Measurements of long-range two-particle correlation over a wide pseudorapidity range in p–Pb collisions at √ s NN = 5.02 TeV

Correlations in azimuthal angle extending over a long range in pseudorapidity between particles, usually called the “ridge” phenomenon, were discovered in heavy-ion collisions, and later found in pp and p–Pb collisions. In large systems, they are thought to arise from the expansion (collective ﬂow) of the produced particles. Extending these measurements over a wider range in pseudorapidity and ﬁnal-state particle multiplicity is important to understand better the origin of these long-range correlations in small collision systems. In this Letter, measurements of the long-range correlations in p–Pb collisions at √ s NN = 5 . 02 TeV are extended to a pseudorapidity gap of ∆ η ∼ 8 between particles using the ALICE forward multiplicity detectors. After suppressing non-ﬂow correlations, e.g., from jet and resonance decays, the ridge structure is observed to persist up to a very large gap of ∆ η ∼ 8 for the ﬁrst time in p–Pb collisions. This shows that the collective ﬂow-like correlations extend over an extensive pseudorapidity range also in small collision systems such as p–Pb collisions. The pseudorapidity dependence of the second-order anisotropic ﬂow coefﬁcient, v 2 ( η ) , is extracted from the long-range correlations. The v 2 ( η ) results are presented for a wide pseudorapidity range of − 3 . 1 < η < 4 . 8 in various centrality classes in p–Pb collisions. To gain a comprehensive understanding of the source of anisotropic ﬂow in small collision systems, the v 2 ( η ) measurements are compared with hydrodynamic and transport model calculations. The comparison suggests that the ﬁnal-state interactions play a dominant role in developing the anisotropic ﬂow in small collision systems


