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The European Physical Journal. C, Particles and Fields
 
Eur Phys J C Part Fields. 2016; 76(5): 271.
Published online 2016 May 17. doi:  10.1140/epjc/s10052-016-4107-8
PMCID: PMC5321247

Centrality dependence of charged jet production in p–Pb collisions at sNN = 5.02 TeV

Alice Collaboration,140 J. Adam,39 D. Adamová,84 M. M. Aggarwal,88 G. Aglieri Rinella,35 M. Agnello,110 N. Agrawal,47 Z. Ahammed,133 S. Ahmad,19 S. U. Ahn,68 S. Aiola,137 A. Akindinov,58 S. N. Alam,133 D. S. D. Albuquerque,121 D. Aleksandrov,80 B. Alessandro,110 D. Alexandre,101 R. Alfaro Molina,64 A. Alici,12,104 A. Alkin,3 J. R. M. Almaraz,119 J. Alme,18,37 T. Alt,42 S. Altinpinar,18 I. Altsybeev,132 C. Alves Garcia Prado,120 C. Andrei,78 A. Andronic,97 V. Anguelov,94 T. Antičić,98 F. Antinori,107 P. Antonioli,104 L. Aphecetche,113 H. Appelshäuser,53 S. Arcelli,27 R. Arnaldi,110 O. W. Arnold,36,93 I. C. Arsene,22 M. Arslandok,53 B. Audurier,113 A. Augustinus,35 R. Averbeck,97 M. D. Azmi,19 A. Badalà,106 Y. W. Baek,67 S. Bagnasco,110 R. Bailhache,53 R. Bala,91 S. Balasubramanian,137 A. Baldisseri,15 R. C. Baral,61 A. M. Barbano,26 R. Barbera,28 F. Barile,32 G. G. Barnaföldi,136 L. S. Barnby,35,101 V. Barret,70 P. Bartalini,7 K. Barth,35 J. Bartke,117 E. Bartsch,53 M. Basile,27 N. Bastid,70 S. Basu,133 B. Bathen,54 G. Batigne,113 A. Batista Camejo,70 B. Batyunya,66 P. C. Batzing,22 I. G. Bearden,81 H. Beck,53,94 C. Bedda,110 N. K. Behera,48,50 I. Belikov,55 F. Bellini,27 H. Bello Martinez,2 R. Bellwied,122 R. Belmont,135 E. Belmont-Moreno,64 V. Belyaev,75 G. Bencedi,136 S. Beole,26 I. Berceanu,78 A. Bercuci,78 Y. Berdnikov,86 D. Berenyi,136 R. A. Bertens,57 D. Berzano,35 L. Betev,35 A. Bhasin,91 I. R. Bhat,91 A. K. Bhati,88 B. Bhattacharjee,44 J. Bhom,117,128 L. Bianchi,122 N. Bianchi,72 C. Bianchin,135 J. Bielčík,39 J. Bielčíková,84 A. Bilandzic,36,81,93 G. Biro,136 R. Biswas,4 S. Biswas,4,79 S. Bjelogrlic,57 J. T. Blair,118 D. Blau,80 C. Blume,53 F. Bock,74,94 A. Bogdanov,75 H. Bøggild,81 L. Boldizsár,136 M. Bombara,40 J. Book,53 H. Borel,15 A. Borissov,96 M. Borri,83,124 F. Bossú,65 E. Botta,26 C. Bourjau,81 P. Braun-Munzinger,97 M. Bregant,120 T. Breitner,52 T. A. Broker,53 T. A. Browning,95 M. Broz,39 E. J. Brucken,45 E. Bruna,110 G. E. Bruno,32 D. Budnikov,99 H. Buesching,53 S. Bufalino,26,35 P. Buncic,35 O. Busch,128 Z. Buthelezi,65 J. B. Butt,16 J. T. Buxton,20 J. Cabala,115 D. Caffarri,35 X. Cai,7 H. Caines,137 L. Calero Diaz,72 A. Caliva,57 E. Calvo Villar,102 P. Camerini,25 F. Carena,35 W. Carena,35 F. Carnesecchi,27 J. Castillo Castellanos,15 A. J. Castro,125 E. A. R. Casula,24 C. Ceballos Sanchez,9 J. Cepila,39 P. Cerello,110 J. Cerkala,115 B. Chang,123 S. Chapeland,35 M. Chartier,124 J. L. Charvet,15 S. Chattopadhyay,133 S. Chattopadhyay,100 A. Chauvin,36,93 V. Chelnokov,3 M. Cherney,87 C. Cheshkov,130 B. Cheynis,130 V. Chibante Barroso,35 D. D. Chinellato,121 S. Cho,50 P. Chochula,35 K. Choi,96 M. Chojnacki,81 S. Choudhury,133 P. Christakoglou,82 C. H. Christensen,81 P. Christiansen,33 T. Chujo,128 S. U. Chung,96 C. Cicalo,105 L. Cifarelli,12,27 F. Cindolo,104 J. Cleymans,90 F. Colamaria,32 D. Colella,35,59 A. Collu,74 M. Colocci,27 G. Conesa Balbastre,71 Z. Conesa del Valle,51 M. E. Connors,137 J. G. Contreras,39 T. M. Cormier,85 Y. Corrales Morales,110 I. Cortés Maldonado,2 P. Cortese,31 M. R. Cosentino,120 F. Costa,35 P. Crochet,70 R. Cruz Albino,11 E. Cuautle,63 L. Cunqueiro,35,54 T. Dahms,36,93 A. Dainese,107 M. C. Danisch,94 A. Danu,62 D. Das,100 I. Das,100 S. Das,4 A. Dash,79 S. Dash,47 S. De,120 A. De Caro,12,30 G. de Cataldo,103 C. de Conti,120 J. de Cuveland,42 A. De Falco,24 D. De Gruttola,12,30 N. De Marco,110 