the Roman pots (RP) of TOTEM, respectively. Vertical bars indicate statistical uncertainties only. The estimated background contamination (beam background events) is represented by the filled histogram, and is estimated from the data, as described in the text. No central gap is required for this plot. The dashed-line arrow represents the requirement applied in the analysis to remove most of the beam background contribution.

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Figure 6-a:
Distribution of $\xi _{\mathrm{p}} (\text {PF}) - \xi _{\mathrm{p}} (\text {RP})$ in sector 45 in data, where $\xi _{\mathrm{p}} (\text {PF})$ and $\xi _{\mathrm{p}} (\text {RP})$ denote the fractional momentum loss of the proton reconstructed with the particle-flow (PF) candidates of CMS and the Roman pots (RP) of TOTEM, respectively. Vertical bars indicate statistical uncertainties only. The estimated background contamination (beam background events) is represented by the filled histogram, and is estimated from the data, as described in the text. No central gap is required for this plot. The dashed-line arrow represents the requirement applied in the analysis to remove most of the beam background contribution.

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Figure 6-b:
Distribution of $\xi _{\mathrm{p}} (\text {PF}) - \xi _{\mathrm{p}} (\text {RP})$ in sector 56 in data, where $\xi _{\mathrm{p}} (\text {PF})$ and $\xi _{\mathrm{p}} (\text {RP})$ denote the fractional momentum loss of the proton reconstructed with the particle-flow (PF) candidates of CMS and the Roman pots (RP) of TOTEM, respectively. Vertical bars indicate statistical uncertainties only. The estimated background contamination (beam background events) is represented by the filled histogram, and is estimated from the data, as described in the text. No central gap is required for this plot. The dashed-line arrow represents the requirement applied in the analysis to remove most of the beam background contribution.

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Figure 7:
Charged particle multiplicity distribution in the $ {| \eta |} < $ 1 region after the dijet and proton selection. Opposite side (OS) dijet events satisfy $\eta ^\text {jet1} \eta ^\text {jet2} < $ 0. Vertical bars represent the statistical uncertainties. The filled histogram represents the residual beam background contamination. The contribution of standard diffractive dijet events that feature a central gap is modeled with the same side (SS) dijet events (left) and with the negative binomial distribution (NBD) function fit (right), as described in the text. The NBD function is fit in the interval $2 \leq N_\text {tracks} \leq 25$, and extrapolated to $N_\text {tracks} = $ 0. The dashed-line arrow represents the region $N_\text {tracks} < 2$ used for signal extraction in the analysis.

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Figure 7-a:
Charged particle multiplicity distribution in the $ {| \eta |} < $ 1 region after the dijet and proton selection. Opposite side (OS) dijet events satisfy $\eta ^\text {jet1} \eta ^\text {jet2} < $ 0. Vertical bars represent the statistical uncertainties. The filled histogram represents the residual beam background contamination. The contribution of standard diffractive dijet events that feature a central gap is modeled with the same side (SS) dijet events, as described in the text. The dashed-line arrow represents the region $N_\text {tracks} < 2$ used for signal extraction in the analysis.

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Figure 7-b:
Charged particle multiplicity distribution in the $ {| \eta |} < $ 1 region after the dijet and proton selection. Opposite side (OS) dijet events satisfy $\eta ^\text {jet1} \eta ^\text {jet2} < $ 0. Vertical bars represent the statistical uncertainties. The filled histogram represents the residual beam background contamination. The contribution of standard diffractive dijet events that feature a central gap is modeled with the negative binomial distribution (NBD) function fit, as described in the text. The NBD function is fit in the interval $2 \leq N_\text {tracks} \leq 25$, and extrapolated to $N_\text {tracks} = $ 0. The dashed-line arrow represents the region $N_\text {tracks} < 2$ used for signal extraction in the analysis.

