Constraining gluon distributions in nuclei using dijets in proton-proton and proton-lead collisions at $\sqrt{s_{_\mathrm{NN}}} =$ 5.02 TeV

The pseudorapidity distributions of dijets as a function of their average transverse momentum ($p_\mathrm{T}^\text{ave}$) are measured in proton-lead (pPb) and proton-proton (pp) collisions. The data samples were collected by the CMS experiment at the CERN LHC, at a nucleon-nucleon center-of-mass energy of 5.02 TeV. A significant modification of the pPb spectra with respect to the pp spectra is observed in all $p_\mathrm{T}^\text{ave}$ intervals investigated. The ratios of the pPb and pp distributions are compared to next-to-leading order perturbative quantum chromodynamics calculations with unbound nucleon and nuclear parton distribution functions (PDFs). These results give the first evidence that the gluon PDF at large Bjorken $x$ in lead ions is strongly suppressed with respect to the PDF in unbound nucleons.

In this Letter, measurements of dijet production are performed in pPb and pp collisions at √ s NN = 5.02 TeV recorded with the CMS detector and corresponding to integrated luminosities of 35 ± 1 nb −1 [43] and 27.4 ± 0.6 pb −1 [44], respectively. To test the theoretical foundation of global analysis of nPDFs on collinear factorization, η dijet distributions, as well as the ratios of the normalized pPb and pp η dijet distributions (Pb/pp), are studied as a function of the dijet average transverse momentum (p ave T = (p T ,1 + p T ,2 )/2) and compared with next-to-leading order (NLO) pQCD calculations involving different Q 2 values.
A detailed description of the CMS experiment can be found in Ref. [45]. The silicon tracker, submerged in the 3.8 T magnetic field of the superconducting solenoid, is used to measure charged particles within range |η| < 2.5. Also located inside the solenoid are an electromagnetic calorimeter (ECAL) and a hadron calorimeter (HCAL). The ECAL consists of more than 75,000 lead tungstate crystals, arranged in a quasi-projective geometry, and distributed in the barrel region (|η| < 1.48) and in the two endcaps that extend up to |η| = 3.00. The HCAL barrel and endcaps are sampling calorimeters composed of brass and scintillator plates, covering |η| < 3.0. Iron hadron forward (HF) calorimeters, with quartz fibers read out by photomultipliers, extend the calorimeter coverage up to |η| = 5.2. A muon system located outside the solenoid and embedded in the steel flux-return yoke is used for the reconstruction and identification of muons up to |η| = 2.4. The detailed Monte Carlo (MC) simulation of the CMS detector response is based on GEANT4 [46].
The event samples are selected online with dedicated triggers requiring at least one jet with p T > 40, 60, or 80 GeV, and are filtered offline to reject the beam-gas interaction induced background events [26]. In addition, pPb collisions are selected by requiring a coincidence of at least one of the HF calorimeter towers, with more than 3 GeV total energy, from the HF detectors on both sides of the interaction point. Events are also required to have at least one reconstructed primary vertex with two or more associated tracks. This vertex is required to have a distance from the nominal interaction point of less than 15 and 0.15 cm in the longitudinal (along the beam axis) direction and in the transverse plane (perpendicular the beam axis), respectively. In the pPb data sample, there is a 3% probability to have at least one additional interaction in the same bunch crossing (pileup). A pileup filter is employed [47], which rejects more than 90% of the pileup events and removes 0.01% of the events without pileup. The filter uses the longitudinal and transverse distance between the leading vertex (the vertex with the highest number of associated tracks) and the vertex with the second largest number of associated tracks as criteria for identifying and removing pileup events. In the pp analysis, the pileup rejection procedure is not applied because of the significantly lower pileup rate (about a factor of three compared to pPb).
Offline, jet reconstruction is performed using the CMS particle-flow (PF) algorithm [48]. By combining information from all subdetector systems, the PF algorithm attempts to identify all stable particles in an event, classifying them as electrons, muons, photons, as well as charged and neutral hadrons. Jets are reconstructed from these PF candidates using the anti-k T sequential recombination algorithm [49, 50] with a distance parameter R = 0.3, as implemented in the FASTJET package [50]. The reconstructed jets are then calibrated following the steps described in Refs. [51,52].
Jets with pseudorapidity in the laboratory frame |η lab | < 3.0 are used in the final pPb analysis. Because of the different energies of the proton (4 TeV) and lead (1.58 TeV per nucleon) beams, the nucleon-nucleon center-of-mass frame is boosted in the detector frame. During part of the data-taking period, the directions of the proton and lead beams were reversed. For the data set taken with the opposite-direction proton beam, the standard CMS definition of η was flipped so that the proton beam always moves towards positive η. Therefore, a massless particle emitted at η cm = 0 in the nucleon-nucleon center-of-mass frame will be detected at η lab = +0.465 in the laboratory frame. As described above, data from pPb collisions are measured and presented in a symmetric region around η = 0 in the laboratory frame. In order to obtain pp data over the same η range in the nucleon-nucleon center-of-mass frame, jets in the interval −3.465 < η < 2.535 are used. When studying pp and pPb data together, and also for the purposes of presentation, η dijet for pp data is shifted by +0.465, so that both sets of data span |η dijet | < 3.0 in the center-of-mass frame.