S. De Pasquale,30 A. Deisting,94,97 A. Deloff,77 E. Dénes,136 C. Deplano,82 P. Dhankher,47 D. Di Bari,32 A. Di Mauro,35 P. Di Nezza,72 M. A. Diaz Corchero,10 T. Dietel,90 P. Dillenseger,53 R. Divià,35 Ø. Djuvsland,18 A. Dobrin,62,82 D. Domenicis Gimenez,120 B. Dönigus,53 O. Dordic,22 T. Drozhzhova,53 A. K. Dubey,133 A. Dubla,57 L. Ducroux,130 P. Dupieux,70 R. J. Ehlers,137 D. Elia,103 E. Endress,102 H. Engel,52 E. Epple,36,93,137 B. Erazmus,113 I. Erdemir,53 F. Erhardt,129 B. Espagnon,51 M. Estienne,113 S. Esumi,128 J. Eum,96 D. Evans,101 S. Evdokimov,111 G. Eyyubova,39 L. Fabbietti,36,93 D. Fabris,107 J. Faivre,71 A. Fantoni,72 M. Fasel,74 L. Feldkamp,54 A. Feliciello,110 G. Feofilov,132 J. Ferencei,84 A. Fernández Téllez,2 E. G. Ferreiro,17 A. Ferretti,26 A. Festanti,29 V. J. G. Feuillard,15,70 J. Figiel,117 M. A. S. Figueredo,120,124 S. Filchagin,99 D. Finogeev,56 F. M. Fionda,24 E. M. Fiore,32 M. G. Fleck,94 M. Floris,35 S. Foertsch,65 P. Foka,97 S. Fokin,80 E. Fragiacomo,109 A. Francescon,29,35 U. Frankenfeld,97 G. G. Fronze,26 U. Fuchs,35 C. Furget,71 A. Furs,56 M. Fusco Girard,30 J. J. Gaardhøje,81 M. Gagliardi,26 A. M. Gago,102 M. Gallio,26 D. R. Gangadharan,74 P. Ganoti,89 C. Gao,7 C. Garabatos,97 E. Garcia-Solis,13 C. Gargiulo,35 P. Gasik,36,93 E. F. Gauger,118 M. Germain,113 M. Gheata,35,62 P. Ghosh,133 S. K. Ghosh,4 P. Gianotti,72 P. Giubellino,35,110 P. Giubilato,29 E. Gladysz-Dziadus,117 P. Glässel,94 D. M. Goméz Coral,64 A. Gomez Ramirez,52 A. S. Gonzalez,35 V. Gonzalez,10 P. González-Zamora,10 S. Gorbunov,42 L. Görlich,117 S. 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Koyithatta Meethaleveedu,47 I. Králik,59 A. Kravčáková,40 M. Krivda,59,101 F. Krizek,84 E. Kryshen,35,86 M. Krzewicki,42 A. M. Kubera,20 V. Kučera,84 C. Kuhn,55 P. G. Kuijer,82 A. Kumar,91 J. Kumar,47 L. Kumar,88 S. Kumar,47 P. Kurashvili,77 A. Kurepin,56 A. B. Kurepin,56 A. Kuryakin,99 M. J. Kweon,50 Y. Kwon,138 S. L. La Pointe,110 P. La Rocca,28 P. Ladron de Guevara,11 C. Lagana Fernandes,120 I. Lakomov,35 R. Langoy,41 K. Lapidus,36,93 C. Lara,52 A. Lardeux,15 A. Lattuca,26 E. Laudi,35 R. Lea,25 L. Leardini,94 G. R. Lee,101 S. Lee,138 F. Lehas,82 S. Lehner,112 R. C. Lemmon,83 V. Lenti,103 E. Leogrande,57 I. León Monzón,119 H. León Vargas,64 M. Leoncino,26 P. Lévai,136 S. Li,7,70 X. Li,14 J. Lien,41 R. Lietava,101 S. Lindal,22 V. Lindenstruth,42 C. Lippmann,97 M. A. Lisa,20 H. M. Ljunggren,33 D. F. Lodato,57 P. I. Loenne,18 V. Loginov,75 C. Loizides,74 X. Lopez,70 E. López Torres,9 A. Lowe,136 P. Luettig,53 M. Lunardon,29 G. Luparello,25 T. H. Lutz,137 A. Maevskaya,56 M. Mager,35 S. 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Morreale,113 A. Morsch,35 V. Muccifora,72 E. Mudnic,116 D. Mühlheim,54 S. Muhuri,133 M. Mukherjee,133 J. D. Mulligan,137 M. G. Munhoz,120 R. H. Munzer,36,53,93 H. Murakami,127 S. Murray,65 L. Musa,35 J. Musinsky,59 B. Naik,47 R. Nair,77 B. K. Nandi,47 R. Nania,104 E. Nappi,103 M. U. Naru,16 H. Natal da Luz,120 C. Nattrass,125 S. R. Navarro,2 K. Nayak,79 R. Nayak,47 T. K. Nayak,133 S. Nazarenko,99 A. Nedosekin,58 L. Nellen,63 F. Ng,122 M. Nicassio,97 M. Niculescu,62 J. Niedziela,35 B. S. Nielsen,81 S. Nikolaev,80 S. Nikulin,80 V. Nikulin,86 F. Noferini,12,104 P. Nomokonov,66 G. Nooren,57 J. C. C. Noris,2 J. Norman,124 A. Nyanin,80 J. Nystrand,18 H. Oeschler,94 S. Oh,137 S. K. Oh,67 A. Ohlson,35 A. Okatan,69 T. Okubo,46 L. Olah,136 J. Oleniacz,134 A. C. Oliveira Da Silva,120 M. H. Oliver,137 J. Onderwaater,97 C. Oppedisano,110 R. Orava,45 M. Oravec,115 A. Ortiz Velasquez,63 A. Oskarsson,33 J. Otwinowski,117 K. Oyama,76,94 M. Ozdemir,53 Y. Pachmayer,94 D. Pagano,131 P. Pagano,30 G. 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Abstract