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Figure 8:
Fraction of color-singlet exchange dijet events, $f_\text {CSE}$, measured as a function of $\Delta \eta _\text {jj}$, $ {p_{\mathrm {T}}} ^\text {jet2}$, and $\Delta \phi _\text {jj}$ in pp collisions at $\sqrt {s} = $ 13 TeV. Vertical bars represent statistical uncertainties, while boxes represent the combination of statistical and systematic uncertainties in quadrature. The results are plotted at the mean values of $\Delta \eta _\text {jj}$, $ {p_{\mathrm {T}}} ^\text {jet2}$, and $\Delta \phi _\text {jj}$ in the bin. For a given plot of $f_\text {CSE}$ versus a kinematic variable of interest ($ {p_{\mathrm {T}}} ^\text {jet2}$, $\Delta \eta _\text {jj}$, or $\Delta \phi _\text {jj}$), the other kinematic variables are integrated over their allowed range. The red solid curve corresponds to theoretical predictions based on the RMK model [54,55] with gap survival probability of $ {| \mathcal {S} |}^2 = 10$%. The EEIM model [53,56] predictions with MPI-only contributions and $ {| \mathcal {S} |}^2 = 1.2$% or MPI+SCI are represented by the purple dashed and orange dotted curves, respectively. The bands around the curves represent the associated theoretical uncertainties. The EEIM model, not shown versus $\Delta \phi _\text {jj}$, has only small contributions far from back-to-back jets since no hard NLO $2\to 3$ processes are included.

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Figure 8-a:
Fraction of color-singlet exchange dijet events, $f_\text {CSE}$, measured as a function of $\Delta \eta _\text {jj}$ in pp collisions at $\sqrt {s} = $ 13 TeV. Vertical bars represent statistical uncertainties, while boxes represent the combination of statistical and systematic uncertainties in quadrature. The results are plotted at the mean values of $\Delta \eta _\text {jj}$, $ {p_{\mathrm {T}}} ^\text {jet2}$, and $\Delta \phi _\text {jj}$ in the bin. For a given plot of $f_\text {CSE}$ versus a kinematic variable of interest ($ {p_{\mathrm {T}}} ^\text {jet2}$, $\Delta \eta _\text {jj}$, or $\Delta \phi _\text {jj}$), the other kinematic variables are integrated over their allowed range. The red solid curve corresponds to theoretical predictions based on the RMK model [54,55] with gap survival probability of $ {| \mathcal {S} |}^2 = 10$%. The EEIM model [53,56] predictions with MPI-only contributions and $ {| \mathcal {S} |}^2 = 1.2$% or MPI+SCI are represented by the purple dashed and orange dotted curves, respectively. The bands around the curves represent the associated theoretical uncertainties. The EEIM model, not shown versus $\Delta \phi _\text {jj}$, has only small contributions far from back-to-back jets since no hard NLO $2\to 3$ processes are included.

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Figure 8-b:
Fraction of color-singlet exchange dijet events, $f_\text {CSE}$, measured as a function of $ {p_{\mathrm {T}}} ^\text {jet2}$ in pp collisions at $\sqrt {s} = $ 13 TeV. Vertical bars represent statistical uncertainties, while boxes represent the combination of statistical and systematic uncertainties in quadrature. The results are plotted at the mean values of $\Delta \eta _\text {jj}$, $ {p_{\mathrm {T}}} ^\text {jet2}$, and $\Delta \phi _\text {jj}$ in the bin. For a given plot of $f_\text {CSE}$ versus a kinematic variable of interest ($ {p_{\mathrm {T}}} ^\text {jet2}$, $\Delta \eta _\text {jj}$, or $\Delta \phi _\text {jj}$), the other kinematic variables are integrated over their allowed range. The red solid curve corresponds to theoretical predictions based on the RMK model [54,55] with gap survival probability of $ {| \mathcal {S} |}^2 = 10$%. The EEIM model [53,56] predictions with MPI-only contributions and $ {| \mathcal {S} |}^2 = 1.2$% or MPI+SCI are represented by the purple dashed and orange dotted curves, respectively. The bands around the curves represent the associated theoretical uncertainties. The EEIM model, not shown versus $\Delta \phi _\text {jj}$, has only small contributions far from back-to-back jets since no hard NLO $2\to 3$ processes are included.