Introduction
High-energy heavy-ion collisions can produce a deconfined state of quarks and gluons, the so-called quark-gluon plasma (QGP).Measurements of azimuthal anisotropic flow, for example, via long-range two-particle correlations, are sensitive to key properties of the QGP [1].The two-particle correlations between an associated particle and a trigger particle are commonly measured as a function of the differences in pseudorapidity (∆η = η trig − η asso ) and azimuthal angle (∆ϕ = ϕ trig − ϕ asso ).Striking correlations over a long range in ∆η on the near side (∆ϕ ∼ 0), the so-called "ridge", have been observed in heavy-ion collisions [2][3][4][5][6][7][8][9][10][11], where they are well understood as a consequence of strong, final-state interactions in the dense system created in heavy-ion collisions and the resulting fluid-like collective expansion of the matter created.The correlation function, associate yield as a function of differences in pseudorapidity and azimuthal angle, projected onto the ∆ϕ direction, can be expressed in terms of a Fourier series, where v n is the Fourier coefficient of n-th flow harmonics.The v n coefficients emerge due to the anisotropic hydrodynamic expansion of the medium and fluctuate along with the collision geometry in heavy-ion collisions.The v n coefficients and their multiplicity and transeverse-momentum (p T ) dependence are well described by relativistic hydrodynamic models at midrapidity [12,13].The pseudorapidity dependence of v n coefficients is sensitive to a temperature dependence of the shear viscosity to entropy density ratio η/s of the QGP [14][15][16].It has been measured over a large pseudorapidity region (|η| < 5) in Au-Au and Pb-Pb collisions at RHIC [17] and the LHC [18].In small collision systems, such as pp and p-Pb collisions, a "ridge" structure was also observed similar to heavy-ion collisions [19][20][21][22][23][24][25][26][27][28][29][30][31].The p T dependence of v n coefficients in small collision systems, which shows a characteristic mass dependence at low p T , is found to be similar to heavy-ion collisions [27,29,31,32].Both hydrodynamic (macroscopic) and kinetic transport (microscopic) models can describe collective-flow observables fairly well in small systems as well as in heavy-ion collisions [33][34][35][36][37][38].However, the underlying physics of the observed anisotropic flow in small collision systems is still under debate.One possible scenario predicts that both contributions from a momentum anisotropy arising in the initial state as well as final interactions are essential in small collision systems [39][40][41].Furthermore, the relative contributions of soft collective processes, concentrated in the dense "core" and modeled with hydrodynamics, and of hard processes such as hard scattering and jet fragmentation (described as a pp-like "corona") are also not well understood.The charged-particle pseudorapidity distribution is asymmetric in p-Pb collisions [42]: the multiplicity is larger in the Pb-going direction compared to the p-going direction.Since the mean free path depends on the charged-particle multiplicity, the pseudorapidity dependence of v 2 reflects the underlying dynamical evolution in p-Pb collisions and is a direct indicator of how local particle densities modulate the collective flow.CMS results on v 2 (η) in p-Pb collisions at the LHC [43,44] show a significant pseudorapidity dependence, beyond what would be expected from the pseudorapidity dependence of the mean p T .However, the acceptance is limited to midrapidity |η| < 2. Various small asymmetric collision systems were used to extract v 2 (η) at RHIC by means of the event plane method.The measurements were carried out within the pseudorapidity range of |η| < 3 [45,46].A hydrodynamic model [47] describes the result of v 2 (η) qualitatively except for the pseudorapidity regions (−3 < η < −2) in p-Au collisions, where non-flow effects appear to be significant because the rapidity gap from the detector that determines the event plane is small.
In this Letter, the measurements of long-range two-particle correlations and v 2 (η) in p-Pb collisions at √ s NN = 5.02 TeV with the ALICE detector at the LHC are presented.These measurements utilize the Forward Multiplicity Detector (FMD) to extract v 2 (η) over the unprecedented range of about 8 units of pseudorapidity (−3.1 < η < 4.8).The results are compared with a hydrodynamic-model calculation and the AMPT transport model.This analysis uses ALICE data taken for p-Pb collisions at a centre-of-mass energy per nucleon pair of √ s NN = 5.02 TeV provided by the LHC in 2016, corresponding to a proton beam energy of 4 TeV and a lead beam energy of 1.58 TeV per nucleon.Due to the asymmetric collision system, the nucleon-nucleon centre-of-mass system was shifted by 0.465 rapidity units in the proton beam direction with respect to the ALICE laboratory system.In this Letter, η denotes the pseudorapidity in the laboratory system, and the positive pseudorapidity points in the Pb-going direction.
This analysis uses 5×10 8 events acquired using a minimum bias trigger.The minimum bias trigger requires the in-time coincidence of signals from V0A and V0C.The first step of the event selection is performed on the amplitude and timing in the V0 and ZDC as described in Ref. [50].The efficiency of the event selection is 99.2% for non-single-diffractive collisions.The primary vertex position is determined with reconstructed tracks in the TPC and ITS by using an analytic χ 2 minimization method as described in Ref. [51].The primary vertex in the beam axis is required to be within 10 cm of the nominal interaction point along the beam line.In addition, pile-up events from beam-induced background are rejected by using correlations between the FMD and V0 multiplicities.
