Observation of a diffractive contribution to dijet production in proton-proton collisions at ffiffi s p 1⁄4 7 TeV

The cross section for dijet production in proton-proton collisions at ffiffi s p 1⁄4 7 TeV is presented as a function of ~ , a variable that approximates the fractional momentum loss of the scattered proton in singlediffractive events. The analysis is based on an integrated luminosity of 2:7 nb 1 collected with the CMS detector at the LHC at low instantaneous luminosities, and uses events with jet transverse momentum of at least 20 GeV. The dijet cross section results are compared to the predictions of diffractive and nondiffractive models. The low-~ data show a significant contribution from diffractive dijet production, observed for the first time at the LHC. The associated rapidity gap survival probability is estimated.


I. INTRODUCTION
A significant fraction of the total inelastic proton-proton cross section at high energies is attributed to diffractive processes, characterized by the presence of a large rapidity region Áy with no hadrons, usually called ''rapidity gap'' [rapidity is defined as y ¼ ð1=2Þ ln½ðE þ p Z Þ=ðE À p Z Þ, where E and p Z are the energy and longitudinal momentum of the final-state particle, respectively].Diffractive scattering is described in the framework of Regge theory as mediated by a strongly interacting color-singlet exchange with the vacuum quantum numbers, the so-called ''pomeron trajectory'' [1].Diffractive events with a hard parton-parton scattering are especially interesting because they can be studied in terms of perturbative quantum chromodynamics (pQCD).In diffractive events the proton emitting the pomeron either remains intact, losing only a few percent of its momentum, or is found in a low mass excited state.In addition, since the vacuum quantum numbers are exchanged, no particles are produced in a large rapidity range adjacent to the scattered proton (or its dissociation products).
Diffraction with a hard scale has been studied in protonantiproton (p" p) and electron-proton (ep) collisions at CERN [2], Fermilab [3][4][5][6], and DESY [7][8][9][10].Such hard diffractive processes can be described in terms of the convolution of diffractive parton distribution functions (dPDFs) and hard scattering cross sections, which are calculable in pQCD.In this approach, the pomeron is treated as a color-singlet combination of partons with the vacuum quantum numbers.The dPDFs have been determined by the HERA experiments [7,9] by means of QCD fits to inclusive diffractive deep inelastic scattering data, and have been successfully used to describe different hard diffractive processes in ep collisions.This success is based on the factorization theorem for diffractive electron-proton interactions, and on the validity of the QCD evolution equations for the dPDFs [11][12][13].However, in hard diffractive hadron-hadron collisions factorization does not hold because of soft scatterings between the spectator partons, leading to the suppression of the observed diffractive cross section.The suppression is quantified by the socalled ''rapidity gap survival probability'' [14], which is a nonperturbative quantity with large theoretical uncertainties [15][16][17][18].It was measured to be about 10% in diffractive dijet production in p" p collisions at the Tevatron [5].
This paper presents a study of dijet production in proton-proton (pp) collisions at a center-of-mass energy of ffiffi ffi s p ¼ 7 TeV.The data were collected with the Compact Muon Solenoid (CMS) detector at the LHC in 2010 and correspond to an integrated luminosity of 2:7 nb À1 .The cross section for production of dijets is presented as a function of , a variable that approximates the fractional momentum loss of the proton, for events in which both jets have transverse momenta p j1;j2 T > 20 GeV and jet axes in the pseudorapidity range j j1;j2 j < 4:4.Pseudorapidity is defined as ¼ À ln½tanð=2Þ, where is the polar angle relative to the anticlockwise proton beam direction, and is equal to the rapidity in the limit of a massless particle.The measurements are compared to the predictions of nondiffractive (ND) and diffractive models, and the rapidity gap survival probability is estimated.
The paper is organized as follows: in Sec.II a brief description of the CMS detector is provided.The definitions of the kinematic variables are introduced in Sec.III.The event selection is explained in Sec.IV.Section V describes the main features of the Monte Carlo (MC) generators used in this analysis.The cross section determination for dijets as a function of and the systematic uncertainties of the measurements are discussed in Sec.VI.
The results are presented in Sec.VII, and the summary is given in Sec.VIII.