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Figure 8-c:
Fraction of color-singlet exchange dijet events, $f_\text {CSE}$, measured as a function of $\Delta \phi _\text {jj}$ in pp collisions at $\sqrt {s} = $ 13 TeV. Vertical bars represent statistical uncertainties, while boxes represent the combination of statistical and systematic uncertainties in quadrature. The results are plotted at the mean values of $\Delta \eta _\text {jj}$, $ {p_{\mathrm {T}}} ^\text {jet2}$, and $\Delta \phi _\text {jj}$ in the bin. For a given plot of $f_\text {CSE}$ versus a kinematic variable of interest ($ {p_{\mathrm {T}}} ^\text {jet2}$, $\Delta \eta _\text {jj}$, or $\Delta \phi _\text {jj}$), the other kinematic variables are integrated over their allowed range. The red solid curve corresponds to theoretical predictions based on the RMK model [54,55] with gap survival probability of $ {| \mathcal {S} |}^2 = 10$%. The EEIM model [53,56] predictions with MPI-only contributions and $ {| \mathcal {S} |}^2 = 1.2$% or MPI+SCI are represented by the purple dashed and orange dotted curves, respectively. The bands around the curves represent the associated theoretical uncertainties. The EEIM model, not shown versus $\Delta \phi _\text {jj}$, has only small contributions far from back-to-back jets since no hard NLO $2\to 3$ processes are included.

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Figure 9:
Fraction of color-singlet exchange dijet events, $f_\text {CSE}$, measured as a function of $ {p_{\mathrm {T}}} ^\text {jet2}$ by the D0 and CDF Collaborations [43,45,46] at $\sqrt {s} = $ 0.63 (red open symbols) and 1.8 TeV (green open symbols), by the CMS Collaboration [47] at 7 TeV (magenta open symbols), and the present results at 13 TeV (filled circles). Vertical bars of the open symbols represent the total experimental uncertainties. Vertical bars of the 13 TeV measurement represent the statistical uncertainties, and boxes represent the combination of statistical and systematic uncertainties in quadrature. The central gap is defined by means of the particle activity in the $ {| \eta |} < $ 1 interval in these measurements, as described in the text.

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Figure 10:
Fraction of color-singlet exchange dijet events, $f_\text {CSE}$, measured as a function of $\Delta \eta _\text {jj}$ by CMS at 7 TeV [47] and the present measurement at 13 TeV. The 7 TeV measurement was performed in three bins of $ {p_{\mathrm {T}}} ^\text {jet2} = $ 40-60, 60-100, and 100-200 GeV, which are represented by the open circle, open square, and open cross symbols, respectively. The present 13 TeV results are represented by the filled circles. Vertical bars of the 7 TeV measurement represent the total experimental uncertainties. Vertical bars of the 13 TeV measurement represent the statistical uncertainties, and boxes represent the combination of statistical and systematic uncertainties in quadrature.

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Figure 11:
Fraction of hard color-singlet exchange dijet events $f_\text {CSE}$, measured as a function of $\Delta \eta _\text {jj}$ (left) and $ {p_{\mathrm {T}}} ^\text {jet2}$ (right) extracted in inclusive dijet event production (labeled CMS, represented by the blue circle markers) and in dijet events with an intact proton at 13 TeV (labeled CMS-TOTEM, represented by the red cross marker). Vertical bars represent the statistical uncertainties, and boxes represent the combination of statistical and systematic uncertainties in quadrature. The CMS results are plotted at the mean values of $\Delta \eta _\text {jj}$ and $ {p_{\mathrm {T}}} ^\text {jet2}$ in the bin. The CMS-TOTEM result is plotted at the mean value of $\Delta \eta _\text {jj}$ and $ {p_{\mathrm {T}}} ^\text {jet2}$ in the allowed range of these variables. The 40 $ < {p_{\mathrm {T}}} ^\text {jet2} < $ 100 GeV and 3.0 $ < \Delta \eta _\text {jj} < $ 6.5 ranges below the CMS-TOTEM legend represent the dijet phase space covered by events with an intact proton with the present sample size, rather than a selection requirement, as described in the text.