Charged-particle tracks are reconstructed in the ITS and TPC within |η| < 0.8 for p T > 0.2 GeV/c as follows.First, the tracks are selected on the number of space points and the quality of the track fit in the TPC.In addition, the tracks are required to have a distance of closest approach (DCA) to the reconstructed primary vertices less than 2 cm in the beam-axis direction.The DCA in the transverse direction is required to be less than 7 σ DCA , where σ DCA is a p T -dependent transverse impact parameter resolution.The efficiency of the charged-particle track selection is estimated with a Monte Carlo (MC) simulation using the DPMJET event generator [52] and GEANT3 [53] to simulate particle transport through the detector.The efficiency is about 65% at p T =0.2 GeV/c, increases to about 79% at p T =0.8 GeV/c, and decreases to about 76% at p T =3 GeV/c.
The selected events are divided into several centrality classes based on the V0A amplitude.Table 1 shows the event classes and corresponding average charged-particle pseudorapidity densities within −3.25 < η < −2.5, |η| < 0.8, 2 < η < 3.75, and 3.75 < η < 5.The multiplicities were measured by the innermost two layers of the ITS at midrapidity and the FMD at forward and backward rapidity [42].For a given event class, two-particle correlations between a trigger and associated particle are measured as a function of the pseudorapidity difference ∆η and the azimuthal angle difference ∆ϕ.The associated yield to a trigger particle as a function of ∆η and ∆ϕ is defined as where N trig is the total number of trigger particles in the given event class, the signal function S(∆η, ∆ϕ) = d∆ηd∆ϕ is the associated yield per trigger particle in the same event, and the background function B(∆η, ∆ϕ) = α d 2 N mixed d∆ηd∆ϕ is the pair yield associated to a trigger particle when the associated particles are taken from other events which fall in the same event class.The α factor is chosen such that B(∆η, ∆ϕ) is unity at its maximum.By dividing S(∆η, ∆ϕ) by B(∆η, ∆ϕ), pair acceptance and single particle efficiency for both particles are corrected.To take into account the vertex position dependence of the above acceptance and efficiency, the correlation function is extracted in 2 cm wide intervals of the vertex position.
To estimate and subtract the non-flow effects due to recoil jets and resonance decays, the template fit procedure, which was introduced by the ATLAS collaboration, is employed [54,55].The correlation function Y (∆ϕ) is assumed to be a superposition of a non-flow contribution, which is estimated by scaling the correlation function from peripheral events, and the flow contribution.The template fit function is defined as  where F, G tmp , and V tmp n,n are free parameters.Y peri (∆ϕ) is the correlation function in peripheral events.V tmp n,n represents the n-th flow coefficient, and F and G are the scaling factors of the non-flow distribution on the away side and a flat, azimuth-independent baseline, respectively.This method assumes no flow components in the peripheral event used for the template and no away-side jet modifications between central and peripheral events.
Figure 2 shows the projection of the correlation functions, i.e., TPC-FMD1,2 (left), TPC-FMD3 (center), FMD1,2-FMD3 (right), onto the ∆ϕ axis in the 0-5% event class.These one-dimensional correlations are fitted by the template fit function using Eq. ( 3).The fit describes the data well with a χ 2 /ndf of about 0.8-2.5 for all correlation functions corresponding to all η gap combinations.The flow-like part of the fit is dominated by the second harmonic for all three correlations.The modulation for the pair correlation is extracted for each harmonic in the template fit.
Assuming that the relative modulation of the two-particle correlation function is solely due to the modulation of the single-particle distribution, the modulation of the two-particle correlation measured in two different pseudorapidity ranges for particles a and b can be factorized as: If this factorization holds, the flow component of a single particle at a certain pseudorapidity can be extracted from three dihadron correlations between different pseudorapidity regions given by where each V n,n is the modulation extracted by TPC-FMD1,2, TPC-FMD3, and FMD1,2-FMD3 correlation, respectevily.This method is similar to the "3×2PC" method used by PHENIX [21,56].The  factorization breaks down if the event plane and/or the flow amplitude depend on pseudorapidity, for example because of initial longitudinal fluctuations or thermal fluctuations [57][58][59][60][61][62].Therefore, the uncertainty due to those decorrelation effects is estimated by changing the η gap, as it will be discussed in Section 3.3.
Since the FMD is not a tracking detector, it is difficult to separate primary particles from secondary particles inside the FMD.Secondary particles are generated around the primary particle and might distort its distribution.The effects of secondary particles on the flow harmonics are estimated using MC simulations based on the AMPT and EPOS event generators [36,63,64].The correction is performed based on the change in the reconstructed particle distribution after particle transport and interaction within the detector material from the original distribution.The correction factor is extracted as the ratio of the v 2 of primary particles over the v 2 of all reconstructed particles (i.e.including primary and secondary particles).In order to match the range of the FMD, which has acceptance down to p T = 0, the charged-particle v 2 at midrapidity is extrapolated to p T = 0 based on the data of the p T spectrum and the p T differential v 2 of charged-particles.The factor is about 0.86 for all four centralities.

