Two-particle azimuthal correlations as a probe of collective behaviour in deep inelastic $\textit{ep}$ scattering at HERA

Two-particle azimuthal correlations have been measured in neutral current deep $\mbox{inelastic}$ $\textit{ep}$ scattering with virtuality $Q^2>5$ GeV$^2$ at a centre-of-mass energy $\sqrt{s}=318$ GeV recorded with the ZEUS detector at HERA. The correlations of charged particles have been measured in the range of laboratory pseudorapidity $-1.5<\eta<2$ and transverse momentum $0.1<p_{\textrm{T}} ~<5$ GeV and event multiplicities $N_{\textrm{ch}}$ up to six times larger than the average $\left<N_{\textrm{ch}} \right>\approx5$. The two-particle correlations have been measured in terms of the angular observables $c_n\{2\}=\left<\left<\cos{ n \Delta\varphi} \right>\right>$, where $n$ is between 1 and 4 and $\Delta\varphi$ is the relative azimuthal angle between the two particles. The correlations observed in HERA data do not indicate the kind of collective behaviour recently observed at the highest RHIC and LHC energies in high-multiplicity hadronic collisions. Available Monte Carlo models of deep inelastic scattering, tuned to reproduce inclusive particle production, provide a qualitative description of the HERA data.


Introduction
The search for a new state of matter, the quark-gluon plasma (QGP), has been a major component of the heavy-ion physics programme at many laboratories. The evidence for its observation in heavy-ion collisions [1][2][3][4][5][6] is strong; one of the key observations being the collective behaviour of final-state particles. Such behaviour has recently been observed in high-multiplicity p + A and pp collisions. This has motivated the first search for such behaviour in ep collisions at the Hadron Electron Ring Accelerator (HERA).
The evolution of a QGP in space and time is successfully described within the framework of relativistic fluid dynamics [7][8][9], employing the thermodynamic and transport properties of QCD matter. The observed correlations between the final-state particles reflect this evolution; this is called collective behaviour or collectivity. Recent measurements [10][11][12][13][14][15][16] at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) have revealed strikingly similar collective behaviour in lighter colliding systems, such as proton nucleus (p + A) and even pp, compared to heavy-ion systems. This came as a surprise, as the spatial extent of the initial state and the interaction time for such systems was thought to be insufficient to produce a QGP and maintain local thermal equilibrium. Experimental investigations of the space-time evolution and fragmentation of a multi-parton state formed in ep collisions at HERA are important to study the presence or absence of collective effects for even smaller interaction regions than those that characterise pp interactions.
It remains to be seen whether a fluid-dynamic description of soft QCD can be applied universally and, in particular, how small the interaction region can be until the picture breaks down. Fluid-dynamic calculations applied to high-multiplicity pp, p + A, and A + A collisions with a single choice of fluid properties are able to reproduce the measurements quite well [17][18][19][20]. This suggests that even in relatively small systems, a state of matter in local thermal equilibrium may be produced, indicating universality of a fluid description. On the other hand, purely initial-state effects arising from gluon saturation in the colour-glasscondensate framework are also able to describe the qualitative features of the data [21].
Collisions between fully overlapping heavy nuclei at RHIC and LHC are capable of producing large interaction regions which are of the order of 7 fm in size. In pp and p+A the interaction region is of the order of the proton size, which ranges from its size of around 1 fm, when undisturbed, to a few fm [22,23]. The average size of the interaction region in ep scattering depends on 1/Q, where the exchanged photon virtuality is defined by the four-momentum difference between the incoming and scattered electron, The terms low and high Q 2 are used to distinguish two regimes of particle production in ep collisions: photoproduction and deep inelastic scattering (DIS) [24]. The latter can be further classified into neutral and charged current DIS. Neutral current (NC) DIS is characterised by the exchange of a virtual photon or Z boson between the incoming electron and proton. Charged current DIS occurs less frequently, when a W boson is exchanged and a scattered neutrino instead of an electron appears in the final state. In photoproduction, the electron emits a quasi-real photon (Q 2 Λ 2 QCD ≈ (200 MeV) 2 ), which can fluctuate into an extended hadronic object with a size of the order of 1/Λ QCD ≈ 1 fm. On the other hand, DIS is characterised by the exchange of a highly virtual and more point-like photon (Q 2 ≫ Λ 2 QCD ) which strikes a single parton with a finer resolution of 1/Q ≪ 1 fm. Thus, NC DIS provides a unique opportunity to investigate the dynamics of a many-body QCD system produced in smaller interaction regions than those available at RHIC and LHC. This is complementary to a corresponding investigation using ALEPH data on e + e − collisions at the Z pole [25].