II. EXPERIMENTAL SETUP
A detailed description of the CMS detector can be found elsewhere [19].The central feature of the CMS apparatus is a superconducting solenoid, of 6 m internal diameter.Within the field volume are the silicon pixel and strip tracker, the crystal electromagnetic calorimeter (ECAL) and the brass-scintillator hadronic calorimeter (HCAL).The tracker measures charged particles within the pseudorapidity range jnj < 2:4.ECAL and HCAL provide coverage in pseudorapidity up to jnj < 3 in the barrel region and two endcap regions.The HCAL, when combined with the ECAL, measures jets with an energy resolution ÁE=E % 100%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ðGeVÞ p È 5%.The calorimeter cells are grouped in projective towers, of granularity Á Â Á ¼ 0:087 Â 0:087 at central rapidities and 0:175 Â 0:175 at forward rapidities, where is the azimuthal angle in radians.In addition to the barrel and endcap detectors, CMS has extensive forward calorimetry.The forward part of the hadron calorimeter, HF, consists of steel absorbers and embedded radiation-hard quartz fibers, which provide a fast collection of Cherenkov light.The pseudorapidity coverage of the HF is 2:9 < jj < 5:2.In the current analysis only the range 3:0 < jj < 4:9 was used, thus restricting the data to a region of well-understood reconstruction efficiency.The first level of the CMS trigger system, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select the most interesting events in a fixed time interval of less than 4 s.The High Level Trigger processor farm further decreases the event rate from around 100 kHz to around 300 Hz, before data storage.

III. KINEMATICS AND CROSS SECTIONS
Diffractive dijet production (Fig. 1) is characterized by the presence of a high-momentum proton (or a system Y with the same quantum numbers as the proton) with fractional momentum loss smaller than a few percent and a system X, which contains high-p T jets and is separated from the proton by a large rapidity gap, with Áy ! 3 or 4 units.The kinematics of this reaction is described by the masses of the systems X and Y, M X and M Y , and the squared four-momentum transfer t at the proton vertex.For the events selected in this analysis both M X and M Y are much smaller than ffiffi ffi s p .The cross section for single-diffractive (SD) dijet production (i.e. when the forward-going system Y is a proton) is usually expressed in terms of the variable ¼ M 2 X =s, which approximates the fractional momentum loss of the scattered proton.Under the assumption of QCD factorization, the cross section can be written as where the sum is over all parton flavors.The variables x 1;2 are the parton momentum fractions in the pomeron and proton, the scale at which the PDFs are evaluated is indicated with , and ð ŝ; tÞ is the hard-scattering subprocess cross section, which is a function of the partonic center-ofmass energy squared ŝ and momentum transfer squared t.
The function f p ðx 2 ; Þ is the inclusive PDF of the proton that breaks up, while the dPDF of the surviving proton is written as f diff ð; t; x 1 ; Þ ¼ fð; tÞf P ðx 1 ; Þ, where fð; tÞ is the so-called pomeron flux and f P ðx 1 ; Þ is the pomeron structure function.The cross section dependence on and t is driven by the pomeron flux, usually parametrized according to Regge theory as fð; tÞ ¼ e Bt 2 P ðtÞÀ1 ; (2) where P ðtÞ is the pomeron trajectory and B is the slope parameter.This ansatz is consistent with the HERA ep data [7][8][9], but is known not to hold between the ep and the Tevatron (p" p) data [3][4][5][6], where an extra suppression (gap survival probability) factor is needed.
In this analysis is approximated by the variables þ (system X going in the Àz direction) and À (system X going in the þz direction) defined at the level of stable particles as where E i and p i z are the energy and longitudinal momentum of the ith final-state particle with À1 < < 4:9 for þ and À4:9 < < þ1 for À .In the region of low AE , this variable is a good approximation of for singlediffractive events.This is illustrated for single-diffractive dijet events simulated by PYTHIA8 [20] in Fig. 2, where the correlations between the values of and þ , determined at generated and reconstructed (see Sec. IV) levels, are shown.The mass of the forward-going system Y, which includes all particles with > 4:9 (or < À4:9), was also estimated with the PYTHIA8 generator; the mass is limited by the pseudorapidity range and is typically smaller than 30-40 GeV, with average $5 GeV.

