Transverse momentum, rapidity, and centrality dependence of inclusive charged-particle production in √

(1)

ATLAS-CONF-2013-107 05November2013

ATLAS NOTE

ATLAS-CONF-2013-107

November 5, 2013

Transverse momentum, rapidity, and centrality dependence of inclusive charged-particle production in √

s

_NN

= 5.02 TeV p + Pb collisions measured by the ATLAS experiment

The ATLAS Collaboration

Abstract

Measurements of transverse momentum distributions of charged particles were per- formed using

p+

Pb collision data collected by the ATLAS experiment at a centre-of-mass energy of

√

s_NN =

5.02 TeV. Charged particles were reconstructed over pseudorapidity

|η|<

2.5 and transverse momentum between 0.1 GeV and 22 GeV in a data set corresponding to an integrated luminosity of 1

µb⁻¹

. The

p+

Pb collision centrality was characterized by the total transverse energy measured in 3.1

< η <

4.9, which is in the direction of the outgo- ing lead beam. The

p+Pb charged particle multiplicities were compared to charged particle

production in

pp

collisions obtained by interpolating measurements at

√

s =

2.76 TeV and 7 TeV to 5.02 TeV. Results are presented in the form of charged particle nuclear modifica- tion factors,

R_pPb

, and the central to peripheral ratios,

R_CP

. The

R_pPb

and

R_CP

values are found to vary significantly as a function of rapidity and transverse momentum. A broad peak is observed for all centralities and rapidities in

R_pPb

(

p_T

) and

R_CP

(

p_T

) in the vicinity of

p_T ∼

3 GeV. However, the magnitude of the peak increases for more central collisions and rapidity ranges closer to the direction of the outgoing lead nucleus.

c

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1 Introduction

Proton-nucleus collisions at high energies provide an ideal environment for understanding the role of the nuclear environment in modifying hard scattering rates. Several physics effects are expected to induce deviations from a simple proportionality with the number of binary nucleon-nucleon collisions, relative to a proton-nucleon reference system. For an extensive review of predictions, see [1]. Nuclear shadowing has been long-observed in both deep inelastic scattering (DIS) on nuclei, as well as in proton-nucleus col- lisions, indicating that nucleons embedded in a nucleus have a modified structure. This tends to suppress hadron production at low to moderate momentum, and is addressed by a variety of approaches [2, 3].

Some theoretical approaches parametrize the relative cross sections per nucleon as a modification of the nuclear parton distribution functions (nPDF) [4–8]. Approaches based on parton saturation in high density QCD at low Bjorken

x, commonly known as the “Color Glass Condensate” (CGC), are used to

predict nuclear e

ff

ects from first principles. These typically lead to a suppression of the nuclear gluon density at low Bjorken

x

and moderate

Q²

[9–14].

At the same time, relative enhancements in hadron production have been observed in proton-nucleus collisions, known as the “Cronin e

ff

ect”, which have generally been attributed to initial state scattering of the incoming nucleon [15, 16]. Finally, many theoretical approaches include energy loss in “cold nuclear matter”, which is expected to modify hadron production rates at high

p_T

[17]. These e

ff

ects can be explored experimentally by the measurement of charged hadrons as a function of transverse momentum (

p_T .

20 GeV), where Cronin, shadowing, energy loss, and Color Glass effects are all expected to contribute.

For proton-lead (p

+

Pb) collisions the expected particle production rate is determined by the product σ

_NN × hT_Pbi, where

σ

_NN

is the inelastic nucleon-nucleon cross section. Neglecting isospin effects, σ

NN ≈

σ

pp

, the

pp

cross section. The

hT_Pbi

is the average value of the nuclear thickness function (in units of inverse barns) over a distribution of proton impact parameters incident on the nuclear target. The impact parameter

b

is not a directly measurable quantity, but it is well defined in Glauber Monte-Carlo simulations [18], which are then used to estimate the centrality of the events. The “nuclear modification factor”

R_pPb

can be written as:

R_pPb

(

p_T

, y

^?

)

=

1

hT_Pbi

1/N

_evt

d

²N_p+Pb

/dy

^?

dp

_T

d

²

σ

_pp

/dy

^?

d

p_T

. (1)

where the numerator is the per-event yield (N

_p₊_Pb

/N

_evt

) of charged particles. Both numerator and de- nominator are presented in terms of y

^?

, the rapidity in the nucleon-nucleon centre-of-mass. In the ab- sence of nuclear effects, the ratio

R_pPb

will be unity at high

p_T

. Alternatively, a similar nuclear mod- ification factor comparing central to peripheral events,

R_CP

, can be constructed without the need for a

pp

reference spectrum and knowledge of y using yields from peripheral

p+

Pb collisions, scaled by the appropriate

hT_Pbi

, as the denominator.

R_CP

is defined as

R_CP

(

p_T

, η)

= hT_Pb,Pi hT_Pb,Ci

(1/N

evt,C

)d

²N_p+_Pb_,C

/dηdp

T

(1/N

_evt,P

)d

²N_p+Pb_,P

/dηd

p_T

, (2) where indices “P” and “C” correspond to peripheral (large impact parameter) and central (small impact parameter) centrality intervals, respectively. This nuclear modification factor is presented as a function of η rather than y since both numerator and denominator are from systems with the same longitudinal boosts.

This note presents measurements of per-event charged particle yields in

√

s_NN =

5.02 TeV

p+Pb

collisions as a function of

p_T

, η and y

^?

. Results are also presented in intervals of collision centrality.

The collision centrality is estimated using the sum of transverse energy measured in the ATLAS forward

calorimeter in the outgoing Pb beam direction, 3.1 < η < 4.9. The modification of charged particle

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production in

p+Pb collisions with respect to pp

collisions is shown with the two nuclear modification factors described above.