Measurements of charged jet production as a function of centrality are presented for  p–Pb  collisions recorded at sNN=5.02 TeV with the ALICE detector. Centrality classes are determined via the energy deposit in neutron calorimeters at zero degree, close to the beam direction, to minimise dynamical biases of the selection. The corresponding number of participants or binary nucleon–nucleon collisions is determined based on the particle production in the Pb-going rapidity region. Jets have been reconstructed in the central rapidity region from charged particles with the anti-kT algorithm for resolution parameters R = 0.2 and R = 0.4 in the transverse momentum range 20 to 120 GeV/c. The reconstructed jet momentum and yields have been corrected for detector effects and underlying-event background. In the five centrality bins considered, the charged jet production in  p–Pb   collisions is consistent with the production expected from binary scaling from pp collisions. The ratio of jet yields reconstructed with the two different resolution parameters is also independent of the centrality selection, demonstrating the absence of major modifications of the radial jet structure in the reported centrality classes.

Introduction

The measurement of benchmark processes in proton–nucleus collisions plays a crucial role for the interpretation of nucleus–nucleus collision data, where one expects to create a system with high temperature in which the elementary constituents of hadronic matter, quarks and gluons, are deconfined for a short time: the quark-gluon plasma (QGP) [1]. Proton–lead collisions are important to investigate cold nuclear initial and final state effects, in particular to disentangle them from effects of the hot medium created in the final state of  Pb–Pb collisions [2].

The study of hard parton scatterings and their subsequent fragmentation via reconstructed jets plays a crucial role in the characterisation of the hot and dense medium produced in  Pb–Pb collisions while jet measurements in  p–Pb   and pp collisions provide allow to constrain the impact of cold nuclear matter effects in heavy-ion collisions. In the initial state, the nuclear parton distribution functions can be modified with respect to the quark and gluon distributions in free nucleons, e.g. via shadowing effects and gluon saturation [2, 3]. In addition, jet production may be influenced, already in  p–Pb   collisions, by multiple scattering of partons and hadronic re-interaction in the initial and final state [4, 5].

In the absence of any modification in the initial state, the partonic scattering rate in nuclear collisions compared to pp collisions is expected to increase linearly with the average number of binary nucleon–nucleon collisions Ncoll. This motivates the definition of the nuclear modification factor RpPb, as the ratio of particle or jet transverse momentum (pT) spectra in nuclear collisions to those in pp collisions scaled by Ncoll.

In heavy-ion collisions at the LHC, binary (Ncoll) scaling is found to hold for probes that do not interact strongly, i.e. isolated prompt photons [6] and electroweak bosons [7, 8]. On the contrary, the yields of hadrons and jets in central  Pb–Pb collisions are strongly modified compared to the scaling assumptions. For hadrons, the yield is suppressed by up to a factor of seven at pT ≈ 6 GeV / c, approaching a factor of two at high pT ( ≳ 30 GeV/c) [911]. A similar suppression is observed for jets [1216]. This observation, known as jet quenching, is attributed to the formation of a QGP in the collision, where the hard scattered partons radiate gluons due to strong interaction with the medium, as first predicted in [17, 18].

In minimum bias  p–Pb  collisions at sNN=5.02 TeV the production of unidentified charged particles [1922] and jets [2325] is consistent with the absence of a strong final state suppression. However, multiplicity dependent studies in  p–Pb  collisions on the production of low-pT identified particles and long range correlations [2629] show similar features as measured in  Pb–Pb collisions, where they are attributed to the collective behaviour following the creation of a QGP. These features in  p–Pb   collisions become more pronounced for higher multiplicity events, which in  Pb–Pb are commonly associated with more central collisions or higher initial energy density.

The measurement of jets, compared to single charged hadrons, tests the parton fragmentation beyond the leading particle with the inclusion of large-angle and low-pT fragments. Thus jets are potentially sensitive to centrality-dependent modifications of low-pT fragments.