Systematic uncertainties
The systematic uncertainties relate to the event selection, the track selection, the correction of secondary particles in the FMD, the material budget in the FMD, the choice of the peripheral event class for nonflow subtraction, the reference pseudorapidity choice of η b , η c to extract v 2 (η a ), and the jet modification.A systematic uncertainty is only assigned when the difference between the nominal data points and variations is statistically significant according to the Barlow criterium [65].Table 2 shows the summary of systematic uncertainties for v 2 , which depend on centrality and pseudorapidity as indicated by the range given.The uncertainty due to the event selection is investigated by changing the selection parameters for V0-FMD multiplicity correlations.The uncertainty slightly depends on centrality, and it is the largest in the 20-40% centrality class.The uncertainty due to track selection is evaluated by varying track selection parameters.This systematic uncertainty is 0.28-0.45%and is also the largest in the 20-40% centrality class.The systematic uncertainty related to the correction of the contamination by secondary particles is estimated using different event generators, EPOS and AMPT.The magnitude of collective-like signal in EPOS and AMPT is very different, and this check investigates how stable the correction is with respect to the magnitude of the flow.This uncertainty is found to be larger in the p-going direction than in the Pb-going direction.The number of secondary particles depends on the material budget in the ALICE environment.This systematic uncertainty is 2.3% estimated using MC simulations with increased or reduced material budget of the detector descriptions in GEANT simulation by ±10%.Uncertainties as-sociated with secondary correction and material budget are assigned only for the FMD acceptance.The systematic uncertainty of the peripheral event choice used for non-flow subtraction is estimated using the 80-100% event class instead of 60-100%.The systematic uncertainty on the reference pseudorapidity choice is investigated by changing the η gap between η b and η c to extract v 2 (η a ).The uncertainty ranges from 2.6% to 5.1% depending on the centrality and the choice of reference pseudorapidity.The shape of the jet is modified depending on the centrality.The uncertainty is evaluated by varying the away-side width of the peripheral collisions and is 0.8-2.7%.These systematic uncertainties are added in quadrature.