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Figure 11-a:
Fraction of hard color-singlet exchange dijet events $f_\text {CSE}$, measured as a function of $\Delta \eta _\text {jj}$ extracted in inclusive dijet event production (labeled CMS, represented by the blue circle markers) and in dijet events with an intact proton at 13 TeV (labeled CMS-TOTEM, represented by the red cross marker). Vertical bars represent the statistical uncertainties, and boxes represent the combination of statistical and systematic uncertainties in quadrature. The CMS results are plotted at the mean values of $\Delta \eta _\text {jj}$ and $ {p_{\mathrm {T}}} ^\text {jet2}$ in the bin. The CMS-TOTEM result is plotted at the mean value of $\Delta \eta _\text {jj}$ and $ {p_{\mathrm {T}}} ^\text {jet2}$ in the allowed range of these variables. The 40 $ < {p_{\mathrm {T}}} ^\text {jet2} < $ 100 GeV and 3.0 $ < \Delta \eta _\text {jj} < $ 6.5 ranges below the CMS-TOTEM legend represent the dijet phase space covered by events with an intact proton with the present sample size, rather than a selection requirement, as described in the text.

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Figure 11-b:
Fraction of hard color-singlet exchange dijet events $f_\text {CSE}$, measured as a function of $ {p_{\mathrm {T}}} ^\text {jet2}$ extracted in inclusive dijet event production (labeled CMS, represented by the blue circle markers) and in dijet events with an intact proton at 13 TeV (labeled CMS-TOTEM, represented by the red cross marker). Vertical bars represent the statistical uncertainties, and boxes represent the combination of statistical and systematic uncertainties in quadrature. The CMS results are plotted at the mean values of $\Delta \eta _\text {jj}$ and $ {p_{\mathrm {T}}} ^\text {jet2}$ in the bin. The CMS-TOTEM result is plotted at the mean value of $\Delta \eta _\text {jj}$ and $ {p_{\mathrm {T}}} ^\text {jet2}$ in the allowed range of these variables. The 40 $ < {p_{\mathrm {T}}} ^\text {jet2} < $ 100 GeV and 3.0 $ < \Delta \eta _\text {jj} < $ 6.5 ranges below the CMS-TOTEM legend represent the dijet phase space covered by events with an intact proton with the present sample size, rather than a selection requirement, as described in the text.
Tables

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Table 1:
Relative systematic uncertainties in percentage for the measurements of $f_\text {CSE}$ in jet-gap-jet and proton-gap-jet-gap-jet events. The jet-gap-jet results summarize the systematic uncertainties in bins of the kinematic variables of interest $ {p_{\mathrm {T}}} ^\text {jet2}$, $\Delta \eta _\text {jj}$, and $\Delta \phi _\text {jj}$. When an uncertainty range is given, the range of values is representative of the variation found in $f_\text {CSE}$ in bins of the kinematic variables of interest.

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Table 2:
Measured values of the fraction of color-singlet exchange events $f_\text {CSE}$ in bins of the pseudorapidity difference between the two leading jets $\Delta \eta _\text {jj}$. The first column indicates the $\Delta \eta _\text {jj}$ intervals and the last column represents the measured fraction. The first and second uncertainties correspond to the statistical and systematic components, respectively. The results are integrated over the allowed $ {p_{\mathrm {T}}} ^\text {jet2}$ and $\Delta \phi _\text {jj}$ values. The mean values of $\Delta \eta _\text {jj}$ in the bin are given in the middle column.

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Table 3:
Measured values of the fraction of color-singlet exchange events $f_\text {CSE}$ in bins of the subleading jet transverse momentum $ {p_{\mathrm {T}}} ^\text {jet2}$. The first column indicates the $ {p_{\mathrm {T}}} ^\text {jet2}$ bin intervals and the last column represents the measured fraction. The first and second uncertainties correspond to the statistical and systematic components, respectively. The results are integrated over the allowed $\Delta \eta _\text {jj}$ and $\Delta \phi _\text {jj}$ values. The mean values of $ {p_{\mathrm {T}}} ^\text {jet2}$ in the bin are given in the middle column.