In addition to the size of the interaction region, its spatial anisotropy also plays an important role in the system's space-time evolution. Depending on the interaction rate during the collective expansion, the spatial anisotropy can be converted into a momentum asymmetry of the produced particles. In a fluid picture, this arises essentially because pressure gradients accelerate the fluid. This final-state asymmetry can be quantified with two-particle azimuthal correlations [26], which coincide with the two-particle cumulants: where ∆ϕ = ϕ 1 − ϕ 2 is the difference in the azimuthal angles of particles 1 and 2. The inner angled brackets denote an average over all pairs in a given event while the outer angled brackets denote an average over all events. In the case of collective fluid-like expansion, measurements of the first four harmonics (n = 1 − 4) are sensitive to directed, elliptic, triangular, and quadrangular spatial anisotropies, respectively. A prominent feature of the collision between partially overlapping heavy ions is the elliptical shape of the interaction region. This results in the dominance of an elliptical asymmetry, c 2 {2}, in the momentum space. In ep DIS, the most prominent feature is the recoil of the hadronic system against the electron, which is reflected in the directed cumulant c 1 {2}.
In this paper, measurements of c n {2} are presented for the first four harmonics projected as a function of the number of charged particles, the laboratory pseudorapidity difference |∆η| = |η 1 − η 2 |, and the mean transverse momentum p T = (p T,1 + p T,2 )/2.

Experimental set-up
The NC DIS data sample used in this analysis was taken with the ZEUS detector at HERA during 2003-2007 (HERA II). During this period, the HERA accelerator collided 27.5 GeV electron/positron 1 beams with 920 GeV proton beams, which yields a nominal centre-ofmass energy of √ s = 318 GeV. The integrated luminosity recorded by ZEUS in HERA II at this energy is 366 ± 7 pb −1 . A detailed description of the ZEUS detector can be found elsewhere [27]. A brief outline of the components that are most relevant for this analysis is given below.
In the kinematic range of the analysis, charged particles were mainly tracked in the central tracking detector (CTD) [28][29][30] and the microvertex detector (MVD) [31]. These components operated in a magnetic field of 1.43 T provided by a thin superconducting solenoid. The CTD consisted of 72 cylindrical drift-chamber layers, organised in nine superlayers covering the polar-angle 2 region 15 • < θ < 164 • . The MVD silicon tracker consisted of a barrel (BMVD) and a forward (FMVD) section. The BMVD contained three layers and provided polar-angle coverage for tracks from 30 • to 150 • . The four-layer FMVD extended the polar-angle coverage in the forward region to 7 • . After alignment, the single-hit resolution of the MVD was 24 µm. The transverse distance of closest approach (DCA) to the nominal vertex in X-Y was measured to have a resolution, averaged over the azimuthal angle, of (46 ⊕ 122/p T ) µm, with p T in GeV denoting the momentum transverse to the beam axis. For CTD-MVD tracks that pass through all nine CTD superlayers, the momentum resolution was σ(p T )/p T = 0.0029p T ⊕ 0.0081 ⊕ 0.0012/p T , with p T in GeV.
The high-resolution uranium-scintillator calorimeter (CAL) [32][33][34][35] consisted of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. Each part was subdivided transversely into towers and longitudinally into one electromagnetic section (EMC) and either one (in RCAL) or two (in BCAL and FCAL) hadronic sections (HAC). The smallest subdivision of the calorimeter was called a cell. The CAL energy resolutions, as measured under test-beam conditions, were σ(E)/E = 0.18/ √ E for electrons and σ(E)/E = 0.35/ √ E for hadrons, with E in GeV. 1 Hereafter, "electron" refers to both electrons and positrons unless otherwise stated. HERA operated with electron beams during 2005 and part of 2006, while positrons were accelerated in the other years of this data sample. 2 The ZEUS coordinate system is a right-handed Cartesian system, with the Z axis pointing in the nominal proton beam direction, referred to as the "forward direction", and the X axis pointing left towards the centre of HERA. The coordinate origin is at the centre of the CTD. The pseudorapidity is defined as η = − ln tan θ 2 , where the polar angle, θ, is measured with respect to the Z axis. The azimuthal angle, ϕ, is measured with respect to the X axis.