This work extends the analysis of the charged jet production in minimum bias  p–Pb  collisions recorded with the ALICE detector at sNN=5.02 TeV to a centrality-differential study for jet resolution parameters R = 0.2 and 0.4 in the pT range from 20 to 120 GeV/c [25]. Section 2 describes the event and track selection, the centrality determination, as well as the jet reconstruction, the corrections for uncorrelated background contributing to the jet momentum [15, 30, 31] and the corrections for detector effects. The impact of different centrality selections on the nuclear modification factor has been studied in detail in [32]. We estimate the centrality using zero-degree neutral energy and the charged particle multiplicity measured by scintillator array detectors at rapidities along the direction of the Pb beam to determine Ncoll. The correction procedures specific to the centrality-dependent jet measurement are discussed in detail. Section 3 introduces the three main observables: the centrality-dependent jet production cross section, the nuclear modification factor, and ratio of jet cross sections for two different resolution parameters. Systematic uncertainties are discussed in Sect. 4 and results are presented in Sect. 5.

Data analysis

Event selection

The data used for this analysis were collected with the ALICE detector [33] during the  p–Pb  run of the LHC at sNN=5.02TeV at the beginning of 2013. The ALICE experimental setup and its performance during the LHC Run 1 are described in detail in [33, 34].

For the analysis presented in this paper, the main detectors used for event and centrality selection are two scintillator detectors (V0A and V0C), covering the pseudo-rapidity range of 2.8 < ηlab < 5.1 and - 3.7 < ηlab <  - 1.7, respectively [35], and the Zero Degree Calorimeters (ZDCs), composed of two sets of neutron (ZNA and ZNC) and proton calorimeters (ZPA and ZPC) located at a distance ±112.5 m from the interaction point. Here and in the following ηlab denotes the pseudo-rapidity in the ALICE laboratory frame.

The minimum bias trigger used in  p–Pb  collisions requires signal coincidence in the V0A and V0C scintillators. In addition, offline selections on timing and vertex-quality are used to remove events with multiple interactions within the same bunch crossing and (pile-up) and background events, such as beam-gas interactions. The event sample used for the analysis presented in this manuscript was collected exclusively in the beam configuration where the proton travels towards negative ηlab (from V0A to V0C). The nucleon–nucleon center-of-mass system moves in the direction of the proton beam corresponding to a rapidity of yNN =  - 0.465.

A van der Meer scan was performed to measure the visible cross section for the trigger and beam configuration used in this analysis: σV0 = 2.09 ± 0.07 b [36]. Studies with Monte Carlo simulations show that the sample collected in the configuration explained above consists mainly of non-single diffractive (NSD) interactions and a negligible contribution from single diffractive and electromagnetic interactions (see [37] for details). The trigger is not fully efficient for NSD events and the inefficiency is observed mainly for events without a reconstructed vertex, i.e. with no particles produced at central rapidity. Given the fraction of events without a reconstructed vertex in the data the corresponding inefficiency for NSD events is estimated to (2.2  ±  3.1) %. This inefficiency is expected to mainly affect the most peripheral centrality class. Following the prescriptions of [32], centrality classes are defined as percentiles of the visible cross section and are not corrected for trigger efficiency.

The further analysis requires a reconstructed vertex, in addition to the minimum bias trigger selection. The fraction of events with a reconstructed vertex is 98.3 % for minimum bias events and depends on the centrality class. In the analysis events with a reconstructed vertex |z| > 10 cm along the beam axis are rejected. In total, about 96 · 106 events, corresponding to an integrated luminosity of 46 μb-1, are used for the analysis and classified into five centrality classes

Centrality determination

Centrality classes can be defined by dividing the multiplicity distribution measured in a certain pseudo-rapidity interval into fractions of the cross section, with the highest multiplicities corresponding to the most central collisions (smallest impact parameter b). The corresponding number of participants, as well as Ncoll and b, can be estimated with a Glauber model [38], e.g. by fitting the measured multiplicity distribution with the Npart distribution from the model, convoluted with a Negative Binomial Distribution (NBD). Details on this procedure for  Pb–Pb and  p–Pb  collisions in ALICE are found in [32, 39], respectively.

In  p–A collisions centrality selection is susceptible to a variety of biases. In general, relative fluctuations of Npart and of event multiplicity are large, due to their small numerical value, in  p–Pb  collisions [32] Npart⟩ = ⟨Ncoll⟩ + 1 = 7.9 ± 0.6 and dNchdη=16.81±0.71, respectively. Using either of these quantities to define centrality, in the Glauber model or the in experimental method, already introduces a bias compared to a purely geometrical selection based on the impact parameter b.

In addition, a kinematic bias exists for events containing high-pT particles, originating from parton fragmentation as discussed above. The contribution of these jet fragments to the overall multiplicity rises with the jet energy and thus can introduce a trivial correlation between the multiplicity and presence of a high-pT particle, and a selection on multiplicity will bias the jet population. High multiplicity events are more likely created in collisions with multiple-parton interactions, which can lead to a nuclear modification factor larger than unity. On the contrary, the selection of low multiplicity (peripheral) events can pose an effective veto on hard processes, which would lead to a nuclear modification factor smaller than unity. As shown in [32] the observed suppression and enhancement for charged particles in bins of multiplicity with respect to the binary scaling assumption can be explained by this selection bias alone. The bias can be fully reproduced by an independent superposition of simulated pp events and the farther the centrality estimator is separated in rapidity from the measurement region at mid-rapidity, the smaller the bias. We do not repeat the analysis for the centrality estimators with known biases here.