Results
The v 2 for charged-particles in a specific pseudorapidity region can be extracted using the template fit procedure and the three dihadron correlations of TPC-FMD1,2, TPC-FMD3, and FMD1,2-FMD3, as described in Section 3.2.The corresponding results of the p T -integrated v 2 as a function of η for the 0-5%, 5-10%, 10-20%, and 20-40% centrality classes are shown in Fig. 3.After applying the nonflow subtraction with the template fit approach, a non-zero v 2 is observed over a wide rapidity range for the first time in p-Pb collisions.The v 2 results in p-Pb collisions were measured previously for the pseudorapidity range of |η| < 2 by CMS [43,44].The v 2 measurements presented in this Letter significantly extend the measurements to a much wider pseudorapidity range, −3.1 < η < 4.8.This result confirms the emergence of anisotropic flow over a wide rapidity region, as in high-energy heavyion collisions [18].In addition, the v 2 measurements show a significant pseudorapidity dependence for all four centrality classes.It is more prominent in the Pb-going direction (positive η) than in the p-going direction (negative η).Additionally, a stronger centrality dependence of v 2 is found in the Pb-going direction than in the p-going direction.
Previous v 2 (η) measurements showed that the magnitude of v 2 is correlated with charged-particle pseudorapidity density [45]; v 2 (η) increases with increasing multiplicity.However, v 2 (η) might not be linearly correlated with dN ch /dη [42].Figure 4 shows v 2 as a function of charged-particle multiplicity density for five different pseudorapidity regions and for different centrality classes: 0-5%, 5-10%, 10-20%, and 20-40%.Figure 4 demonstrates that the pseudorapidity dependence of v 2 is not just simply driven by the local multiplicity, v 2 independently depends on both η and dN ch /dη.In a fixed pseudorapidity range, v 2 depends on local multiplicity, but at fixed local multiplicity, there is still a significant dependence on the pseudorapidity.
Figure 5 shows the comparisons of v 2 in 0-5% p-Pb collisions and in 60-70% and 70-80% Pb-Pb collisions, where the multiplicity is similar in the Pb-going direction between the two collision systems [42,66].The charged-particle pseudorapidity density at η ∼ 3 is about 60 in p-Pb collisions and 80 and 37 in 60-70% and 70-80% Pb-Pb collisions, respectively.Here, the results from Pb-Pb collisions     The v 2 (η) in central p-Pb collisions compared with v 2 (η) in peripheral Pb-Pb collisions with a compatible mean charged-particle multiplicity in Pb-going direction.The v 2 Pb-Pb results were obtained using the Q-cumulant method [18].are based on the 2-particle cumulant method [18].The v 2 results in p-Pb collisions are compatible with the v 2 in 60-70% and 70-80% Pb-Pb collisions over the entire η range within the sizable uncertainties of the Pb-Pb results.Somewhat unexpectedly, given the potential differences in the initial collision overlap geometry, it is observed that peripheral Pb-Pb collisions and central p-Pb collisions have comparable v 2 at similar multiplicities.
To further investigate the origin of the flow in small collision systems, the v 2 (η) measured in p-Pb collisions is compared with hydrodynamical calculations [67] in Fig. 6, and with the AMPT transport model in Fig. 7.The 3+1 hydrodynamical model employs 3D Glauber initial conditions, viscous hydrodynamics based on MUSIC, and the UrQMD model to simulate the dynamics in the hadronic phase.The shear viscosity and color string width in the transverse plane are adjusted to η T /(e + P) = 0.08 and σ x = 0.4 fm, respectively, to reproduce the mean transverse momentum of identified particles and the p T dependence of charged-particle v 2 measured with the template fit procedure by ATLAS at midrapidity in p-Pb collisions at √ s NN = 5.02 TeV [67].The hydrodynamical model underestimates the pseudorapidity dependence of charged-particle multiplicity density when centrality is determined at forward pseudorapidity, while it is reproduced when centrality is determined at midrapidity [68].The correlation between the multiplicities at forward and midrapidity is weaker in the model than in the data.In this model, v 2 mainly originates from the 3D initial geometry and develops in the course of the hydrodynamical evolution.The model describes the v 2 (η) measurement in 0-5% and 5-10%, while it somewhat overestimates the data in 10-20% and 20-40% at both forward and backward rapidity.
Similarly, Fig. 7 shows the comparisons with calculations by the AMPT model in the string-melting configuration.Unlike the hydrodynamical model, the AMPT with string melting is a transport model that produces collective behaviour microscopically by final-state scattering in both the partonic and hadronic phases.The v 2 (η) calculation from AMPT describes the data qualitatively in the 0-5% centrality class and reproduces the asymmetry between the Pb-going and p-going directions.However, the centrality dependence is less significant than observed in the data.
The comparisons between the v 2 (η) measurements and the calculations from the hydrodynamical and  AMPT transport models suggest that strong final-state interactions are possibly the origin of a significant v 2 over a wide pseudorapidity range in small collision systems such as p-Pb collisions.Initial momentum anisotropy from Colour-Glass Condensate (CGC) could also play a role in high-multiplicity p-Pb collisions.However, a recent study using gluon saturation from the IP-Glasma model shows that the initial momentum anisotropy results to short-range correlation [69].The observed finite v 2 extracted from ultra-long correlations will likely not be influenced by contributions from initial momentum anisotropy from CGC but more likely originates from the fluctuating initial geometry giving rise to final-state interactions.