R_pPb

is presented as a function of

p_T

in slices of y

^?

for a set of selected centrality intervals spanning the 90% most central

p+Pb collisions. The centrality dependence of charged particle

production was separately evaluated using central-to-peripheral ratios,

R_CP

, presented as a function of

p_T

in slices of η.

These measurements are an extension of a similar program started at RHIC, where all experiments reported the absence of suppression at high

p_T

in d+Au collisions [19–22]. These observations were in contrast to the strong suppression found in Au

+

Au collisions [23, 24]. Some of the rapidity dependent results from the d+Au program at RHIC [25–27] and back-to-back hadron correlations [27] were inter- preted as indicating the onset of the CGC at RHIC energies in the forward rapidity region. However, other theoretical models describe those results equally well [28], generating interest in the much higher centre-of-mass energy at the LHC as a potentially more favorable environment to establish the onset of deviations from binary scaling in nuclear targets. Identified particle spectra have been reported by ALICE [29] and CMS [30], and a first measurement in

p+

Pb collisions of centrality-integrated charged hadron production in a narrow pseudorapidity window relative to the centre-of-mass frame (|η

_cms|

< 0.3) was reported by ALICE [31]. In the latter work, no suppression was observed at high-p

T

. The mea- surements presented in this work should also provide useful input for constraining models of shadowing, energy loss and the Cronin e

ff

ect. They should also provide useful input for the determination of nPDF, in particular as a function of proton impact parameter and Bjorken

x

[6].

2 The ATLAS detector

The measurements presented in this note are performed using the ATLAS Inner Detector (ID), calorime- ters and the minimum-bias trigger scintillators (MBTS) [32]. The ID measures hits of charged particles with a combination of silicon pixel and silicon micro-strip detectors, and a straw-tube transition radia- tion tracker, all immersed in a 2 T axial magnetic field [33]. Hits are reconstructed into charged particle tracks over

|η|

< 2.5. The electromagnetic and hadronic calorimeters, used in the event selection, cover

|η|

< 4.9 using a combination of lead-liquid argon, copper-liquid argon and steel-scintillator sampling calorimeters and the forward calorimeters (FCal). The FCal consists of two sections, one on either side of the interaction point, that cover 3.1 <

|η|

< 4.9. and are composed of tungsten and copper absorbers with liquid argon as active medium. Together, the two sections provide 10 interaction lengths of material.

The MBTS detects charged particles over 2.1 <

|η|

< 3.9 using two hodoscopes of 16 counters positioned at

z=±3.6 m.

3 Data sets and event selection

3.1 Event selection in p + Pb collisions

The

p+Pb collisions were obtained by the ATLAS detector during the pilot run of the LHC in September

2012. The Pb ions had an energy per nucleon of 1.57 TeV and collided with the 4 TeV proton beam, yielding a centre-of-mass energy

√

s=

5.02 TeV with a longitudinal rapidity boost of -0.465 relative to the ATLAS laboratory frame

¹

. In this configuration, the proton had negative rapidity and the lead

1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and thez-axis along the beam pipe. Thex-axis points from the IP to the center of the LHC ring, and theyaxis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane,φbeing the azimuthal angle around the beam pipe. For thep+Pb collisions, the incident Pb beam traveled in the+zdirection. The pseudorapidity is defined in laboratory coordinates in terms of the polar angleθas η = −ln tan(θ/2) All pseudorapidity values quoted in this note are defined in laboratory

y=0.5 ln + )/(E

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nucleus had positive rapidity. For the remainder of this note, the terms Pb beam direction and proton beam direction will be used to refer to positive and negative pseudorapidities, respectively.

In the offline analysis, charged particle tracks and collision vertices were reconstructed from clusters in the pixel detector and the SCT using an algorithm optimized for minimum-bias

pp

measurements [34].

The

p+

Pb events selected for this analysis were required to have a collision vertex satisfying

|z_vtx|

<

150 mm, at least one hit in each side of the MBTS and a difference between the times measured in the two MBTS hodoscopes of less than 10 ns. Events containing multiple

p+Pb collisions (pileup) were

suppressed by rejecting events with a second reconstructed vertex having a scalar transverse momentum sum with

Σp_T

> 5 GeV. The residual pileup fraction has been estimated to be 10

⁻⁴

[35]. About 2 million events pass these event selection criteria.

To remove potentially significant contributions from electromagnetic and di

ff

ractive processes, a rapidity gap analysis similar to that applied in a recent measurement of diffraction in 7 TeV proton-proton collisions [36] was applied to the

p+Pb data. The detector is divided into slices of∆

η

=

0.2 and “edge”

gaps are calculated as the distance from the edge of the calorimeter to the nearest slice that contains a cluster with a minimum transverse energy of 200 MeV. Events with a large edge gap (

∆

η

^Pb_gap

> 2) in the positive η (Pb) direction are excluded from the analysis. No requirement was imposed on edge gaps on the negative η (p) side. The gap requirement removed a fraction,

f_gap =

1%, of the events passing the vertex and MBTS timing cuts and yielded a total of 2.1

×

10

⁶

events used in this analysis. This is described in more detail in a recent ATLAS measurement of the inclusive charged-particle multiplicity in

p+

Pb collisions [37].

3.2 Event selection in pp collisions

The proton-proton data sets used in this note were obtained during low luminosity data taking periods.