IV. EVENT SELECTION
The data were collected with the CMS detector in 2010 at low luminosities.The average number of extra pp interactions for any given event (the so-called pileup interactions) in the data is 0.09.The low number of pileup interactions simplified the extraction of the diffractive signal, since the particles produced in such interactions may fill the rapidity gap and hence reduce the visible diffractive cross section.However, the requirement of low pileup limits the available data sample since only a small amount of low-luminosity runs was collected.
At the trigger level events were selected by requiring at least one jet with uncorrected transverse-momentum greater than 6 GeV.The efficiency of the trigger, estimated using a minimum-bias data sample, was found to be greater than 95% for the dijet events considered in this analysis.
Offline, the jets were reconstructed with the anti-k T inclusive jet finding algorithm [21] with a distance parameter of 0.5.The jet clustering algorithm was used to reconstruct jets from particle-flow (PF) objects [22], which are particle candidates obtained by combining the information of the tracking system and of the calorimeters in an optimal way.The reconstructed jet momenta were fully corrected to the level of stable particles (with lifetime such that c > 10 mm, hereafter referred to as ''particle level''), by means of a procedure partially based on MC simulation and partially on data [23].
The quantities þ and À were reconstructed using Eq. ( 3) from the energies and longitudinal momenta of all PF objects measured in the jj < 4:9 range.For charged PF objects (jj < 2:4, the region covered by the tracker) a minimum transverse momentum of 0.2 GeV was required.In the forward region, 3:0 < jj < 4:9, particularly relevant for this analysis, PF candidates were selected with energy greater than 4 GeV.A constant scale factor C ¼ 1:45 AE 0:04, determined from the MC simulation by comparing the generated and reconstructed values of AE , is applied to the measured AE .The error on the correction factor C is estimated by changing the MC models used to evaluate it.The value of C reflects the fact that not all finalstate particles are detected because of the limited acceptance and imperfect response of the detector.It also takes into account the inefficiency of PF object reconstruction.In practice, C acts as a scale calibration for AE ; it depends only slightly on the value of AE and on the MC generator used.This dependence, of the order of a few percent, is included in the systematic uncertainty.The resolution of AE , in the region of the present measurement, is $25%, and practically independent of AE .
Events were selected offline by applying the following requirements: (i) the jets should pass the standard CMS quality criteria [23]; (ii) events should have at least two jets, each with transverse momentum, corrected to particle level, greater than 20 GeV.This requirement ensures high trigger efficiency; (iii) the axes of the two leading jets (jets were ordered in p T with the first, leading jet having the highest p T ) should be in the pseudorapidity region j j1;j2 j < 4:4 so that the reconstructed jets are fully contained in the detector; (iv) a primary vertex should be within a longitudinal distance jzj < 24 cm of the center of CMS; (v) beam-scraping events, in which long horizontal sections of the pixel tracker are hit by charged particles traveling parallel to the beam, were rejected with a special algorithm [24]; (vi) to enhance the diffractive contribution, the requirements max < 3 ( min > À3) were also applied.
Here max ( min ) is the pseudorapidity of the most forward (backward) PF object.The max ( min ) selection together with the pseudorapidity coverage of the detector, jj < 4:9, is equivalent to imposing a pseudorapidity gap of at least 1.9 units, with no PF objects with energy greater than 4 GeV in the HF calorimeter.The number of selected events before the max ( min ) requirement is 277 953.The number of events passing also the max < 3 ( min > À3) selection is 804 (774); of these, 222 (220) have þ < 0:01 ( À < 0:01).The differential cross section for dijet production was calculated separately as a function of þ and À .The final results were averaged, and the average is presented as a function of .
The max , min requirements reject most pileup interactions.The remaining pileup background was estimated with minimum-bias MC samples (PYTHIA6 Z1 and PYTHIA8; see next section) and was found to be less than 2%.
Diffractive dijet events were simulated with the POMPYT [29], POMWIG [30], and PYTHIA8 generators.The PYTHIA8 generator can simulate inclusive, nondiffractive as well as diffractive dijet events; separate samples were produced for the two processes.The modeling of diffractive events in these generators is based on the Ingelman and Schlein approach [31], which considers the diffractive reaction as a two-step process: one proton emits a pomeron with fractional momentum and then the pomeron interacts with the other proton.All three diffractive generators were used with dPDFs from the same fit to diffractive deep inelastic scattering data (H1 fit B [7]).The parametrization of the pomeron flux in POMPYT and POMWIG is also based on the QCD fits to the HERA data [7], while it is different in PYTHIA8 [32].This leads to different predictions for the diffractive cross sections calculated by PYTHIA8 and POMPYT or POMWIG (notably in their normalization).The effect of the rapidity gap survival probability is not simulated in any of the three diffractive generators.
The main difference between POMPYT and POMWIG is that POMPYT uses the PYTHIA framework while POMWIG is based on HERWIG [33].Both programs generate singlediffractive dissociation.In PYTHIA8 double-diffractive dissociation (DD), in which both protons dissociate, is also included.The contribution from central diffractive dissociation, in which both protons stay intact, was estimated with POMWIG.It amounts to $1% of the diffractive contribution in the region used in the analysis and was neglected.Only pomeron exchange was assumed; the Reggeon exchange contribution in the region < 0:01 was estimated with POMPYT and was found to be less than 2%, and less than 1% in the lowest bin used in the analysis.
The diffractive component of the dijet cross section was also computed at next-to-leading (NLO) accuracy with the POWHEG [34] framework using the CTEQ6M PDF for the proton that breaks up and H1 fit B for the dPDF.The parton shower and hadronization were carried out with PYTHIA8 (tune 1).
The generators used are listed in Table I along with some of their features.All generated events were processed through the simulation of the CMS detector, based on GEANT4 [35] and reconstructed in the same manner as the data.All samples were generated without pileup.The measurements were corrected for detector acceptance and resolution with a suitable combination of nondiffractive (PYTHIA6 Z2) and diffractive (POMPYT) models (see Sec. VA).
Figure 3 shows the comparison between the uncorrected data and detector-level MC simulations for the reconstructed p T distributions of the leading and second-leading jets with axes in the range j j1;j2 j < 4:4.The simulated distributions are normalized to the number of events in the corresponding distributions for the data.The data and MC simulations are in agreement, for both PYTHIA6 Z2 and PYTHIA8 tune 1.
Figure 4 presents the comparison between data and MC simulations for the reconstructed (detector-level) pseudorapidity distributions of the leading and second-leading jets.