Summary
In this Letter, the two-particle correlation function is presented as a function of ∆η and ∆ϕ in p-Pb collisions at √ s NN = 5.02 TeV with ALICE.The "ridge" structure is observed up to a rapidity gap of 8 units between the trigger and the associate particles, in central events.A double-ridge structure is visible after the non-flow subtraction.The p T -integrated v 2 is extracted from the correlation function and presented as a function of pseudorapidity and centrality class.Non-zero v 2 is observed over a wide pseudorapidity range in central p-Pb collisions for the first time.The pseudorapidity dependence as well as its asymmetric shape of v 2 could be well explained by charged-particle multiplicity distributions.In addition, the v 2 (η) in p-Pb central events is comparable with the v 2 (η) in peripheral Pb-Pb collisions at similar multiplicity.Finally, both hydrodynamical [67] and AMPT transport model calculations [36] describe the data qualitatively over a wide pseudorapidity region.The comparison with the model calculations suggests the emergence of collective flow at very forward pseudorapidity (|η| ∼ 5) region in p-Pb collisions, just like in high-energy heavy-ion collisions.The results suggest an important role of final-state interactions in developing anisotropic flow in small collision systems.
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex.To examine the robustness of the observation, two different derived template-fit methods for non-flow suppression are employed: the zero-yield-at-minimum (ZYAM) and the improved-template-fit method [54,70].Henceforth, the peripheral subtraction will denote the ZYAM template-fit method.The term of FY peri (∆ϕ) in Eq. ( 3) is substituted by FY peri (∆ϕ) −Y 0 , where Y 0 is the baseline of the correlation function in peripheral events, which is determined at ∆ϕ ∼ 0. The peripheral subtraction method assumes that the 2nd-order modulation is zero when the multiplicity is zero.An improved-template-fit method was developed to estimate the non-flow effects in peripheral collisions more realistically.This method assumes that there are no flow components in the peripheral events.On the other hand, this procedure takes into account the residual flow components in peripheral events.The flow harmonics in the second-most peripheral events are extracted by the template fit using the correlation function in the most peripheral events given by where Y peri (∆ϕ) and Y non−flow (∆ϕ) are the correlation functions in the second-most and the most peripheral events, respectively.By substituting Eq. (A.1) with Eq. ( 3), it can be seen that Finally, the non-flow subtracted flow coefficient from the improved-template-fit method, v imp n,n , can be obtained as .1 shows the p T -integrated v 2 as a function of η with two different non-flow suppression methods for 0-5%, 5-10%, 10-20%, and 20-40% p-Pb collisions.The improved-template-fit method, which considers v 2 in peripheral collisions, gives smaller v 2 than the template-fit method; however, the difference is insignificant for the presented pseudorapidity regions.The effect of the second-order component in the peripheral collision is small.The result of v 2 from the peripheral subtraction method, which assumes no elliptic flow in the peripheral collision, is about 15% smaller than the template procedure for the 0-5% centrality class.Regardless of which non-flow subtraction method is applied, non-zero v 2 results are observed for the entire presented pseudorapidity region with more than 5-σ confidence, further confirming the observations of anisotropic flow in high-multiplicity p-Pb collisions.3 also shows the comparisons of v 2 in 0-5% central p-Pb collisions and in peripheral Pb-Pb collisions with the improved-template-fit method and the peripheral subtraction.The v 2 of the improved-template-fit method is comparable to the v 2 in peripheral Pb-Pb collisions with similar multiplicity at forward rapidity as well as the v 2 of the template fit.At the same time, the v 2 result from the peripheral subtraction is consistent with the results in Pb-Pb in the Pb-going direction within the uncertainty; however, it is smaller in the p-going direction.Figure A.4 compares the AMPT calculation and the results with the improved-template-fit and the peripheral subtraction methods.Similar to the experimental measurements, improved-template-fit and peripheral subtraction methods are also applied in these AMPT calculations.It is found that the AMPT calculations also exhibit the differences in v 2 from the improved-template-fit method and the peripheral subtraction, just as the data.This is because both template-fit and improved-template-fit methods consider possible flow generated in peripheral collisions, which is the case in the AMPT model, while such flow contributions are treated as non-flow and subtracted in the peripheral subtraction method.