Proton-proton collisions at

√

s =

2.76 TeV with total integrated luminosity 202 nb

⁻¹

were obtained by the ATLAS experiment in March 2011. Proton-proton collisions at

√

s =

7 TeV with total integrated luminosity 188 µb

⁻¹

were obtained in April 2010. The average number of collisions per bunch crossing during these run periods reached significantly higher values than in

p+Pb, especially at 2.76 TeV where

peak values are

∼

0.4, while they remain low at 7 TeV (∼ 10

⁻²

). Events were used within the vertex range

|z_vtx|

< 150 mm, and at least one hit in each of the MBTS detectors. In addition, a time di

ff

erence of less than 10 ns was required between the two MBTS sides.

3.3 Monte Carlo data sets

The response of the ATLAS detector and the performance of reconstruction algorithms were evaluated using one million minimum-bias 5.02 TeV Monte Carlo

p+

Pb events, produced by version 1.38b of the HIJING event generator [38]. Di

ff

ractive processes were disabled. The events were then fully simulated using GEANT4 [39, 40]. To match the LHC

p+Pb beam conditions, the momentum four-vector of

each generated particle was longitudinally boosted by a rapidity of -0.465. The simulated events were then digitized using data conditions appropriate to the pilot

p+

Pb run and reconstructed using the same algorithms that were applied to the experimental data.

The LHC did not provide

pp

collisions at the same energy as the

p+

Pb collisions. Thus, the

pp

spectrum used as a reference for the

p+

Pb is based on an interpolation of two data samples measured at

√

s=2.76 TeV and 7 TeV. To evaluate event selection and tracking efficiencies, corresponding MC

samples with 20 million events each were generated based on PYTHIA6 [41]. The simulated detector

conditions were chosen to model the evolution of the detector status during each run period.

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4 Centrality selection

The centrality determination of ATLAS uses the total transverse energy,

ΣE_T^Pb

, measured in the positive rapidity sections of the forward calorimeter, in the direction of the Pb beam. The procedure used in this note is identical to that used for the analysis of the charged particle multiplicity [37].

The transverse energy in the forward calorimeter is evaluated at the electromagnetic energy scale and has not been corrected for hadronic response.

ΣE_T^Pb

is sensitive to the particle production expected to be associated with multiple interactions of the proton in the target nucleus in central collisions. As was shown in Ref. [37], the corresponding

hΣE_T^pi

on the proton beam side saturates as a function of

ΣE^Pb_T

. Thus,

ΣE^Pb_T

is used to characterize

p+

Pb collision centrality for the analysis presented here. In previous Pb+Pb [42] and

p+Pb analyses, centrality intervals were defined in terms of percentiles of the ΣE^Pb_T

distribution after accounting for an estimated ine

ffi

ciency of

≈

2± 2% for inelastic

p+

Pb events to pass the applied event selection criteria. The following centrality intervals are used in this analysis: 0-1%, 1- 5%, 5-10%, 10-20%, 20-30%, 30-40%, 40-60%, 60-90%. The most peripheral 90–100% collisions were excluded because of uncertainties regarding the event composition and their reconstruction e

ffi

ciency.

An estimate of

hT_Pbi

for each of the centrality intervals used in this analysis is based on the

ΣE^Pb_T

distribution reconstructed in the FCal; for a detailed description of the theoretical approach used in this analysis, see Ref. [37]. First, the contribution from nucleon-nucleon interactions was modelled using the response of the FCal for simulated

pp

events, generated using PYTHIA6 and PYTHIA8 [43] at

√s=5.02 TeV and boosted towards negative rapidity by 0.465. Second, the dependence of p+Pb colli-

sions on the number of participating nucleons (N

part

) was estimated using two models: (i) the Glauber model [18] and (ii) the Glauber-Gribov approach in which the nucleon-nucleon (NN) cross section is allowed to fluctuate event-by-event [44, 45], with the relative fluctuations determined primarily by the parameter

Ω

. In the Glauber-Gribov model, larger values of

Ω

give larger event-by-event fluctuations of the NN cross section, and di

ff

erent incorporations of existing data lead to estimates of

Ω =

0.55 [44]

and

Ω =

1.01 [45]. Using the distribution

P(Npart

) provided by each of these geometrical models and the convolution properties of gamma distributions, the measured

ΣE^Pb_T

distribution observed in data was re- produced well. This allowed the determination of

hN_parti

and

hT_Pbi

by applying the same

ΣE^Pb_T

selections to the model as in the data.

Based on the above analysis, the centrality parameters, including

hN_parti

and

hT_Pbi

with correspond- ing systematic uncertainties, were calculated for all three geometrical models, for the same selections in

ΣE_T^Pb

. The value of

hT_Pbi

is directly related to

hN_parti

via the relation

hN_parti −

1

= hT_Pbiσ_NN

, with σ

_NN

taken to be 70

±

5 mb [37]. The obtained

hT_Pbi

values for the Glauber and Glauber-Gribov models in di

ff

erent centrality intervals are listed in Table 1. For central collisions, the

hT_Pbi

uncertainties are dominated by the uncertainty in the Glauber model and its extensions and the uncertainty of the

pp

cross section. For more peripheral collisions the uncertainty on the efficiency for inelastic events makes a sig- nificant contribution. Values of the

hT_Pbi

ratios in centrality intervals divided by the value in the 60-90%

centrality interval are given in Table 2.

5 Reconstruction of charged particle spectra

5.1 Track selection

Charged particle tracks are reconstructed in the ID using an algorithm optimized for

pp

events [34].

Tracks originating from the selected vertices are required to have a minimum

p_T

> 0.1 GeV and

|η|

< 2.5.