Event selection
The ZEUS experiment operated a three-level trigger system [41,42]. For this analysis, events were selected at the first level if they had an energy deposit in the CAL consistent with an isolated scattered electron. At the second level, a requirement on the energy and longitudinal momentum of the event was used to select NC DIS event candidates. At the third level, the full event was reconstructed and tighter requirements for a DIS electron were made.
NC DIS events are characterised by the observation of a high-energy scattered electron in the CAL and were selected with the following criteria: • the scattered electron was identified using information from the distribution of energy deposited in the CAL, including information from a silicon-detector system embedded in the RCAL and from its associated track, when available. A neural-network algorithm [43,44] assigned a probability that a given electron candidate was correctly identified as an electron. The probability was required to be larger than 90%; • the event vertex was obtained from a fit to the measured tracks. To ensure reliable tracking within the CTD, the position of the event vertex along the Z axis, V Z , was required to be within 30 cm of its nominal value. The transverse distance of the event vertex from the interaction point was required to be within 0.5 cm. For the measurements of two-particle correlations, events were required to have at least one track associated with the primary vertex. The fraction of primary-vertex tracks to the total number of reconstructed tracks was required to be larger than 0.1 to reject beam-gas background; • the scattered-electron energy, E e , as measured in the CAL, was larger than 10 GeV to ensure good electron identification; • the virtuality, Q 2 , as determined by the electron method [45], was required to be larger than 5 GeV 2 , just above the minimum reconstructable value; • the polar angle of the scattered electron, θ e , was required to be larger than 1 radian to ensure a reliable measurement in the RCAL or BCAL, which results in an effective upper limit of Q 2 < 10 4 GeV 2 ; • the radial position of the electron on entering the RCAL was required to be larger than 15 cm (θ e 3 radians) to help reject photoproduction events and to ensure a well understood acceptance. Entrance locations (X, Y ) with poor acceptance were excluded from the analysis: 5 < X < 11 cm for Y > 0 cm and −15 < X < −9 cm for Y < 0 cm. Additionally, the region −10 < X < 10 cm for Y > 110 cm contains a significantly higher material budget and was therefore excluded; • for further rejection of photoproduction events, as well as rejection of DIS events with large initial-state photon radiation, a cut based on the quantity The sum is over all energy-flow objects [46,47] which are formed from calorimeter-cell clusters and tracks, with energy E i and polar angle θ i . For a fully contained NC DIS event, E − p Z should be twice the beam-electron energy (55 GeV) owing to energy and longitudinal momentum conservation. This cut also removes background events caused by collisions of protons with residual gas in the beam pipe or the beam pipe itself. Events were accepted in the interval 47 < E − p Z < 69 GeV.
These constraints on the scattered electron implicitly remove events with an inelasticity y 0.65 [24]. A total of 45 million NC DIS events were selected for the analysis. The contamination from photoproduction events has been estimated to be on the order of 1% as determined from studies of photoproduction Monte Carlo data as well as from events with scattered-electron candidates with the incorrect charge.

Track selection
Reconstructed tracks were used in this analysis if their momentum transverse to the beamaxis and laboratory pseudorapidity were within 0.1 < p T < 5 GeV and −1.5 < η < 2, respectively. To reject unwanted secondary tracks and false reconstructions, each track was required to have at least one MVD hit. The track associated to the scattered electron candidate used to identify the NC DIS event was rejected in the correlation analysis. Owing to occasional showering of the electron in the beam pipe and tracker material, this track is not always uniquely identified. Thus, all tracks around the scattered electron candidate within a cone of 0.4 in pseudorapidity and azimuthal angle were rejected.