FIG. 4 (color online)
. Reconstructed pseudorapidity distributions of the leading (top panel) and second-leading (bottom panel) jets (black dots) compared to detector-level MC simulations (histograms) generated with two nondiffractive models (PYTHIA6 Z2 and PYTHIA8 tune 1).The statistical uncertainties are smaller than the data points.The MC distributions are normalized to the number of events in the corresponding distributions for the data.Also here, the MC distributions are normalized to the number of events in the data.Data are better described by PYTHIA6 tune Z2 than by PYTHIA8 tune 1.
The pseudorapidity distributions of the two leading jets for events selected with the max < 3 requirement are presented in Fig. 5. Events with the min > À3 condition are also included in Fig. 5 with j1;j2 !À j1;j2 .The pseudorapidity gap condition enhances the diffractive component in the data, and selects events with the jets mainly in the hemisphere opposite to that of the gap.A combination of PYTHIA6 Z2 and POMPYT events reproduces the data reasonably well; the relative normalization of the models is optimized with the procedure described in Sec.VA.

A. Reconstructed distributions and determination of the relative POMPYT and PYTHIA6 normalization
The reconstructed distribution is shown in Fig. 6 before the max , min selections.Here again, the shape of the distribution can be described by the combination of diffractive and nondiffractive MC models.The best combination was obtained by minimizing the difference between the distributions of the data and of the sum of nondiffractive and diffractive models.The relative contribution of diffractive dijet production and the overall normalization of the sum were found in this fit, and the diffractive contribution was scaled accordingly.The overall normalization of the fit result is not relevant.The effect of the calorimeter energy scale uncertainty, estimated by varying by AE10% the energy of all PF objects not associated with the leading jets, is shown by the band.The solid line in Fig. 6(a) indicates the result of the fit, according to which the diffractive dijet cross section predicted by POMPYT should be multiplied by a factor ' 0:23 to match the data.The uncertainty of this correction factor was estimated by changing the fitting procedure and was found to be $20%.Figure 6(b) presents the same data compared to PYTHIA6 D6T þ POMPYT; here the fit requires the POMPYT normalization to be scaled by a factor of ' 0:17.
Figure 6(c) compares the data to PYTHIA8 tune 1; both the single-diffractive and the double-diffractive components are added to the nondiffractive part, all simulated by PYTHIA8.The result of the fit is very different from that for POMWIG and PYTHIA6: the normalization of the diffractive components of PYTHIA8 needs to be multiplied by a factor ' 2:5 to match the data.This large difference is a consequence of the different implementation of the pomeron flux in PYTHIA8 and POMPYT.
In all three cases, after normalization, the shape of the reconstructed distribution in the data is described satisfactorily by the MC models (PYTHIA6 Z2 þ POMPYT resulting in the best description).However, the predicted nondiffractive component in the lowest bin varies from about 0.1% for PYTHIA6 D6T to as much as 10%-20% for PYTHIA6 Z2 and PYTHIA8.
The effect of the max < 3 ( min > À3) requirement is illustrated in Fig. 7, where the reconstructed distributions with and without the max < 3 ( min > À3) condition are compared to MC simulations.These pseudorapidity gap selections reject events at high values of .The region of low , where the diffractive contribution dominates, is only marginally affected.The data and MC simulations are in agreement at low .The relative normalization of PYTHIA6 Z2 and POMPYT in the figure is the same as in Fig. 6.