In this work, centrality classification is based solely on the zero-degree energy measured in the lead-going neutron detector ZNA, since it is expected to have only a small dynamical selection bias. However, the ZNA signal cannot be related directly to the produced multiplicity for the Ncoll determination via NBD. As discussed in detail in [32] an alternative hybrid approach is used to connect the centrality selection based on the ZNA signal to another Ncoll determination via the charged particle multiplicity in the lead-going direction measured with the V0A (NcollcPb-side). This approach assumes that the V0 signal is proportional to the number of wounded lead (target) nucleons (Nparttarget=Npart-1=Ncoll). The average number of collisions for a given centrality, selected with the ZNA, is then given by scaling the minimum bias value NcollMB = 6.9 with the ratio of the average raw signal S of the innermost ring of the V0A:

NcollPb-sidec=NcollMB·ScSMB.
1

The values of Ncoll obtained with this method are shown in Table 1 for different ZNA centrality classes [32].

Table 1
Average Ncoll values for centrality classes selected with the ZNA determined with the hybrid approach (NcollPb-side) [32], as well as moments of the background density and background fluctuation distributions shown in Fig. 1 (negligible statistical ...

Jet reconstruction and event-by-event corrections

The reported measurements are performed using charged jets, clustered starting from charged particles only, as described in [15, 25, 40] for different collision systems. Charged particles are reconstructed using information from the Inner Tracking System (ITS) [41] and the Time Projection Chamber (TPC) which cover the full azimuth and |ηlab| < 0.9 for tracks reconstructed with full length in the TPC [42].

The azimuthal distribution of high-quality tracks with reconstructed track points in the Silicon Pixel Detector (SPD), the two innermost layers of the ITS, is not completely uniform due to inefficient regions in the SPD. This can be compensated by considering in addition tracks without reconstructed points in the SPD. The additional tracks constitute approximately 4.3 % of the track sample used for analysis. For these tracks, the primary vertex is used as an additional constraint in the track fitting to improve the momentum resolution. This approach yields a uniform tracking efficiency within the acceptance, which is needed to avoid geometrical biases of the jet reconstruction algorithm caused by a non-uniform density of reconstructed tracks. The procedure is described first and in detail in the context of jet reconstruction with ALICE in  Pb–Pb collisions [15].

The anti-kT algorithm from the FastJet package [43] is employed to reconstruct jets from these tracks using the pT recombination scheme. The resolution parameters used in the present analysis are R = 0.2 and R = 0.4. Reconstructed jets are further corrected for contributions from the underlying event to the jet momentum as

pT,chjet=pT,chjetraw-Achjet·ρch,
2

where Ach jet is the area of the jet and ρch the event-by-event background density [44]. The area is estimated by counting the so-called ghost particles in the jet. These are defined as particles with a finite area and vanishing momentum, which are distributed uniformly in the event and included in the jet reconstruction [45]. Their vanishing momentum ensures that the jet momentum is not influenced when they are included, while the number of ghost particles assigned to the jet provides a direct measure of its area. The background density ρch is estimated via the median of the individual momentum densities of jets reconstructed with the kT algorithm in the event

ρch=medianpT,kAk·C,
3

where k runs over all reconstructed kT jets with momentum pT, i and area Ai. Reconstructed kT jets are commonly chosen for the estimate of the background density, since they provide a more robust sampling of low momentum particles. C is the occupancy correction factor, defined as

C=jAjAacc,
4

where Aj is the area of each kT jet with at least one real track, i.e. excluding ghosts, and Aacc is the area of the charged-particle acceptance, namely (2 × 0.9) × 2π. The typical values for C range from 0.72 for most central collisions (0–20 %) to 0.15 for most peripheral collisions (80–100 %). This procedure takes into account the more sparse environment in  p–Pb  collisions compared to  Pb–Pb and is described in more detail in [25]. The probability distribution for ρch for the five centrality classes and minimum bias is shown in Fig. 1 (left) and the mean and width of the distributions are given in Table 1. The event activity and thus the background density increases for more central collisions, though on average the background density is still two orders of magnitude smaller than in  Pb–Pb collisions where ρch is  ≈ 140 GeV/c for central collisions [31].

Fig. 1
(Color online) Left Centrality dependence of the background momentum density ρch determined with kT jets and R = 0.4. Right: δpT, ch distributions for different centralities obtained with random cones and R = 0.4

Jet spectrum unfolding

Residual background fluctuations and instrumental effects can smear the jet pT. Their impact on the jet spectrum needs to be corrected on a statistical basis using unfolding, which is performed using the approach of Singular-Value-Decomposition (SVD) [46]. The response matrix employed in the unfolding is the combination of the (centrality-dependent) jet response to background fluctuations and the detector response. The general correction techniques are discussed in detail in the context of the minimum bias charged jet measurement in  p–Pb   [25].

Region-to-region fluctuations of the background density compared to the event median, contain purely statistical fluctuations of particle number and momentum and in addition also intra-event correlations, e.g. those characterised by the azimuthal anisotropy v2 and higher harmonics, which induce additional variations of the local background density. The impact of these fluctuations on the jet momentum is determined by probing the transverse momentum density in randomly distributed cones in (ηϕ) and comparing it to the average background via [31]:

δpT,ch=ipT,i-ρch·A,A=πR2
5

where pT, i is the transverse momentum of each track i inside a cone of radius R, where R corresponds to the resolution parameter in the jet reconstruction. ρch is the background density, and A the area of the cone. The distribution of residuals, as defined by Eq. 5, is shown for different centralities in Fig. 1 (right). The corresponding widths are given in Table 1. The background fluctuations increase for more central events, which is expected from the general increase of statistical fluctuations (N) with the particle multiplicity. The δpT, ch distributions measured for R = 0.2 and 0.4 are used in the unfolding procedure.