Tracks corresponding closely to primary charged particles were selected in the analysis by requiring the distances of closest approach to the primary vertex in the transverse (DCA XY ) and longitudinal (DCA Z ) directions to be less than 2 cm. Some secondary tracks, e.g. from small-angle scattering in the beam pipe, were therefore retained. Such tracks, which are often reconstructed with parameters close to the corresponding primary particle contain information about the correlations that is thereby retained.

Monte Carlo generators
The LEPTO 6.5 [48] and ARIADNE 4.12 [49] Monte Carlo event generators were used for the comparison of the measurements to known physics mechanisms and for the extraction of efficiency corrections and the associated systematic uncertainties in the correlation analysis.
Both models are interfaced with PYTHIA 5.724 and JETSET 7.410 [50] to handle hadronisation and decays. The initial hard scattering in ARIADNE is treated with PYTHIA and JETSET. The LEPTO and ARIADNE generators differ chiefly in the treatment of the QCD cascade process. In LEPTO, the cascade is treated as a DGLAP-based backward-evolution shower [51][52][53]. The ARIADNE generator treats the cascade within the colour dipole model (CDM) [54]. Initial-state radiation (before the central hard scatter) and final-state radiation are treated independently in LEPTO while ARIADNE includes initial-and final-state interference effects. In the CDM prescription, the production amplitudes of soft gluon emissions are summed coherently while in LEPTO the angular-ordering technique [55,56] is used to emulate the coherence effect.
The selected ZEUS data sample includes a diffractive component [57] where the ep scattering is mediated by an object carrying the quantum numbers of the vacuum-a Pomeron. A distinguishing feature of diffractive events is the absence of hadronic activity in the forward direction. The pseudorapidity of the most-forward energy deposit in the CAL greater than 400 MeV is defined as η max . A diffractive and a non-diffractive ARIADNE sample were combined in this analysis using a weighting scheme chosen to reproduce the η max distribution in ZEUS data. The diffractive component was generated with SATRAP [58] which was interfaced with ARIADNE and RAPGAP [59]. Purely non-diffractive ARIADNE predictions were also used to illustrate the expected effect of the diffractive component. The LEPTO Monte Carlo sample only contains a non-diffractive component since a simulation of the diffractive component was not available. Generated events were passed through GEANT3.21 [60] to simulate the ZEUS detector. Additionally, a fraction of the low-p T tracks was rejected to compensate for the imperfectly simulated loss of such tracks [61,62]. The selection of Monte Carlo events to compute reconstructed distributions and efficiency corrections followed the same criteria as for the reconstructed ZEUS data, see Section 3.1. Primary generated particles were defined as charged hadrons with a mean proper lifetime, τ > 1 cm, which were produced directly or from the decay of a particle with τ < 1 cm. This definition is similar to that used by ALICE at the LHC [63].

Comparison of reconstructed data and Monte Carlo
A comparison of the ARIADNE model predictions to data at reconstruction level is shown in Fig. 1. In addition, Fig. 1 shows distributions at generator level. For this, Monte Carlo events were selected based on Q 2 , E e , θ e , and E − p Z , which were calculated using initialand final-state electron momenta. These quantities were required to be in the same intervals as used at reconstruction level. Generated primary particles were selected from the same kinematic p T and η intervals as at reconstruction level.  Figure 1(b) shows the equivalent distributions in Q 2 . The reconstructed N rec and Q 2 distributions as predicted by ARIADNE are compatible with the data to within about 10%, except for the high-N rec region, where the discrepancy is about 50%. The mean value of N rec is about 5 and the mean value of Q 2 is about 30 GeV 2 .
Reconstructed p T and η track distributions are shown in Fig. 2. The reconstructed singleparticle distributions in ARIADNE are compatible with the data to within about 10% except for the high-p T region, where the discrepancy is about 15%. Owing to the asymmetric electron and proton beam energies and the occurrence of a beam remnant in the proton direction, particle production is expected to peak in the forward direction near η = 4. From the comparison of the full ARIADNE distributions with the distributions predicted by the non-diffractive component only, it is clear that the impact of diffraction on these distributions is small. Thus, ARIADNE and LEPTO can be compared to the data on an equal footing. It is clear that ARIADNE describes c 1 {2} better than LEPTO in panels (a) and (c) while the opposite is true with c 2 {2} in panel (d) with a |∆η| and stronger p T cut. For c 2 {2}, in panel (b), which corresponds to the full kinematic interval, neither model fully satisfactorily describes the data.