Additional requirements on the number of hits in the ID subsystems improve the purity of the track

sample. All tracks are required to have at least one hit in the Pixel detector and a hit in the first Pixel

layer when one is expected by the tracking model. Tracks with

p_T ≤

0.2 GeV are required to have at least

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Centrality Glauber Glauber-Gribov

Ω =

0.55

Ω =

1.01 60-90% 42.3

⁺_−4.3^2.8₊_6.7%

−10.2%

36.6

⁺_−2.2^2.7₊_7.3%

−6.1%

34.4

⁺_−2.1^3.7₊_10.8%

−6.1%

40-60% 91.5

^+4.2_−6.7_+4.6%

−7.4%

80.2

^+4.6₋_3.3_+5.7%

−4.2%

75.9

^+6.5₋_3.3_+8.6%

−4.3%

30-40% 125.6

⁺_−4.5^3.3₊_2.6%

−3.6%

116.7

⁺_−3.2^3.8₊_3.2%

−2.7%

113.1

⁺_−3.3^6.6₊_5.9%

−2.9%

20-30% 147.9

⁺_−2.6^3.6₊_2.4%

−1.8%

145.5

⁺_−3.0^3.6₊_2.5%

−2.1%

144.6

⁺_−3.1^5.6₊_3.9%

−2.2%

10-20% 172

⁺₋₃⁷₊_4%

−2%

181.9

⁺_−3.1^4.4₊_2.4%

−1.7%

186.8

⁺_−2.9^5.0₊_2.7%

−1.6%

5-10% 194

⁺₋₄¹⁵₊_8%

−2%

221.0

⁺_−5.0^6.2₊_2.8%

−2.3%

234.8

⁺_−6.9^6.6₊_2.8%

−2.9%

1-5% 215

⁺²²₋₅ _+10%

−2%

263.7

^+9.1_−9.7_+3.5%

−3.7%

291.5

^+7.9_−22.7_+2.7%

−7.8%

0-1% 245.4

⁺_−6.6^36.6₊_14.9%

−2.7%

330

⁺₋₂₃¹⁵₊_5%

−7%

377

⁺₋₆₀¹²₊_3%

−16%

0-90% 106.3

⁺_−2.7^4.4₊_4.2%

−2.5%

107.3

⁺_−2.6^3.9₊_3.7%

−2.4%

109

⁺₋₂⁴₊_4%

−2%

Table 1: Mean values of

T_Pb

in b

⁻¹

for all centrality bins, along with the corresponding total systematic uncertainty, described in the text below. The columns correspond to the Glauber model (left), Glauber- Gribov model with

Ω =

0.55 (middle), and Glauber-Gribov model with

Ω =

1.01 (right).

Centrality Glauber Glauber-Gribov

Ω =

0.55

Ω =

1.01 40-60%

/

60-90% 2.16

⁺_−0.06^0.09₊_4%

−3%

2.19

⁺_−0.06^0.04₊_2.6%

−2.7%

2.21

⁺_−0.06^0.05₊_2.4%

−2.8%

30-40%

/

60-90% 2.97

⁺_−0.13^0.22₊_7%

−4%

3.19

⁺_−0.13^0.13₊_4%

−4%

3.29

⁺_−0.16^0.12₊_4%

−5%

20-30%

/

60-90% 3.49

⁺_−0.17^0.34₊_10%

−5%

3.98

⁺_−0.21^0.18₊_5%

−5%

4.21

⁺_−0.28^0.19₊_4%

−7%

10-20%

/

60-90% 4.06

^+0.5₋_0.21_+13%

−5%

4.98

^+0.25₋_0.31_+5%

−6%

5.43

^+0.28_−0.5 _+5%

−9%

5-10%

/

60-90% 4.58

⁺_−0.24^0.8 ₊_16%

−5%

6.05

⁺_−0.5^0.33₊_5%

−7%

6.8

⁺_−0.8^0.4₊_6%

−12%

1-5%

/

60-90% 5.08

⁺_−0.27^0.9 ₊_18%

−5%

7.2

⁺_−0.6^0.4₊_6%

−9%

8.5

⁺_−1.4^0.5₊_6%

−16%

0-1%

/

60-90% 5.80

⁺_−0.33^1.3 ₊_23%

−6%

9.0

⁺_−1.1^0.5₊_6%

−12%

11.0

⁺_−2.6^0.6₊_5%

−23%

Table 2: Ratios of the mean values of

T_Pb

for all centrality bins, along with the corresponding total systematic uncertainty. The columns correspond to the Glauber model (left), Glauber-Gribov model with

Ω =

0.55 (middle), and Glauber-Gribov model with

Ω =

1.01 (right).

2 hits in the SCT, tracks with 0.2 <

p_T≤

0.3 GeV at least 4 hits, and tracks with larger

p_T

at least 6 hits.

To ensure that the tracks originate from the event vertex, the transverse (d

₀

) and longitudinal (z

₀

sin θ) impact parameters are required to be less than 1.5 mm. Tracks selected for the analysis are required to satisfy the conditions on the significances:

|d₀

/σ

d₀|

< 3 and

|z₀

sin θ/σ

z₀sinθ|

< 3. The quantities σ

d₀

and σ

z0sinθ

are the uncertainties on the determination of

d₀

and

z₀

sin θ obtained from the covariance matrix provided by the ATLAS track model.

The criteria above are complete for

p+Pb collisions. In pp

collisions, tracks originating from all reconstructed vertices were used to construct the cross section, no correction is thus needed for pileup.

The track to vertex connection is established using the track

z₀

parameter and the

z

coordinate of the vertex. Vertices in

pp

are generally less precisely defined than in

p+Pb due to the smaller number

of tracks contributing to them. The track selection cuts related to the vertex were relaxed for vertices with fewer tracks: the requirement on the

z₀

sin θ parameter condition was increased to 2.5 mm and the selection criteria based on the transverse and longitudinal significances were increased to be less than 4.

The momentum 3-vector of each track is used to calculate the rapidity for each particle, assuming all

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particles have the pion mass (m

π

). This variable is called y

_π

. This note presents results both as a function of pseudorapidity and a function of y

^?