In addition to the background fluctuations the unfolding procedure takes into account the instrumental response. The dominating instrumental effects on the reconstructed jet spectrum are the single-particle tracking efficiency and momentum resolution. These effects are encoded in a response matrix, which is determined with a full detector simulation using PYTHIA6 [47] to generate jets and GEANT3 [48] for the transport through the ALICE setup. The detector response matrix links the jet momentum at the charged particle level to the one reconstructed from tracks after particle transport through the detector. No correction for the missing energy of neutral jet constituents is applied.

Observables

Jet production cross sections

The jet production cross sections dσcdpT, for different centralities c, are provided as fractions of the visible cross section σV0. The fraction of the cross section is determined with the number of selected events in each centrality bin Nevc and takes into account the vertex reconstruction efficiency εvtxc determined for each centrality

dσcdpT=εvtxcNevcdNdpT·σV0·NevcNevMB=εvtxcNevMBdNdpT·σV0,
6

where εvtxc decreases from 99.9 % for the most central selection (0–20 %) to 95.4 % in peripheral.

Quantifying nuclear modification

The nuclear modification factor compares the pT-differential per-event yield, e.g. in  p–Pb  or  Pb–Pb collisions, to the differential yield in pp collisions at the same center-of-mass energy in order to quantify nuclear effects. Under the assumption that the jet or particle production at high pT scales with the number of binary collisions, the nuclear modification factor is unity in the absence of nuclear effects.

In  p–Pb  collisions the jet population can be biased, depending on the centrality selection and Ncoll determination, hence the nuclear modification factor may vary from unity even in the absence of nuclear effects as described in detail in Sect. 2.2 (see also [32]). To reflect this ambiguity the centrality-differential nuclear modification factor in  p–Pb   collisions is called QpPb, instead of RpPb as in the minimum bias case. QpPb is defined as

QpPb=d2NpPbc/dηdpTNcollc·d2Npp/dηdpT.
7

Here, Ncollc is number of binary collisions for centrality c, shown in Table 1.

For the construction of QpPb, we use the same pp reference as for the study of charged jet production in minimum bias  p–Pb   collisions [25]. This reference has been determined from the ALICE charged jet measurement at 7 TeV [40] via scaling to the  p–Pb  center-of-mass energy and taking into account the rapidity shift of the colliding nucleons. The scaling behaviour of the charged jet spectra is determined based on pQCD calculations using the POWHEG framework [49] and PYTHIA parton shower (see [25] for details). This procedure fixes the normalisation based on the measured data at 7 TeV, while the evolution of the cross section with beam energy is calculated, taking into account all dependences implemented in POWHEG and PYTHIA, e.g. the larger fraction of quark initiated jets at lower collision energy.

Jet production cross section ratio

The angular broadening or narrowing of the parton shower with respect to the original parton direction can have an impact on the jet production cross section determined with different resolution parameters. This can be tested via the ratio of cross sections or yields reconstructed with different radii, e.g. R = 0.2 and 0.4, in a common rapidity interval, here |ηlab| < 0.5:

R(0.2,0.4)=dσpPb,R=0.2/dpTdσpPb,R=0.4/dpT.
8

Consider for illustration the extreme scenario where all fragments are already contained within R = 0.2. In this case the ratio would be unity. In addition, the statistical uncertainties between R = 0.2 and R = 0.4 would be fully correlated and they would cancel completely in the ratio, when the jets are reconstructed from the same data set. If the jets are less collimated, the ratio decreases and the statistical uncertainties cancel only partially. For the analysis presented in this paper, the conditional probability varies between 25 and 50 % for reconstructing a R = 0.2 jet in the same pT-bin as a geometrically close R = 0.4 jet. This leads to a reduction of the statistical uncertainty on the ratio of about 5–10 % compared to the case of no correlation.

The measurement and comparison of fully corrected jet cross sections for different radii provides an observable sensitive to the radial redistribution of momentum that is also theoretically well defined [50]. Other observables that test the structure of jets, such as the fractional transverse momentum distribution of jet constituents in radial and longitudinal direction or jet-hadron correlations [10, 5154], are potentially more sensitive to modified jet fragmentation in   p–Pb  and  Pb–Pb . However, in these cases the specific choices of jet reconstruction parameters, particle pT thresholds and the treatment of background particles often limit the quantitative comparison between experimental observables and to theory calculations.

Systematic uncertainties

The different sources of systematic uncertainties for the three observables presented in this paper are listed in Table 2 for 0–20 % and 60–80 % most central collisions.

Table 2
Summary of systematic uncertainties on the fully corrected jet spectrum, the corresponding nuclear modification factor, and the jet production cross section ratio in 0–20 % central and 60–80 % peripheral events for the ...