Reconstructed two-particle correlations c 1 {2} as a function of |∆η| and p T are shown in Fig. 4. It is clear that ARIADNE describes the data much better than LEPTO in all of the kinematic intervals shown. In contrast, c 2 {2} as a function of |∆η| and p T is described much better by LEPTO as shown in Fig. 5. In all cases the data are described by at least one of the two Monte Carlo models reasonably enough, such that the efficiency corrections can be derived reliably.

Efficiency corrections
The measurement of two-particle correlations can be affected by non-uniform particletracking efficiency. The single-and two-particle efficiencies were estimated by comparing the number of primary particles or pairs as generated with ARIADNE to the corresponding reconstructed numbers. The single-particle efficiencies were extracted differentially in p T , η, ϕ, charge, and data-taking period. Two-particle efficiencies, which characterise the degree to which two tracks close in ϕ can be distinguished in the CTD, were extracted differentially in ∆ϕ, |∆η|, N ch , and relative charge.
Corrections for non-uniform efficiency were applied using two types of weights. They were extracted in two steps from Monte Carlo event samples. In the first step, the single-particle tracking efficiencies were calculated as the ratio of the number of reconstructed to generated particles passing the track-selection criteria. The weight for particle i, w (i) p , is the inverse of the single-particle tracking efficiency. The typical magnitude of w (i) p projected against p T is about 1.05 above 1 GeV and decreases to about 0.85 at 0.1 GeV, where secondary contamination becomes larger. The typical variation of w (i) p projected against ϕ is about 5%. The true number of charged primary particles within the fiducial region in a given event was estimated with a weighted sum over the reconstructed tracks passing the track-selection criteria, N rec : In a second pass over the Monte Carlo events, the w (i) p weights were applied to the reconstructed particles and two-particle reconstruction efficiencies were calculated as a function of ∆ϕ. The ratio of the number of generated to reconstructed pairs passing the track-selection criteria forms the second weight w ∆ϕ . The typical variation of w ∆ϕ is about 10% and is largest for same-sign pairs with |∆ϕ| < 0.3 radians.

Analysis method
The two-particle correlation functions measured in this analysis are defined by where ϕ i and ϕ j are the azimuthal angles of the two particles. The first sum over e is performed for all events, N ev , and the sums over i and j run over all selected charged particles in the event with multiplicity N rec . The pair-correction factor for non-uniform acceptance is given by Two-particle correlations are also reported in a more visually intuitive two-dimensional form, which is defined as: where S(∆η, ∆ϕ) = dN same /(d∆η d∆ϕ) and B(∆η, ∆ϕ) = dN mixed /(d∆η d∆ϕ) are the signal and background distributions, respectively. These pair distributions were formed by taking the first particle from a given event and the other from either the same event or a different event (mixed) with similar values of N rec and vertex Z position. The S distribution was corrected with w ij , while B was corrected with w p . Both distributions were symmetrised along ∆η and then individually normalised to unity before division.

Systematic uncertainties
In principle, the application of the efficiency corrections as defined in Eq. 3 to the reconstructed Monte Carlo data should recover the distributions of c n {2} at generator level. However, residual differences persist. This is called Monte Carlo non-closure. Qualitatively, the Monte Carlo non-closure was observed to be similar for ARIADNE and LEPTO. Quantitatively, differences were observed, because the models predict different event configurations to which the detector responds differently. For the results, the Monte Carlo non-closure values from ARIADNE, δ ARIADNE nc , and LEPTO, δ LEPTO nc , were averaged, δ nc , and are quoted as a signed separate uncertainty. The typical values of this uncertainty on c n {2} versus N ch without a cut on |∆η| are < 15%.