VI. CROSS SECTION DETERMINATION AND SYSTEMATIC UNCERTAINTIES
The differential cross section for dijet production as a function of is evaluated as where N i jj is the measured number of dijet events in the ith bin, A i is the correction factor defined as the number of reconstructed MC events in that bin divided by the number of generated events in the same bin, Á i is the bin width, L is the integrated luminosity, and is the trigger efficiency.The factors A i include the effects of the geometrical acceptance of the apparatus, and that of all the selections listed in Sec.IV, as well as the unfolding corrections to account for the finite resolution of the reconstructed variables used in the analysis.Various unfolding techniques (bin-by-bin, singular value decomposition [36] and Bayesian [37]) yield consistent results and the bin-by-bin correction was kept.In addition, the measured number of events, N i jj , is corrected for the effect of pileup.This correction takes into account the probability of single pp interactions, evaluated on a run-by-run basis, as well as the probability that pileup interactions do not destroy the visible gap, estimated with the minimum-bias MC samples (PYTHIA6 Z1 and PYTHIA8 tune 1); the average correction is 1.07.The cross section is measured for dijets with the axes in the pseudorapidity range j j1;j2 j < 4:4 and p j1;j2 T > 20 GeV in the bins 0:0003 < < 0:002, 0:002 < < 0:0045, and 0:0045 < < 0:01.The cross section results for þ and À are averaged, yielding the cross section as a function of .
The systematic uncertainties are estimated by varying the selection criteria and by modifying the analysis procedure as follows: (1) The uncertainty on the jet energy scale varies between 2% and 9% depending on the jet p T and [23].It decreases with the jet p T and is typically higher at high .The energy of the reconstructed jets is varied accordingly.
(2) The effect of the uncertainty on the jet energy resolution is studied by changing the resolution by up to AE10% in the central region (jj < 2:3) and by up to AE20% in the forward regions (jj > 2:3) [23].(3) The systematic uncertainty related to the reconstruction is determined as follows: (i) the effect of the calorimeter energy scale uncertainty is estimated by varying the energy of all PF objects not associated with the leading jets by AE10%; (ii) the p T threshold for tracks is increased from 200 to 250 MeV; (iii) the correction factor C is varied by AE3%, i.e. by its uncertainty (as discussed in Sec.IV). ( 4) The uncertainty on the correction factor A i in Eq. ( 4) is estimated by changing the MC models used to evaluate it.In addition, the relative fraction of diffraction is changed by AE20%, i.e. by the uncertainty of the scaling factors obtained in the fits discussed in Sec.VA. (5) The sensitivity to pileup is studied by restricting the analysis to events with only one reconstructed vertex.(6) The sensitivity to the jet reconstruction procedure is studied by repeating the analysis with jets reconstructed only with calorimetric information instead of particle-flow objects.This affects the results by 4% at most.(7) The difference in the results obtained for the cross section as a function of þ and À is found to be less than 11% and is included in the systematic uncertainty.(8) The uncertainty on the trigger efficiency is estimated from the comparison of the turn-on curves as a function of the jet p T in the minimum-bias data and the MC simulation.The resulting uncertainty is 3%.(9) The uncertainty on the integrated luminosity is estimated to be 4% [38,39].
The total systematic uncertainty is calculated as the quadratic sum of the individual contributions.The resulting uncertainty of the cross section measurement is $30%, dominated by the jet energy scale.The effect of each systematic check on the cross section uncertainty is given in Table II.