, the rapidity in the centre-of-mass system. This is needed since the

pp

reference data has no boost relative to the lab frame. Transforming the laboratory system to the

p+Pb centre-of-mass system for a particle of any mass (m) is defined as

y

^? =

y

−

y

_CM =

y

+

0.465, and for the particle assuming pion mass as y

^?_π =

y

π+

0.465. No boost is required in

pp, where the data was

taken in the centre-of-mass system, so y

^?=

y (y

^?_π =

y

_π

) for the

pp

data.

5.2 Reconstruction of the invariant particle distributions

Fully-corrected per-event

p+Pb charged particle multiplicity, measured differentially as a function ofp_T

and η or y

^?

, referred to as the di

ff

erential invariant yield, are constructed using the following formulae:

1 2πp

_T

dN

ch

dp

_Tdη =

1 2πp

_TN_evt∆

η

N_ch

(

p_T

, η)

∆p_T

P(p_T

, η)

_trk

(p

_T

, η) and (3)

1 2πp

_T

dN

ch

dp

_Tdy^? =

1 2πp

_TN_evt∆

y

^?_π

N_ch

(

p_T

, y

^?_π

)

∆p_T

P(p_T

, y

^?_π

)A(p

T

, y

^?_π

)

_trk

(p

_T

, y

^?_π

) . (4)

In these expressions,

∆p_T

,

∆

η and

∆

y

^?_π

are the widths of the transverse momentum, pseudorapidity and rapidity intervals being studied, and

N_evt

is the number of events in the analysed centrality interval. The correction factors

trk

,

P, andA

are used to account for track e

ffi

ciency, track purity, and to transform the distributions from y

_π

to hadron rapidity. For the

pp

data at each measured energy the corrections are applied analogously to derive the inclusive charged-particle cross sections in the same y

^?

intervals as for

p+

Pb.

The efficiency,

_trk

for track reconstruction is defined as:

_trk

(

p_T

, η)

= N_Primary^Rec

(

p^Rec_T

, η)

N^Gen

(

p^Gen_T

, η) ;

_trk

(p

_T

, y

^?_π

)

= N_Primary^Rec

(

p^Rec_T

, y

^?_π

)

N^Gen

(

p^Gen_T

, y

^?_π

) . (5) where “Gen” indicates the number of generated particles in a chosen

p_T

interval, and “Rec” indicates the number of reconstructed tracks that match to a generated particle, both at their corresponding transverse momentum

p_T

. “Primary” refers to charged particles which originate directly from the collision or result from decays of particles with

cτ <

10 mm. The algorithm to match reconstructed tracks to generated particles is discussed further in Ref. [46]. These e

ffi

ciencies are calculated using Monte Carlo events generated with the HIJING event generator and events generated with PYTHIA6 for

p+Pb and for thepp

analysis respectively. The e

ffi

ciencies were calculated after reweighting the generated spectra which was done to achieve a better agreement in the transverse momentum distribution between data and simulation.

Figure 1 shows a subset of the tracking efficiencies used for correcting the track distributions, for the 0-90% centrality interval and for a set of subranges in η (in the left panel) and y

^?_π

(in the right panel).

Due to the limited size of the MC sample available for the pilot run data, the e

ffi

ciencies shown in Fig. 1 are smoothed with the functional form (p

T

)

=

₀−

α/p

_T

for

p_T

> 3 GeV. The uncertainty associated with this smoothing procedure is added in quadrature to the other uncertainties.

The e

ffi

ciencies shown in the figure have a very weak centrality dependence in

p+

Pb. The maximum

variation from peripheral to central intervals does not exceed 2% over the range of measured centralities

at any

p_T

and η. As a function of pseudorapidity, the efficiency is generally higher in the centre of the

detector, reaching above 80% at high

p_T

for η

=

0, and decreasing toward the edges of the detector

to approximately 60%. The shape of the curves shown in Fig. 1 is similar as a function of both η

and y

^?_π

. The efficiency is smaller at low

p_T

, starting at around 20% in the lowest measured interval of

0.1 <

p_T

< 0.2 GeV, and then increases rapidly, reaching its plateau value at approximately 1 GeV.

(8)

[GeV]

pT

10-1 1 10

Efficiency

0 0.2 0.4 0.6 0.8

1 ATLAS Simulation Preliminary p+Pb HIJING

=5.02 TeV sNN

0-90%

< -2.25 η -2.5 <

< -2.0 η -2.25 <

< -1.0 η -1.25 <

< -0.75 η -1.0 <

< 0 η -0.25 <

[GeV]

pT

10-1 1 10

Efficiency

0 0.2 0.4 0.6 0.8

=5.02 TeV sNN

0-90%

-1.75

π≤ -2.0 < y*

-1.5

π≤ -1.75 < y*

-0.5

π≤ -0.75 < y*

0.25

π≤ -0.5 < y*

≤ 0.5 0.25 < y*π

Figure 1: The

p_T

dependence of track reconstruction e

ffi

ciency for several pseudorapidy ranges (left) and for several rapidity ranges (right).

The correction factors to remove the contributions from fake and residual secondary tracks are given by:

P(p_T

, η)

= N_Primary^Rec

(

p_T

, η)

N^Rec

(p

T

, η) and

P(p_T

, y

^?_π

)

= N_Primary^Rec

(

p_T

, y

^?_π

)

N^Rec

(p

T

, y

^?_π

) (6) which is the ratio of the number of reconstructed tracks associated to primary charged particles

N_Primary^Rec

, to that of all reconstructed tracks

N^Rec

. This correction is applied differentially as a function of η (y

^?_π

) and centrality interval and has a strong dependence on both variables for low

p_T

. In the most central

p+Pb

collisions at the edges of the measured η interval the fraction of primary particles decreases to 80% for reconstructed tracks with

p_T

< 0.15 GeV. However, for

p_T

> 1 GeV, the fraction of primary particles rises above 98% for all η and centrality.