Further systematic uncertainties were estimated by comparing the correlations obtained with the default event-and track-selection criteria to those obtained with varied settings. The difference between the c n {2} results obtained with the default and the varied settings was assigned as the systematic uncertainty. The sources of systematic uncertainty that were considered are given below (with the typical values of the uncertainty on c n {2} versus N ch without a cut on |∆η|): • secondary-particle contamination: The default analysis used DCA XY,Z < 2 cm, while for the variation DCA XY,Z < 1 cm was used. The uncertainty was symmetrised (< 10%); • efficiency-correction uncertainty due to the choice of Monte Carlo generator: The default analysis used ARIADNE, while for the variation, LEPTO was used. The uncertainty was largest at high N ch (< 10%); • consistency of c n {2} from events with different primary-vertex positions, V Z : The default analysis used |V Z | < 30 cm. For the variations either −30 < V Z < 0 cm or 0 < V Z < 30 cm were selected. The resulting deviations were weighted by their relative contribution (< 5%); • low-p T tracking efficiency: The default simulation included the low-p T track rejection, while for the variation it did not. The uncertainty was assigned to be half of the difference between the default and varied procedure and was symmetrised (< 3%); • different data-taking conditions: The default analysis used all available data, while for the variations, separate data taking periods weighted by their relative contribution were used and the differences were added in quadrature and used as a symmetric uncertainty (< 2%); • DIS event-selection criteria: The chosen E − p Z interval, the scattered-electron polar angle, the neural-network identification probability, and the excluded entrance locations of the scattered electron in the CAL were found to have a negligible effect.
Each variation was applied to ZEUS data as well as Monte Carlo data for the recalculation of efficiency corrections. Positive and negative systematic uncertainties were separately summed in quadrature to obtain the total systematic uncertainty, δ syst . The values of each systematic uncertainty and the full information for the two models are also provided in Tables 1-26.

Results
Results are presented 3 in the kinematic region defined by: GeV, θ e > 1 radian, and primary charged particles with −1.5 < η < 2 and 0.1 < p T < 5 GeV. Figure 6 shows C(∆η, ∆ϕ) for low and high N ch and for particles with 0.5 < p T < 5 GeV. For both ranges in N ch , a dominant near-side (∆ϕ ∼ 0) peak is seen at small ∆η. The displayed range in C was truncated to illustrate better the finer structures of the correlation. Also in both N ch ranges, at ∆ϕ ∼ π (away-side), a broad ridge-like structure is observed. At low N ch , a dip in this away-side ridge is visible, while at high N ch it is more uniform. There is no indication of a near-side ridge, which would be an indication of hydrodynamic collectivity, in contrast to what has been observed in high-multiplicity pp collisions [11,13]. Similarly, an analysis of two-particle correlations in e + e − shows no indication of a near-side ridge [25]. Figure 7 shows the N ch dependence of the two-particle correlations c n {2} for the first four harmonics, n = 1 − 4. Results are presented for the full ranges of |∆η| and p T , and with a rapidity-separation condition, |∆η| > 2, for p T > 0.1 and p T > 0.5 GeV. Without a rapidity separation, the c n {2} correlations are strongest and positive at low N ch for all n, indicating that particles are preferentially emitted into the same hemisphere, as expected for the fragments of the struck parton in quark parton processes. This is largely absent for |∆η| > 2, indicating that c n {2} at small multiplicities is dominated mostly by shortrange correlations. All c n {2} correlations depend only weakly on N ch for N ch > 15. For |∆η| > 2, c 1 {2} and c 3 {2} become negative, which is expected from the effects of momentum conservation, e.g. back-to-back dijet-like processes with large eta separation between jets.
GeV. This is expected from particle production via hard scattering processes.