VII. RESULTS
Table III and Fig. 8 present the differential cross section for dijet production as a function of .The data are compared to the predictions of nondiffractive (PYTHIA6 Z2 and PYTHIA8 tune 1) and diffractive (POMPYT SD, POMWIG SD, PYTHIA8 SD þ DD, and POWHEG) models.The normalization of the predictions is absolute, unlike in Fig. 6.
The following conclusions can be drawn from Fig. 8: (i) The generators PYTHIA6 Z2 and PYTHIA8 tune 1, without hard diffraction, cannot by themselves describe the low-data, especially in the first bin, 0:0003 < < 0:002.(ii) It was noted already in Sec.VA that the contribution of SD MC models, e.g.POMWIG and POMPYT, is needed to describe the low-data, reflecting the presence of hard diffractive events in this region.However, these MC models predict more events than are observed, by a factor of about 5 in the lowest bin.(iii) The ratio of the measured cross section to that expected from the POMPYT and POMWIG simulations is 0:21 AE 0:07 in the first bin, where the nondiffractive contribution is small.This ratio can be taken as an upper limit of the rapidity gap survival probability (not simulated by the event generators considered).This is an upper limit because the measured cross section includes a contribution from proton-dissociative events in which the scattered proton is excited into a low mass state, which escapes undetected in the forward region; the dPDFs also include a proton-dissociative contribution.If the amount of proton-dissociative events in the data is assumed to be 41%, as estimated at particle level with PYTHIA8, and that in the dPDFs is taken to be 23% [7], then this upper limit can be turned into an estimate of the rapidity gap survival probability of 0:12 AE 0:05.(iv) POMPYT and POMWIG are LO MC generators.If POWHEG is used to predict the diffractive cross section at NLO in the first bin and PYTHIA8 tune 1 is used for hadronization, the ratio between data and predictions becomes 0:14 AE 0:05.With the assumptions just discussed on the protondissociative contribution, the rapidity gap survival probability becomes 0:08 AE 0:04.(v) Figure 8 also shows that the normalization of the SD þ DD PYTHIA8 prediction disagrees with that of POMPYT and POMWIG, and would have to be scaled up by a factor of about 2 to match the data.This is a consequence of the different modeling of diffraction in these generators: while they all use the same H1 dPDFs, the parametrization of the pomeron flux in PYTHIA8 is different-and, notably, not the one used in the H1 fit.Because of this, PYTHIA8 (version 8.135) cannot be used to extract the rapidity gap survival probability.While the rapidity gap survival probability measured at the Tevatron [5,6] is close to that found in the present analysis, the two measurements cannot be directly compared because of the different kinematic regions they cover: 0:035 < < 0:095 for the CDF data and 0:0003 < < 0:002 for the present CMS data.This difference is TABLE II.Contributions to the systematic uncertainty on the dijet cross section in the three lowest bins considered.The total systematic uncertainty calculated as the quadratic sum of the individual contributions is given in the last row.