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Table 4:
Measured values of the fraction of color-singlet exchange events $f_\text {CSE}$ in bins of the azimuthal angular difference between the two leading jets $\Delta \phi _\text {jj}$. The first column indicates the $\Delta \phi _\text {jj}$ bin intervals and the last column represents the measured fraction. The first and second uncertainties correspond to the statistical and systematic components, respectively. The results are integrated over the allowed $ {p_{\mathrm {T}}} ^\text {jet2}$ and $\Delta \eta _\text {jj}$ values. The mean values of $\Delta \phi _\text {jj}$ in the bin are given in the middle column.
Summary
Events with two leading jets separated by a large pseudorapidity ($\eta$) gap have been studied in proton-proton (pp) collisions at $\sqrt{s} = $ 13 TeV with the CMS and TOTEM experiments at the CERN LHC in 2015. The pseudorapidity gap is defined by the absence of charged particles with transverse momentum ${p_{\mathrm{T}}} > $ 200 MeV in the $|{\eta}| < $ 1 region. Each of the two leading ${p_{\mathrm{T}}}$ jets has 1.4 $ < |{\eta^\text{jet}}| < $ 4.7 and ${p_{\mathrm{T}}}^\text{jet} > $ 40 GeV, with $\eta^\text{jet1} \eta^\text{jet2} < $ 0, where jet1 and jet2 are the leading and subleading jets in ${p_{\mathrm{T}}}$. The pseudorapidity gap signature is assumed to be caused by hard color-singlet exchange, which is described in terms of two-gluon exchange in perturbative quantum chromodynamics. Color-singlet exchange events appear as an excess of events over the expected charged particle multiplicity contribution from color-exchange dijet events at the lowest charged particle multiplicity. The ratio of color-singlet exchange events to all dijet events, $f_\text{CSE}$, has been measured as a function of ${p_{\mathrm{T}}}^\text{jet2}$, the $\eta$ difference between the two leading jets, $\Delta\eta_\text{jj} \equiv |{\eta^\text{jet1} - \eta^\text{jet2}}|$, and the azimuthal angular separation between the two leading jets, $\Delta\phi_\text{jj} \equiv |{\phi^\text{jet1} - \phi^\text{jet2}}|$.

The measured $f_\text{CSE}$ values are in the range of 0.6-1.0%. The ratio $f_\text{CSE}$ increases with $\Delta\eta_\text{jj}$, has a weak dependence on ${p_{\mathrm{T}}}^\text{jet2}$, and increases as $\Delta\phi_\text{jj}$ approaches $\pi$. No significant difference in $f_\text{CSE}$ is observed between the 13 TeV results and those presented by the CMS Collaboration at 7 TeV. This is in contrast to the trend found at lower energies of 0.63 and 1.8 TeV by the D0 and CDF Collaborations, where a significant decrease of $f_\text{CSE}$ with increasing $\sqrt{s}$ was observed, as illustrated in Fig. 9. The results are compared with calculations based on the Balitsky-Fadin-Kuraev-Lipatov framework [3,4,5] with resummation of large logarithms of energy at next-to-leading logarithmic accuracy using leading order impact factors, and various treatments of gap survival probability effects. The implementation by Royon, Marquet, and Kepka [54,55] describes some features of the data, but is not able to simultaneously describe all aspects of the measurements. The implementation by Ekstedt, Enberg, Ingelman, and Motyka [53,56] gives a fair description of the data in $\Delta\eta_\text{jj}$ and ${p_{\mathrm{T}}}^\text{jet2}$ within the uncertainties only when considering survival probability effects based on multiple-parton interactions and their soft color interaction model.

In addition, a sample of dijet events with intact protons collected by the CMS and TOTEM experiments is used to study jet-gap-jet events with intact protons, which correspond to proton-gap-jet-gap-jet topologies. This is the first analysis of this diffractive event topology. The $f_\text{CSE}$ value extracted in this sample is 2.91 $\pm$ 0.70 (stat)$^{+ 1.02}_{- 0.94}$ (syst) times larger than that found in inclusive dijet production, possibly suggesting a larger abundance of jets with central gaps in events with detected intact protons. This can be interpreted in terms of a lower spectator parton activity in events with intact protons, which decreases the likelihood of the central gap signature being spoiled.
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