This analysis is carried out using events required to have a dijet with a leading jet of p T ,1 > 90 GeV, a subleading jet of p T ,2 > 20 GeV, and ∆φ 1,2 = |φ 1 − φ 2 | > 2π/3. Further selections are applied to p ave T to select data that test NLO pQCD calculations with various nPDFs at different Q 2 values. The p ave T intervals used in the analysis are 55-75, 75-95, 95-115, 115-150, and 150-400 GeV. The last interval is denoted by '>150 GeV' in the figures. The pPb results differ from the ones reported in Ref. [26] in that a lower p T for the leading and subleading jets was used (90 vs. 120 GeV, and 20 vs. 30 GeV, respectively), and in that the present measurement is differential versus p ave T (5 vs. 1 intervals). In the following, we introduce the relation between the kinematics of a dijet event to parton level quantities. We define x p as the Bjorken x of the parton from the nucleon going in the +z direction and x Pb as the Bjorken x of the parton from the nucleon going in the −z direction. Different regions of x p and x Pb can be chosen by selecting ranges of η dijet . In a simple case of two partons colliding without initial-state radiation (ISR) or final-state radiation (FSR), η dijet in the center-of-mass frame would be equal to 1 2 ln(x p /x Pb ). The effect of ISR and FSR on this correlation was studied using the PYTHIA event generator [53] (version 6.423, tune Z2) [54], and was found to be small, as shown in Fig. 1 (left) for the 75 < p ave T < 95 GeV interval. The Pearson's correlation coefficient between x Pb /x p and η dijet is −0.58 in this p ave T interval. In the presence of a strong correlation, this coefficient would be close to ±1, while in the absence of any correlation it would be closer to 0. The correlation between x Pb and η dijet shown in Fig. 1 (right) allows the identification of η dijet intervals which are sensitive to shadowing (η dijet 1.5), antishadowing (−0.5 η dijet 1.5), and EMC effects (η dijet −0.5).
The systematic uncertainty related to the jet energy scale (JES) is important since the width of the η dijet distribution decreases with increasing p ave T [26]. Studies with dijet and γ + jet events [51] show that the JES in data can deviate from that in simulated events by up to 2%. To evaluate the corresponding uncertainties, the JES is shifted by ±2% for both pp and pPb data and the deviations of the observed spectra are taken as systematic uncertainties. To account for the uncertainties related to the jet energy (angular) resolution, the differences between the η dijet spectra obtained from detector-level (i.e. reconstructed) jet p T (η) and generator-level (i.e., MC truth) jet p T (η) with PYTHIA for pp and PYTHIA events embedded in simulated pPb underlying events (PYTHIA+HIJING ) for pPb collisions are quoted as a systematic uncertainty. To model the pPb UE, minimum bias pPb events are simulated with the HIJING event generator [55], version 1.383 [56]. The parameters used in the HIJING simulation are tuned to reproduce the total particle multiplicities and charged-hadron spectra, and to approximate the UE fluctuations seen in data.
Other sources of uncertainties are the effects of the UE and pileup events in pPb collisions. Combinatorial jets coming from nucleon-nucleon collisions that happen simultaneously with the hard-scattering of interest are studied using PYTHIA+HIJING simulations. The effect of the remaining pileup events in pPb collisions is evaluated by comparing the results with and without the pileup filter. Those uncertainties are negligible compared to other sources. The  total systematic uncertainties in η dijet and in the ratios of the pPb and pp spectra are evaluated by summing in quadrature over the contributions from the above sources. In the pPb/pp η dijet ratio measurements, the uncertainties due to the JES, jet energy resolution, and jet angular resolution are partially canceled and the total systematic uncertainties are between 2 and 20%, increasing from high-to low-p ave T values, and towards higher |η dijet | values. The measured η dijet spectra in pp collisions, shifted to match the range of the pPb data as described previously, are shown in Fig. 2. The width of the η dijet distributions decreases as a function of the p ave T . The results are compared to NLO pQCD calculations with CT14 [57] and MMHT14 [58] nucleon PDFs. The corresponding pPb results are available in Appendix A.
In order to construct an observable that is relatively insensitive to the pp PDF calculation [41], the ratios of the pPb and pp reference distributions, individually normalized to one, are chosen. This assumption was tested by comparing the NLO spectra ratio in pQCD calculations with CT14 and MMHT14 PDFs [60]. The shape of the ratios of the pPb and pp distributions in data are compared with NLO pQCD calculations based on the EPS09 and DSSZ nPDFs in Fig. 3. In addition, in Fig. 4, the ratio of the pPb/pp η dijet distributions in data is compared also to that from calculations based on the nCTEQ15 and EPPS16 nPDFs, for 115 < p ave T < 150 GeV. The ratios of pPb and pp data are seen to deviate significantly from unity at small (EMC) and large (shadowing) η dijet regions. In the interval η dijet < −1, which is sensitive to the gluon EMC effect, NLO pQCD calculations with EPS09 nPDF match the data at the edge of the theoretical uncertainty, while the calculations with DSSZ nPDF, where no gluon EMC effect is present in the global fit, overpredict the data.