Since not all particles are pions, a correction is applied to recover the rapidity distribution of all hadrons, as if the correct hadron mass was used in the calculated rapidities:

A

(

p_T

, y

^?_π

)

= N^Gen

(m,

p_T

, y

^?

)

N^Gen

(m

π

,

p_T

, y

^?_π

)

y

^?=

y

^?_π

. (7)

The correction is shown in Fig. 2 for

p+

Pb as a two-dimensional distribution (left) and as a

p_T

dependent correction function in selected intervals in y

^?_π

. The correction is smaller than 1.1 at y

^?_π=0 and decreases

to unity with increasing

p_T

. At the edges of acceptance it is approximately 0.8 for particles with

p_T ≈

0.7 GeV. The correction has the geometrical boundary at low

p_T

that corresponds to the acceptance of pions in the ATLAS ID. For the results presented as a function of the y

^?

variable, a selection of

p_T

> 0.5 GeV is used for y

^?_π

<

−1.4 and

y

^?_π

> 2.3 in

p+Pb and for|y^?_π|

> 2.0 in

pp

collisions. The systematic uncertainties on this correction are discussed in Section 7.

6 Reference spectra from pp collisions

Figure 3 shows the fully corrected charged particle cross section as a function of

p_T

in four rapidity windows, the left panel shows the results extracted from 2.76 TeV

pp

collisions and the right panel shows the corresponding spectra at 7 TeV.

Once the differential cross sections at 2.76 and 7 TeV are measured, the charged particle cross section at

√

s=5.02 TeV is obtained by interpolation. Two interpolations are performed for everyp_T

bin in each

(9)

A

0.6 0.7 0.8 0.9 1 1.1

y*π

-2 -1 0 1 2 3

[GeV] Tp

10-1

1

=5.02 TeV sNN

0-90%

[GeV]

pT

10-1 1 10

A

0.6 0.7 0.8 0.9 1

1.1 ATLAS Simulation Preliminary p+Pb HIJING

=5.02 TeV sNN

0-90%

-1.75

π≤ -2.0 < y*

-1.5

π≤ -1.75 < y*

-0.5

π≤ -0.75 < y*

0.25

π≤ -0.5 < y*

≤ 0.5 0.25 < y*π

Figure 2: (left)

A(p_T

,y

^?

) as a function of

p_T

and y

^?_π

for the

p+

Pb MC sample. (right)

A(p_T

, y

^?

) for several y

^?_π

intervals and 0-90% centrality interval.

[GeV]

pT

10-1 1 10

]-2 ) [mb/GeV T/(dy* dpσ2 ) d T pπ1/(2

10-9

10-7

10-5

10-3

10-1

10 103

Preliminary ATLAS

=202 nb-1

p+p 2011 Lint

=2.76 TeV s

2.5

≤ 2 < y*

10-1

×

≤ 2) (1 < y*

10-2

×

≤ 0) (-1 < y*

10-3

× -2)

≤ (-2.5 < y*

[GeV]

pT

10-1 1 10

]-2 ) [mb/GeV T/(dy* dpσ2 ) d T pπ1/(2

10-9

10-7

10-5

10-3

10-1

10 103

b-1

µ

=188 p+p 2010 Lint

=7 TeV s

2.5

≤ 2 < y*

10-1

×

≤ 2) (1 < y*

10-2

×

≤ 0) (-1 < y*

10-3

× -2)

≤ (-2.5 < y*

Figure 3: Fully-corrected invariant cross sections extracted in four y

^?

intervals for

pp

collisions at two different energies. (left) Invariant cross sections extracted from

pp

collisions at 2.76 TeV, and (right) invariant cross sections from

pp

collisions at 7 TeV. The cross sections at the highest rapidities are only measured for

p_T

> 0.5 GeV. Systematic uncertainties are indicated by boxes, but are generally much smaller than the size of the symbols. To separate the curves, the distributions are scaled by powers of ten.

rapidity interval used in the

p+

Pb analysis. The first interpolation is proportional to

√

s, and the second to

(10)

ln(

√

s). Possible distortions introduced by the interpolation algorithm are studied with MC simulations

based on PYTHIA8 (with tune 4C) at the three centre-of-mass energies,

√

s=

2.76, 5.02 and 7 TeV.

Charged particle cross sections obtained by the two interpolation methods are compared to the generated cross section at

√

s=5.02 TeV at each p_T

and y

^?

value. The ratio of the generated cross section to the interpolated one is taken as a multiplicative factor for each interpolation. The ln(

√

s)-based interpolation

is used in the analysis mainly due to its consistency with the behavior of

pp

total cross sections at high energy [47].

Figure 4 summarizes the results of interpolation for the acceptance (−2 < y

^?

< 2.5) in

pp

rapidity.

The square markers show the ratio of the input cross section at

√

s=2.76 TeV divided by the interpolated

cross section at

√

s=5.02 TeV using ln(√

s). Circles show the same ratio but with the √

s=7 TeV cross

section in the numerator. The diamond markers show the comparison between the interpolation that uses

√s

as ordinate divided by that using ln(

√

s). This difference is included in the systematic uncertainties

on the cross section interpolation.