VIII. SUMMARY
The differential cross section for dijet production as a function of , a variable that approximates the fractional momentum loss of the proton in single-diffractive processes, has been measured with the CMS detector for events with at least two jets with p j1;j2 T > 20 GeV in the pseudorapidity region j j1;j2 j < 4:4.The results are compared to diffractive (POMPYT, POMWIG, and PYTHIA8 SD þ DD) and nondiffractive (PYTHIA6 Z2, D6T, and PYTHIA8 tune 1) MC models.The low-data show a significant contribution from diffractive dijet production, observed for the first time at the LHC.The associated rapidity gap survival probability is estimated.Leading-order diffractive generators (POMPYT and POMWIG), based on dPDFs from the HERA experiments, overestimate the measured cross section and their normalization needs to be scaled down by a factor of $5.This factor can be interpreted as the effect of the rapidity gap survival probability.The results are also compared with NLO predictions.The rapidity gap survival probability, estimated from the comparison of the cross section measured in the first bin, 0:0003 < < 0:002, with LO and NLO diffractive MC models, ranges from 0:08 AE 0:04 (NLO) to 0:12 AE 0:05 (LO).

FIG. 1 .
FIG. 1. Schematic diagram of diffractive dijet production.The diagram shows the example of the gg !jet process; the qq and gq initial states also contribute.

FIG. 2 (
FIG. 2 (color online).The generated versus generated (top panel) and reconstructed (bottom panel) þ correlations for single-diffractive dijet events simulated by PYTHIA8; events in the bottom panel are those passing the selection described in Sec.IV.

FIG. 3 (
FIG. 3 (color online).Reconstructed transverse-momentum distributions of the leading (left panel) and second-leading (right panel) jets (black dots) compared to detector-level MC simulations (histograms) generated with two nondiffractive models (PYTHIA6 Z2 and PYTHIA8 tune 1).The error bars indicate the statistical uncertainty.The MC distributions are normalized to the number of events in the corresponding distributions for the data.The ratios of the data and MC distributions are also shown.

FIG. 5 (
FIG. 5 (color online).Reconstructed pseudorapidity distributions of the leading (top panel) and second-leading (bottom panel) jets after the max < 3 selection (black dots) compared to three detector-level MC simulations (histograms).Events with the min > À3 condition are also included in the figure with j1;j2 !À j1;j2 .The error bars indicate the statistical uncertainty.The predictions of the nondiffractive (PYTHIA6 Z2) and diffractive (POMPYT, scaled by the value quoted in the legend) contributions and their sum are also shown.The sum of the predictions of the two MC simulations is normalized to the number of events in the corresponding distributions for the data.

FIG. 6 (
FIG. 6 (color online).Reconstructed distribution compared to detector-level MC predictions with and without diffractive dijet production.The predictions of (a) PYTHIA6 Z2 þ POMPYT, (b) PYTHIA6 D6T þ POMPYT, and (c) PYTHIA8 tune 1 are shown (in all the cases the relative diffractive contributions from the MC simulation are scaled by the values given in the legend).The error bars indicate the statistical uncertainty; the band represents the calorimeter energy scale uncertainty.The sum of the predictions of the two MC simulations is normalized to the number of events in the corresponding distributions for the data.

FIG. 7 (
FIG. 7 (color online).Reconstructed distributions with (open symbols) and without (closed symbols) the max < 3 (or min > À3) condition are compared to detector-level MC predictions including diffractive dijet production (PYTHIA6 Z2 þ POMPYT).The error bars indicate the statistical uncertainty; the band represents the calorimeter energy scale uncertainty.The relative diffractive dijet contribution from the MC simulation has been scaled by the factor 0.23.The sum of the predictions of the two MC simulations is normalized to the number of events in the corresponding distributions for the data.

FIG. 8 (
FIG.8(color online).The differential cross section for inclusive dijet production as a function of for jets with axes in the range j j1;j2 j < 4:4 and p j1;j2 T > 20 GeV.The points are plotted at the center of the bins.The error bars indicate the statistical uncertainty and the band represents the systematic uncertainties added in quadrature.The predictions of nondiffractive (PYTHIA6 Z2 and PYTHIA8 tune 1) and diffractive (POMPYT SD, POMWIG SD and PYTHIA8 SD þ DD) MC generators are also shown, along with that of the NLO calculation based on POWHEG (first bin only).The predictions of POMPYT and POMWIG in the first bin are identical.

TABLE I .
Monte Carlo generators used in this work with details on their model ingredients.