The dominant source of uncertainty for the pT-differential jet production cross section is the uncertainty of the single-particle tracking efficiency that has a direct impact on the correction of the jet momentum in the unfolding, as discussed in Sect. 2.4. In  p–Pb  collisions, the single-particle efficiency is known with a relative uncertainty of 4 %, which is equivalent to a 4 % uncertainty on the jet momentum scale. To estimate the effect of the tracking efficiency uncertainty on the jet yield, the tracking efficiency is artificially lowered by randomly discarding the corresponding fraction of tracks (4 %) used as input for the jet finder. Depending on the shape of the spectrum, the uncertainty on the single-particle efficiency (jet momentum scale) translates into an uncertainty on the jet yield ranging from 8 to 15 %.

To estimate the effect of the single-particle efficiency on the   p–Pb  nuclear modification factor for jets, one has to consider that the uncertainty on the efficiency is partially correlated between the pp and  p–Pb  data set. The correction is determined with the same description of the ALICE detector in the Monte Carlo and for similar track quality cuts, but changes of detector conditions between run periods reduce the degree of correlation between the data sets. The uncorrelated uncertainty on the single-particle efficiency has been estimated to 2 % by varying the track quality cuts in data and simulations. Consequently, the resulting uncertainty for the nuclear modification factor is basically half the uncertainty due to the single particle efficiency in the jet spectrum (cf. Table 2). It was determined by discarding 2 % of the tracks in one of the two collision systems, as also described in [25].

Uncertainties introduced by the unfolding procedure, e.g. choice of unfolding method, prior, regularisation strength, and minimum pT cut-off, are determined by varying those methods and parameters within reasonable boundaries. Bayesian [55, 56] and χ2 [57] unfolding have been tested and compared to the default SVD unfolding to estimate the systematic uncertainty of the chosen method. The quality of the unfolded result is evaluated by inspecting the Pearson coefficients, where a large (anti-)correlation between neighbouring bins indicates that the regularisation is not optimal.

The overall uncertainty on the jet yield due to the background subtraction is estimated by comparing various background estimates: track-based and jet-based density estimates, as well as pseudo-rapidity-dependent corrections. The estimated uncertainty amounts to 3.8 % at low pT and decreases for higher reconstructed jet momenta.

The main uncertainty related to the background fluctuation estimate is given by the choice of excluding reconstructed jets in the random cone sampling. While the probability of a jet to overlap with another jet in the event scales with Ncoll - 1, it scales in the case of the random cone sampling with Ncoll. This can be emulated by rejecting a given fraction of cones overlapping with signal jets, which introduces an additional dependence on the definition of a signal jet. The resulting uncertainty due to the treatment of jet overlaps is of the order of 0.1 % and can be considered negligible.

In addition, several normalisation uncertainties need to be considered: the uncertainty on Ncoll (8 % in the hybrid approach), on the visible cross section σV0 (3.3 %) and from the assumptions made to obtain the scaled pp reference from 7 to 5 TeV (9 %).

Further details on the evaluation of the centrality-independent systematic uncertainties can be found in [25].

Results

The pT-differential cross sections for jets reconstructed from charged particles for five centrality classes in  p–Pb collisions at sNN=5.02 TeV are shown in Fig. 2. For both resolution parameters, the measured yields are higher for more central collisions, as expected from the increase of the binary interactions (cf. Table 1). The pp reference at s=5.02 TeV is also shown. In addition to the increase in binary collisions the larger total cross section in  p–Pb compared to pp further separates the data from the two collision systems; by an additional factor of 20%·σV0pPb/σinelpp6.

Fig. 2
(Color online) pT-differential production cross sections of charged jet production in  p–Pb collisions at 5.02 TeV for several centrality classes. Top and bottom panels show the result for R = 0.4 and R = 0.2, respectively. In ...

The scaling behaviour of the  p–Pb spectra with respect to the pp reference is quantified by the nuclear modification factor QpPb (Eq.7). The nuclear modification factor with the hybrid approach, shown in Fig. 3, is compatible with unity for all centrality classes, indicating the absence of centrality-dependent nuclear effects on the jet yield in the kinematic regime probed by our measurement. This result is consistent with the measurement of single charged particles in  p–Pb collisions presented in [32], where the same hybrid approach is used.

Fig. 3
(Color online) Nuclear modification factors QpPb of charged jets for several centrality classes. Ncoll has been determined with the hybrid model. Top and bottom panels show the result for R = 0.4 and R = 0.2, respectively. The combined global normalisation ...

For other centrality selections, closer to mid-rapidity, a separation of QpPb for jets is observed for the different centralities that is caused by dynamical biases of the selection, similar to the QpPb for charged particles. If we use e.g. the centrality selection based on the multiplicity in the V0A, QpPb decreases from about 1.2 in central to approximately 0.5 in peripheral collisions [58].

The centrality dependence of full jet production in  p–Pb collisions, i.e. using charged and neutral jet fragments, has been reported by the ATLAS collaboration in [23] over a broad range of the center-of-mass rapidity (y) and transverse momentum. Centrality-dependent deviations of jet production have been found for large rapidities in the proton-going direction and pT,jet ≳ 100 GeV/c. In the nucleon–nucleon center-of-mass system as defined by ATLAS, our measurement in |ηlab| < 0.5 corresponds to - 0.96 < y <  - 0.04. As shown in Fig. 4, the measurement of the nuclear modification factor of charged jets in central and peripheral collisions is consistent with the full jet measurement of ATLAS, where the kinematical selection of jet momentum and rapidity overlap, note however that the underlying parton pT at a given reconstructed pT is higher for charged jets.