[GeV]

pT

10-1 1 10

Ratio

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

p+p -2<y*<2.5 )

s 7 TeV / 5.02 TeV (ln

) s 2.76 TeV / 5.02 TeV (ln

) s ) / 5.02 TeV (ln s

5.02 TeV (

Figure 4: Ratios of the input invariant cross section to the interpolated cross section at

√

s=

5.02 TeV.

The input spectrum measured at

√

s=

7 TeV is shown with circles and the one at

√

s=

2.76 TeV is shown with squares. The error bars reflect the statistical uncertainties of the input spectra. The comparison between interpolation using

√

s

and ln(

√

s)is shown with diamond markers. The grey band shows the

overall systematic uncertainty assigned to the generation of the

pp

spectra. All three ratios were extracted within the full acceptance of the ID detector.

7 Systematic uncertainties

The systematic uncertainties on the measurement of invariant charged particle yield arise from inaccu-

racies of the detector description in the simulation, sensitivity to selection criteria used in the analysis

and differences between the generated particles used in the simulation and in the data. To extract uncer-

tainties for each source, each one of the parameters used in the analysis, such as track selection criteria,

simulated particle composition, etc. was altered within reasonable limits.

(11)

The uncertainty on the detector description arises from the details of the Pixel and SCT detector acceptances and e

ffi

ciencies. The locations of the inactive modules were matched between the data and simulation. The track selection cuts on the number of hits in the detectors and on the

d₀

, given in Section 5.1, were varied and the results compared to standard cuts. This results in an approximately 1%

variation of the track reconstruction e

ffi

ciency. The uncertainties related to the description of the inactive detector material were evaluated using a

p+Pb MC sample with 10% extra material. The changes to the

final result are found to vary between 1-7% depending primarily on η. The systematic error estimated this way is applied identically to

pp

and

p+

Pb.

The HIJING event generator used in the analysis is known to be inconsistent with the

p_T

distributions measured in data, and PYTHIA does not perfectly describe the measured distributions in

p_T

and η. This was addressed by reweighting the HIJING and PYTHA distributions using the reconstructed spectra.

Reweighting was performed independently in centrality and η intervals. The systematic uncertainty was assigned to be 1%, equal to the full magnitude of the correction derived from this procedure.

To assess the sensitivity to the particle composition in HIJING, the fraction of pions, kaons and protons in HIJING were varied within a range according to the di

ff

erences between

pp

and Pb

+

Pb measured by the CMS and ALICE experiments [29, 30]. The change in the particle yields are found to be 1% at high

p_T

to 6% at the low edge of the

p_T

measured interval. This limited knowledge of the particle composition in

p+

Pb collisions is also the dominant source of the systematic uncertainty of the η

→

y

^?

transformation for the invariant yields and ratios presented in the note. Variation of the particle species results in an 8% di

ff

erence at the edges of the measured y

^?

interval at low

p_T

. This uncertainty was found to be correlated with the uncertainty on the e

ffi

ciency, which was taken into account in the results.

The uncertainty associated with the trigger e

ffi

ciency and residual di

ff

ractive contribution in the

p+

Pb event sample a

ff

ects the

ΣE^Pb_T

cuts which define centrality intervals in the analysis. The centrality intervals were redefined assuming 96% or 100% total event selection efficiency and the change in the multiplicity spectrum reconstructed in each centrality interval was taken as a systematic uncertainty associated with the centrality determination. The uncertainties associated with

hT_Pbi

contain the e

ff

ects of the trigger, vertex and inelastic event selection criteria.

The trigger and vertex reconstruction e

ffi

ciency in

pp

collisions has been estimated in [34]. The systematic uncertainty assigned to the trigger e

ffi

ciency is 1% for events with two tracks and decreases rapidly with higher track multiplicities, and a conservative average uncertainty of 0.5% is assigned. The uncertainty in the vertex reconstruction efficiency is taken to be 1%, which is the upper bound of the results presented in [34].

The systematic uncertainty on the invariant cross sections extracted for

pp

at

√

s=5.02 TeV due to

the interpolation was obtained by considering the relative difference between spectra obtained using the two di

ff

erent interpolation schemes (

√

s

or ln(

√

s)). An additional systematic uncertainty is assigned to

account for the use of the PYTHIA prediction for the change in spectra shapes between the interpolated values. The uncertainty was evaluated from the changes in shape predicted by the interpolation based on

√

s

rather than ln(

√ s).

The uncertainty on the luminosity for the 7 TeV

pp

data has been estimated to be 1.8% [48], and that corresponding to the 2.76 TeV

pp

data has been estimated to be 2.7% [49]. The uncertainty on the normalization of interpolated spectra is obtained by adding in quadrature the luminosity uncertainties of the inputs. The uncertainty on the

p+Pb luminosity is not needed since the results are presented in terms

of per-event invariant yields.

A summary of the systematic uncertainties on the charged particle yields in

p+

Pb and

pp

collisions

is shown in Table. 3. For the nuclear modification factors, some of the errors are correlated between

numerator and denominator. Many uncertainties cancel for

R_CP

, since the corrections do not vary with

centrality interval and the yields are compared in the same

p_T

and η bins. However, for

R_pPb

, there is

(12)

Uncertainty

p+Pb pp

Variation

Track selection 1% 1% decreases with

p_T

, increases with

|η|

Particle composition 1-6% 2% changes with

p_T

Material budget 1-7% decreases with

p_T

, increases with

|η|

p_T

reweighting 1% flat in

p_T

and η

Rapidity transformation 0-8% decreases with

p_T

Centrality selection 1-6% – flat in

p_T

and η, increases with centrality

Trigger Efficiency – 0.5%

Luminosity – 2.7% (2%)

√

s=2.76 TeV (7 TeV)

√s

interpolation – 3-9% increases with

p_T

and flat in η

Vertex reconstruction – 1%

Table 3: Systematic uncertainties on charged particle yields for

p+

Pb and

pp

at

√

s_NN=

5.02 TeV. The uncertainty in the luminosity does not contribute to the

p+Pb results, since they are expressed as per-

event invariant yields. The uncertainty on the trigger and event selection is expressed in the uncertainty on the e

ffi

ciency for selecting inelastic events, and thus is already contained in the uncertainties on

hT_Pbi.

little cancellation between

p+

Pb and

pp, since the

y

^?

variable does not respect the detector boundaries, especially given that the two systems are in two different centre-of-mass frames. The systematic uncer- tainties on

hT_Pbi

and their ratios given in Tables 1 and 2 are added in quadrature to the experimental uncertainties of

R_pPb

and

R_CP

respectively. In some figures these are shown separately as an overall scale uncertainty, as explained in the figure captions.