Figure 2 :
Figure 2: Projection of the correlation function of TPC-FMD1,2 (left), TPC-FMD3 (central), and FMD1,2-FMD3 (right) correlations in 0-5% p-Pb collisions with the template fit using Eq.(3).The open circle blue marker represents the scaled peripheral distribution plus the Flow baseline, G.The red and green dashed lines represent the second-and third-order components plus the baseline, respectively.

Figure 3 :
Figure 3: p T -integrated v 2 {2} as a function of η in various centrality classes using the template fitting method.Boxes show the total systematic uncertainties.

Figure 4 :
Figure 4: v 2 as a function of charged-particle pseudorapidity density for five different pseudorapidity regions.
Figure5: The v 2 (η) in central p-Pb collisions compared with v 2 (η) in peripheral Pb-Pb collisions with a compatible mean charged-particle multiplicity in Pb-going direction.The v 2 Pb-Pb results were obtained using the Q-cumulant method[18].
The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration.The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundac ¸ão de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research -Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l'Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research A Non-flow subtraction with the improved-template-fit method and peripheral subtraction procedure Figure A.1 shows the p T -integrated v 2 as a function of η with two different non-flow suppression methods for 0-5%, 5-10%, 10-20%, and 20-40% p-Pb collisions.The improved-template-fit method, which considers v 2 in peripheral collisions, gives smaller v 2 than the template-fit method; however, the difference is insignificant for the presented pseudorapidity regions.The effect of the second-order component in the peripheral collision is small.The result of v 2 from the peripheral subtraction method, which assumes no elliptic flow in the peripheral collision, is about 15% smaller than the template procedure for the 0-5% centrality class.Regardless of which non-flow subtraction method is applied, non-zero v 2 results are observed for the entire presented pseudorapidity region with more than 5-σ confidence, further confirming the observations of anisotropic flow in high-multiplicity p-Pb collisions.Figure A.2 shows the v 2 as a function of local charged-particle density for five different pseudorapidity regions with the peripheral subtraction (left) and the improved-template-fit (right) methods.Similar to the template fit results shown in Fig. 4, v 2 from peripheral subtraction and improved-templated-fit methods show a charged multiplicity density dependence.Fig. A.3 also shows the comparisons of v 2 in 0-5% central p-Pb collisions and in peripheral Pb-Pb collisions with the improved-template-fit method and the peripheral subtraction.The v 2 of the improved-template-fit method is comparable to the v 2 in peripheral Pb-Pb collisions with similar multiplicity at forward rapidity as well as the v 2 of the template fit.At the same time, the v 2 result from the peripheral subtraction is consistent with the results in Pb-Pb in the Pb-going direction within the uncertainty; however, it is smaller in the p-going direction.Figure A.4 compares the AMPT calculation and the results with the improved-template-fit and the peripheral subtraction methods.Similar to the experimental measurements, improved-template-fit and peripheral subtraction methods are also applied in these AMPT calculations.It is found that the AMPT calculations also exhibit the differences in v 2 from the improved-template-fit method and the peripheral subtraction, just as the data.This is because

Figure A. 1 :
Figure A.1: p T -integrated v 2 {2} as a function of η in various centrality classes using the improved-template-fit method, and the peripheral subtraction method.

Figure A. 2 :
Figure A.2: v 2 as a function of charged particle density for five different pseudorapidity regions with the peripheral subtraction (left) and the improved template method (right).

Figure A. 3 :
Figure A.3: Pseudorapidity dependence of p T -integrated v 2 as measured in peripheral Pb-Pb collisions and central p-Pb collisions.The Pb-Pb results were obtained with the Q-cumulant method [18].The p-Pb results were obtained with the improved-template-fit and peripheral subtraction methods.

Figure A. 4 :
Figure A.4: Pseudorapidity dependence of p T -integrated v 2 as measured in different p-Pb centrality classes and as obtained from the AMPT calculation with the string melting configuration.The v 2 were extracted using the improved-template-fit method and the peripheral subtraction.

Table 1 :
Average charged-particle pseudorapidity density for p T > 0 GeV/c in different pseudorapidity regions.

Table 2 :
The summary of systematic uncertainties, which is absolute value on v 2 .The uncertainties take values within the given range depending on the centrality and pseudorapidity for each source.