Similar conclusions can be drawn by comparing Fig. 6 to Fig. 7. For low N ch and no |∆η| cut, the peak in Fig. 6 is the dominant structure from which c 1 {2} = cos ∆ϕ > 0 and c 2 {2} = cos 2∆ϕ > 0 are expected. For large values of N ch , |∆η| and p T , the away-side ridge becomes the dominant structure, which leads to the pattern cos 2∆ϕ > 0 and cos ∆ϕ < 0. It can be seen that |c 1 {2}| is much larger than |c 2 {2}| at high N ch and |∆η|. This reflects that inclusive NC DIS events have a more directed than elliptic event topology. This is in contrast to systems with larger interaction regions, where the positive magnitude of c 2 {2} is much larger than the negative magnitude of c 1 {2} [64], which is an expected signature of hydrodynamic collectivity. Figure 8 shows the two-particle correlations as a function of rapidity separation |∆η|. Compared to results for p T > 0.1 GeV, the correlations with p T > 0.5 GeV are more pronounced, as expected from particles in jet-like structures. The mean values of p T in the low-and highp T intervals are 0.6 and 1.0 GeV, respectively. The correlations c 1 {2} and c 3 {2} have qualitatively similar dependence on |∆η| but with different modulation strengths. Both change sign near |∆η| = 1, which shows that the short-range correlations extend up to about one unit of rapidity separation, after which the long-range effects, such as momentum conservation, become dominant contributions to In Fig. 9, c 1 {2} and c 2 {2} are plotted versus p T with |∆η| > 2 in low-and high-multiplicity regions. The third and fourth harmonic correlation functions have much larger statistical uncertainties and are therefore not shown. Correlations at low N ch were down-scaled by the factor N ch low / N ch high = 0.4, where N ch low ( N ch high ) = 6.7 (16.8). Studies in heavyion collisions suggest that correlations unrelated to hydrodynamic collectivity contribute to c n {2} as 1/N ch [65,66]. Applying the scaling factor provides a better means to compare and investigate the possible collective effects, which enter each multiplicity interval differently, and investigate if there is an excess of the correlations at high multiplicities. For both c 1 {2} and c 2 {2}, the correlation strength grows with increasing p T up to a few GeV, which is universally observed in all collision systems [10][11][12][13][14][15][16]. Despite the observed excess of correlation strength for c 2 {2} at high compared to low multiplicity, an even stronger excess is observed for c 1 {2}, which, as described above, is dominated by dijet-like processes. This suggests that the 1/N ch scaling inspired by observations in heavy-ion collisions may not be appropriate for ep scattering.
Comparisons of c 2 {2} at low and high multiplicity, as well as fits to C(∆η, ∆ϕ), have been performed at RHIC and LHC. The laboratory rapidity window used in the analysis presented here is located about 2-5 units away from the peak of the proton fragmentation region at η ≈ 4 (Fig. 2). The LHC measurements in pp collisions were made in between two wide fragmentation peaks which are separated by about 4 units [67][68][69]. Despite this difference in rapidity coverage, the typical magnitudes of c 2 {2} are compared. The value of c 2 {2} at RHIC [15,16] and LHC [10][11][12][13][14] lies in the range 0.002-0.01 at p T ≈ 1 GeV [14]. At a similar p T value, the corresponding difference between the central values of c 2 {2} at low and high multiplicity in Fig. 9 is about 0.01. The further understanding of the similarity of the c 2 {2} excess observed in both ep and pp, together with the much larger c 1 {2} excess relative to that for c 2 {2} in ep, would require a consistent modelling of multi-particle production in both collision systems. The correlations projected against |∆η| and p T in Figs. 11 and 12 confirm the observation at reconstruction level (Section 5) that ARIADNE describes c 1 {2} better than LEPTO while the opposite is true for c 2 {2}. In particular, it is clear that long-range correlations (|∆η| 2) are underestimated by LEPTO for the first harmonic while they are overestimated by ARIADNE for the second harmonic. The growth of c 2 {2} correlations with p T is greatly overestimated by the ARIADNE model.

Summary and outlook
Two-particle azimuthal correlations have been measured with the ZEUS detector at HERA in neutral current deep inelastic ep scattering at √ s = 318 GeV, using an integrated luminosity of 366 ± 7 pb −1 . The kinematic region of the selected primary charged particles in the laboratory frame is 0.1 < p T < 5 GeV and −1.5 < η < 2. The DIS scattered electron was constrained to have a polar angle greater than 1 radian relative to the proton beam direction, with energy larger than 10 GeV, Q 2 > 5 GeV 2 . The events were required to have The correlations were measured for event multiplicities up to six times larger than the average N ch ≈ 5. There is no indication of a near-side ridge in C(∆η, ∆ϕ). Strong long-range anti-correlations are observed with c 1 {2} as expected from momentum conservation. For p T > 0.5 GeV, the observed anti-correlations in c 1 {2} are stronger than the correlations in c 2 {2}, which indicates that they originate from hard processes and not the collective effects that characterise RHIC and LHC data at high multiplicities.