8 Results

The differential invariant yields of charged particles measured in

p+Pb collisions at √

s=5.02 TeV are

shown in Fig. 5. The left panel shows

p_T

spectra integrated over the largest available pseudorapidity interval

|η|

< 2.5 in five selected centrality intervals. The right panel shows the spectra in the 0-90%

centrality interval for several η intervals.

The left panel of Fig. 6 shows the invariant charged particle yield as a function of

p_T

integrated over the interval

−1.5

< y

^?

< 2 in several centrality intervals. The right panel shows the invariant yields measured for several y

^?

intervals in the 0-90% centrality interval. The solid lines indicate the

pp

invariant cross section measured as a function of

p_T

in y

^?

intervals corresponding to the same range as y

^?

of the

p+

Pb distributions. The

pp

data is scaled by the

hT_Pbi

values based on the Glauber calculation given in Table 1. The low

p_T

cuto

ff

s for the distributions in the right panel of Fig. 6 are di

ff

erent for

pp

and

p+Pb.

The nuclear modification factors

R_pPb

and

R_CP

are shown in Figure 7, in the upper and lower panels, respectively, as a function of the charged-particle transverse momentum. The nuclear modification fac- tors are calculated assuming three different geometrical models: Glauber (left), Glauber-Gribov

Ω =

0.55 (middle) and

Ω =

1.01 (right). The data are integrated over

−1.5

< y

^?

< 2 for

R_pPb

and

|η|

< 2.5 for

R_CP

. The circles indicate the most central 0-1% collisions. The other set of data points in each panel correspond to the most peripheral interval measured in the analysis, other than the reference itself. For

R_pPb

it is the 60-90% centrality interval, while for

R_CP

, where the 60-90% interval is used in the reference sample, it corresponds to the 40-60% centrality interval.

The data from the 0-1% centrality interval show similar features in all panels. Both

R_pPb

and

R_CP

increase with transverse momentum, reaching a maximum at approximately

p_T ∼

3 GeV, and then

decrease until reaching

p_T ∼

8 GeV. Above this value, the ratios are approximately constant, within the

(13)

[GeV]

pT

10-1 1 10

]-2 ) [GeV T dpη/(dchN2 ) d T pπ 1/(2evt1/N

10-11

10-8

10-5

10-2

10 103

b-1

µ

int=1 p+Pb L

=5.02 TeV sNN

|<2.5 η

|

0 - 1 % 10-1

× 5 - 10 %

10-2

× 20 - 30 %

10-3

× 40 - 60 %

10-4

× 60 - 90 %

[GeV]

pT

10-1 1 10

]-2 ) [GeV T dpη/(dchN2 ) d T pπ 1/(2evt1/N

10-11

10-8

10-5

10-2

10 103

b-1

µ

int=1 p+Pb L

=5.02 TeV sNN

0 - 90 %

2.5

≤ η 2 <

10-1

×

≤ 2) η (1 <

10-2

×

≤ 0) η (-1 <

10-3

× -2)

≤ η (-2.5 <

Figure 5: (left) Invariant di

ff

erential spectra of charged particles produced in

p+

Pb collisions at

√s=5.02 TeV shown in five centrality intervals averaged over |η|

< 2.5. The same data presented for four η intervals for the 0-90% centrality interval (right). The individual spectra are scaled by constant factors (indicated in the legend) for visibility. The statistical uncertainties are indicated with vertical lines and the systematic uncertainties are indicated with boxes, which are small due to the logarithmic scale.

experimental uncertainties. The peak is usually attributed to the Cronin e

ff

ect [50] and reaches a larger magnitude in

R_CP

compared to

R_pPb

. It also depends quantitatively on the choice of geometrical model.

However, the magnitude of the peak with respect to the constant region (

p_T '

8 GeV) is larger for

R_pPb

than for

R_CP

, and this does not depend on the choice of geometrical model. The peripheral events show a smaller rise at low

p_T

, only a slight indication of a Cronin peak around

p_T=3 GeV inR_CP

, and then the ratios are also approximately constant within uncertainties at higher transverse momentum.

The magnitude of

R_pPb

and

R_CP

in the constant region (

p_T '

8 GeV) in both central and in peripheral intervals strongly depends on the choice of the geometrical model. Using the standard Glauber model, this magnitude in the central

R_pPb

is consistent with unity, but in peripheral events it shows strong sup- pression of 0.7. The

R_CP

shows very di

ff

erent behaviour. The most central

R_CP

has the plateau above 1.5 and the most peripheral events above 1.1. These values are significantly above unity, given the stated statistical and systematic uncertainties. The peripheral

R_CP

depends only weakly on the choice of the Glauber or Glauber-Gribov model and is similar in all panels. The choice of the model strongly a

ff

ects the level of the plateau in the central events and its magnitude with respect to peripheral. For the three models considered in the note, the values found in central events are above peripheral when using the Glauber model; are close to them for Glauber-Gribov with

Ω =

0.55; or even below peripheral events for Glauber-Gribov with

Ω =

1.01. Figure 8 shows

R_pPb

as a function of

p_T