Fig. 4
(Color online) Nuclear modification factor of charged jets compared to the nuclear modification factor for full jets as measured by the ATLAS collaboration [23]. Note that the underlying parton pT for fixed reconstructed jet pT is higher in the case of ...

The centrality evolution for QpPb as measured by ALICE is shown for three pT-regions and R = 0.4 in Fig. 5. No significant variation is observed with centrality for a fixed pT interval. The same holds for R = 0.2 (not shown).

Fig. 5
(Color online) Centrality evolution of QpPb for selected pT, ch jet-bins and R = 0.4

Recently, the PHENIX collaboration reported on a centrality dependent modification of the jet yield in  d–Au collisions at sNN=200 GeV in the range of 20 < pT < 50 GeV /c [59]: a suppression of 20 % in central events and corresponding enhancement in peripheral events is observed. Even when neglecting the impact of any possible biases in the centrality selection, the measurement of the nuclear modification at lower sNN cannot be directly compared to the measurements at LHC for two reasons. First, in case of a possible final state energy loss the scattered parton momentum is the relevant scale. Here, the nuclear modification factor at lower energies is more sensitive to energy loss, due to the steeper spectrum of scattered partons. Second, for initial state effects the nuclear modification should be compared in the probed Bjorken-x, which can be estimated at mid-rapidity to xT2pT/sNN, and is at a given pT approximately a factor of 25 smaller in  p–Pb  collisions at the LHC.

The ratio of jet production cross sections reconstructed with R = 0.2 and 0.4 is shown in Fig. 6. For all centrality classes, the ratio shows the expected stronger jet collimation towards higher pT. Moreover, the ratio is for all centralities consistent with the result obtained in minimum bias  p–Pb   collisions, which agrees with the jet cross section ratio in pp collisions as shown in [25]. The result is fully compatible with the expectation, since even in central  Pb–Pb collisions, where a significant jet suppression in the nuclear modification factor is measured, the cross section ratio remains unaffected [15].

Fig. 6
(Color online) Charged jet production cross section ratio for different resolution parameters as defined in Eq. 8. Different centrality classes are shown together with the result for minimum bias collisions. Note that the systematic uncertainties ...

Summary

Centrality-dependent results on charged jet production in  p–Pb  collisions at sNN=5.02 TeV have been shown for transverse momentum range 20 < pT, ch jet < 120 GeV/ c and for resolution parameters R = 0.2 and R = 0.4. The centrality selection is performed using the forward neutron energy, and the corresponding number of binary collisions Ncoll is estimated via the correlation to the multiplicity measured in the lead-going direction, in order use a rapidity region well separated from the one where jets are reconstructed.

With this choice of centrality and data driven Ncoll estimate, the nuclear modification factor QpPb is consistent with unity and does not indicate a significant centrality dependence within the statistical and systematical uncertainties. In the measured kinematic range momentum between 20  GeV/ c and up to 120  GeV/ c and close to mid-rapidity, the observed nuclear modification factor is consistent with results from full jet measurements by the ATLAS collaboration in the same kinematic region. The jet cross section ratio for R = 0.2 and 0.4 shows no centrality dependence, indicating no modification of the degree of collimation of the jets at different centralities.

These measurements show the absence of strong nuclear effects on the jet production at mid-rapidity for all centralities.

Acknowledgments

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. 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: State Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds Kidagan, Armenia; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); National Natural Science Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the Ministry of Science and Technology of China (MSTC); Ministry of Education and Youth of the Czech Republic; Danish Natural Science Research Council, the Carlsberg Foundation and the Danish National Research Foundation; The European Research Council under the European Community’s Seventh Framework Programme; Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA, France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und Technologie (BMBF) and the Helmholtz Association; General Secretariat for Research and Technology, Ministry of Development, Greece; National Research, Development and Innovation Office (NKFIH), Hungary; Department of Atomic Energy and Department of Science and Technology of the Government of India; Istituto Nazionale di Fisica Nucleare (INFN) and Centro Fermi, Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Italy; Japan Society for the Promotion of Science (JSPS) KAKENHI and MEXT, Japan; Joint Institute for Nuclear Research, Dubna; National Research Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT), Direccion General de Asuntos del Personal Academico(DGAPA), México, Amerique Latine Formation academique, European Commission (ALFA-EC) and the EPLANET Program (European Particle Physics Latin American Network); Stichting voor Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway (NFR); National Science Centre, Poland; Ministry of National Education/Institute for Atomic Physics and National Council of Scientific Research in Higher Education (CNCSI-UEFISCDI), Romania; Ministry of Education and Science of Russian Federation, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science and Innovations and The Russian Foundation for Basic Research; Ministry of Education of Slovakia; Department of Science and Technology, South Africa; Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT), E-Infrastructure shared between Europe and Latin America (EELA), Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta de Galicia (Consellería de Educación), Centro de Aplicaciones TecnolÃşgicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy Agency); Swedish Research Council (VR) and Knut and Alice Wallenberg Foundation (KAW); Ukraine Ministry of Education and Science; United Kingdom Science and Technology Facilities Council (STFC); The United States Department of Energy, the United States National Science Foundation, the State of Texas, and the State of Ohio; Ministry of Science, Education and Sports of Croatia and Unity through Knowledge Fund, Croatia; Council of Scientific and Industrial Research (CSIR), New Delhi, India; Pontificia Universidad Católica del Perú.

Footnotes

See Appendix A for the list of collaboration members.

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