The differences between data and the various NLO pQCD calculations with nPDFs in the interval η dijet < −1 are quantified by comparing the two distributions with a χ 2 -test, taking into account the point-to-point correlations from the nPDFs. The uncertainties from data are taken to be uncorrelated point-to-point. For 115 < p ave T < 150 GeV, the p-values from the test are 0.19, < 10 −8 , and < 10 −8 for the EPS09, DSSZ, and nCTEQ15 nPDFs, respectively. Across the full p ave T range, the p-values for EPS09 range from 0.19 to 0.95, whereas the p-values for the DSSZ and nCTEQ15 nPDFs are never larger than 0.015. This shows that, with a p-value cutoff of 0.05, the data are incompatible with the DSSZ and nCTEQ15 nPDFs, but not incompatible with the EPS09. This supports the interpretation of the RHIC pion data by the EPS09 nPDF, in which the modification of the pion spectra gives rise to the gluon EMC effect. The data also show smaller shadowing, antishadowing, and EMC effects than what is implemented in the nCTEQ15 PDF set. The results are consistent with EPPS16 with relaxed constraints on the nuclear PDF parameterization, which results in larger PDF uncertainties [16]. The conclusions obtained from different p ave T intervals are similar, which provide important tests of the nuclear PDF at various Q 2 values. The significantly smaller experimental uncertainties, in most of the p ave T and η dijet intervals probed, as compared to the uncertainties of calculations using NLO PDF, indicate that the present data, when included in the calculations of the next generation nPDFs, will result in an improved description of the gluon nPDF.
In summary, measurements of the dijet pseudorapidity (η dijet ) in different average transverse momentum (p ave T ) intervals in pPb and pp collisions at a nucleon-nucleon center-of-mass energy √ s NN = 5.02 TeV are reported. Ratios of the pPb and pp η dijet spectra using the pp reference data are also reported. Significant modifications of the η dijet distributions are observed in pPb data compared to the pp reference in all p ave T intervals, which show shadowing, antishadowing, and EMC effects in nuclear parton distribution functions (nPDFs). The ratios of the pPb and pp distributions are compared to next-to-leading order calculations with nucleon and nPDFs. Based on these comparisons, the results present the first evidence that the gluon PDF at large Bjorken x in lead ions is strongly suppressed with respect to that in unbound nucleons. The data are incompatible with predictions using nucleon PDFs or using nPDFs without large-x gluon suppression. Based on a statistical analysis, the EPS09 nPDF provides the best overall agreement with the data. This data can be used to place strong constraints on the nextgeneration of nPDFs, which are crucial for the understanding of high p T and high mass particle production at collider energies.  Figure 3: The ratio of pPb to pp η dijet spectra compared to NLO pQCD calculations with DSSZ [18] and EPS09 [14] nPDFs, using CT14 [57] as the baseline nucleon PDF. The red boxes indicate systematic uncertainties in data and the height of the NLO pQCD calculation boxes represent the nPDF uncertainties. DSSZ EPS09 nCTEQ15 EPPS16 Figure 4: The ratio of theory to data, for the ratio of the pPb to pp η dijet spectra for 115 < p ave T < 150 GeV. The theory points are from the NLO pQCD calculations of DSSZ [18], EPS09 [14], nCTEQ15 [15], and EPPS16 [16] nPDFs, using CT14 [57] as the baseline PDF. The red boxes indicate the total (statistical and systematic) uncertainties in data, and the error bars on the points represent the nPDF uncertainties.  [24] ATLAS Collaboration, "Transverse momentum, rapidity, and centrality dependence of inclusive charged-particle production in √ s NN = 5.02 TeV p+Pb collisions measured by the ATLAS experiment", Phys. Lett. B 763 (2016) 313, doi:10.1016/j.physletb.2016.10.053, arXiv:1605.06436.   [36] ALICE Collaboration, "Transverse momentum dependence of inclusive primary charged-particle production in p-Pb collisions at √ s NN = 5.02 TeV", Eur. Phys. J. C 74 (2014) 3054, doi:10.1140/epjc/s10052-014-3054-5, arXiv:1405.2737.
[38] CMS Collaboration, "Study of B meson production in pPb collisions at √ s NN = 5.02 TeV using exclusive hadronic decays", Phys. Rev. Lett. 116 (2016)   The measured pPb dijet pseudorapidity spectra in bins of p ave T , overlaid with the NLO pQCD calculations of DSSZ [18], EPS09 [14], and nCTEQ15 [15] nPDFs, using the CT14 [57] as the baseline PDF. The red boxes indicate systematic uncertainties in data and the height of the NLO pQCD calculation boxes represent the nPDF uncertainties. The measured pPb dijet pseudorapidity spectra in bins of p ave T , overlaid with the NLO pQCD calculations of DSSZ [18], EPS09 [14], and nCTEQ15 [15] nPDFs, using the MMHT14 [58] as the baseline PDF. The red boxes indicate systematic uncertainties in data and the height of the NLO pQCD calculation boxes represent the nPDF uncertainties.