Measurement of the centrality dependence of open heavy flavour production in lead-lead collisions at √

ATLAS-CONF-2012-050 26May2012

ATLAS NOTE

ATLAS-CONF-2012-050

May 26, 2012

Measurement of the centrality dependence of open heavy flavour production in lead-lead collisions at √

s = 2.76 TeV with the ATLAS detector

The ATLAS Collaboration

Abstract

Measurements of heavy quark production and suppression in ultra-relativistic nuclear collisions probe the interactions of heavy quarks with the hot, dense medium created in the collisions. ATLAS has measured heavy quark production in

s =

2.76 TeV Pb

Pb colli- sions via semi-leptonic decays of open heavy flavour hadrons to muons. Results obtained from an integrated luminosity of approximately 7

collected in 2010 are presented for the per-event muon yield as a function of muon transverse momentum,

, over the range of 4

14 GeV. Over that momentum range single muon production results largely from heavy quark decays. The centrality dependence of the muon yields is characterized by the

“central to peripheral” ratio,

. Using this measure, muon production from heavy quark

decays is found to be suppressed by a centrality-dependent factor that increases smoothly

from peripheral to central collisions. Muon production is suppressed by approximately a

factor of two in central collisions relative to peripheral collisions. Within the experimental

errors, the observed suppression is independent of muon

for all centralities.

1 Introduction

Collisions between lead ions at the LHC are thought to produce strongly interacting matter at temper- atures well above the QCD critical temperature. At such temperatures, strongly interacting matter is expected to take the form of “quark-gluon plasma.” High- p

quarks and gluons generated in hard- scattering processes during the initial stages of the nuclear collisions are thought to lose energy in the quark-gluon plasma resulting in “jet quenching” [1] . Since the energy loss results from the interaction of a quark or gluon with the medium, jet quenching is thought to provide a valuable tool for probing the properties of the quark-gluon plasma [2–4].

Measurements of heavy quarks are an important complement to studies of light quark and gluon quenching. The contributions from radiative [5] and collisional [6, 7] energy loss in weakly coupled calculations are expected to depend on the heavy quark mass. In particular, the mass of heavy quarks is expected to reduce radiative energy loss for quark transverse momenta less than or comparable to the quark mass (m), p

m, through the dead-cone effect [8]. However, measurements of heavy quark production at RHIC via semi-leptonic decays to electrons showed a combined charm and bottom sup- pression in Au

Au collisions comparable to that observed for inclusive hadron production [9–11]. There is disagreement in the theoretical literature regarding the interpretation of the RHIC heavy quark sup- pression measurements [6,12–14] particularly regarding the role of non-perturbative e

ects [15–17]. It is clear that measurements of heavy quark quenching at the LHC are an essential complement to inclusive jet [18, 19] or single hadron measurements [20, 21].

The rates for hard scattering processes in nucleus-nucleus (A

A) collisions are frequently compared to p

p measurements using the “nuclear modification factor”, R

, defined

R

dn

T

dσ

N

dn

dσ

(1)

Here, dn

represents the per-event di

erential rate for producing some hard-scattering final state in A

A collisions, dσ

represents the corresponding cross-section in p

p collisions, and the nuclear overlap function, T

, represents the integrated partonic luminosity of the A+A collision relative to that in p

p collisions. N

, the “number of collisions”, is defined N

T

, where

is the nucleon-nucleon total inelastic cross-section. T

and N

represent equivalent evaluations of the geometric enhancement of hard scattering processes in A+A collisions, though N

is more often used in the literature. If factorization were to hold in A

A collisions and in the absence of nuclear modifications of nucleon parton distribution functions, R

would be unity.

T

and N

depend on the collision “centrality”, the degree of overlap between the nuclei during the collision. That overlap is frequently characterized by the number of “participating” nucleons, N

– the number of nucleons that undergo at least one hadronic scattering during the A

A collision. N

can vary from a few nucleons in “peripheral” collisions – collisions with little overlap between the nuclei – to

≈

2A in “central” collisions – collisions with nearly complete overlap between the nuclei. In cases where reference p

p data are not available, the “central-to-peripheral” ratio, R

, is commonly used. R

is defined

R

N

N

dn

dn

(2)

where dn

and dn

represent the per-event differential rate for the same hard-scattering observable

in central and peripheral collisions, respectively. N

and N

represent N

values calculated for

the corresponding centralities (see Sec. 3). The use of R

is motivated by the presumption that nuclear

effects such as jet quenching have little impact in peripheral collisions, in which case R

and R

should, in principle, provide similar evaluation of nuclear modifications of hard scattering observables in

central collisions. In practice, R

measurements are typically limited by the statistics of the peripheral

measurement due to the small T

or N

values in such collisions. However, R

has the advantage that systematic uncertainties often partially cancel when taking ratios between measurements within the same data set.

This note presents ATLAS measurements of inclusive muon production in Pb+Pb collisions at

s

2.76 TeV from an integrated luminosity of approximately 7

collected in 2010. The measurements were performed for several intervals of collision centrality over the muon transverse momentum range 4

p

14 GeV and the yields compared to those in a peripheral bin using R

. Over this p

range, muon production in p

p collisions results predominantly from a combination of charm and bottom quark semi-leptonic decays; all other sources including J/ψ decays contribute less than 1% of the prompt muon yield [22]. The results presented here complement previous measurements by the CMS Collabo- ration [23] of bottom quark suppression performed using measurements of non-prompt J/ψ production.

2 Experimental setup

The measurements presented in this note were obtained using the ATLAS muon spectrometer (MS), inner detector (ID), calorimeter, trigger and data acquisition systems. A detailed description of these detectors and their performance in proton-proton collisions can be found in Refs. [24, 25]. Muons were detected by combining independent measurements of the muon trajectories from the ID and the MS. The ID mea- sures charged particles within the pseudo-rapidity

interval

2.5 using silicon pixel detectors, silicon microstrip detectors, and a straw tube tracker, all immersed in a 2 T axial magnetic field. A charged particle typically traverses three layers of silicon pixel detectors, four layers of double-sided microstrip sensors, and 36 straws. The inner detector is surrounded by electromagnetic and hadronic calorime- ters that absorb efficiently the copious charged and neutral hadrons produced in Pb+Pb collisions. A muon loses typically 3 to 5 GeV of energy, depending on the muon pseudorapidity, while crossing the calorimeters. The MS surrounds the calorimeters and provides tracking for muons within

2.7 in the magnetic field produced by three air-core toroid systems. Muon momenta were measured in the MS using three stations of precision drift chambers.

Two forward calorimeters [24] placed symmetrically with respect to z

0 and covering 3.2

4.9 are used in this analysis to characterize Pb+Pb collision centrality. They are composed of tungsten and copper absorbers with liquid argon as the active medium; each calorimeter has a total thickness of about 10 interaction lengths.

Minimum bias Pb+Pb collisions were identified using measurements from the zero degree calorime- ters (ZDCs) and the minimum-bias trigger scintillator (MBTS) counters [24]. The ZDCs are located symmetrically at z

8.3. In Pb

Pb collisions the ZDCs measure primarily

“spectator” neutrons, which originate from the incident nuclei and do not interact hadronically. The MBTS detects charged particles over 2.1

3.9 using two counters placed at z

counter is azimuthally divided into 16 sections, and the MBTS provides measurements of both the pulse heights and arrival times of ionization energy deposits in each section.

Events used in this analysis were selected for recording by the data acquisition system using a logical

OR of ZDC and MBTS coincidence triggers. The MBTS coincidence required at least one hit in both

sides of the detector, and the ZDC coincidence trigger required the summed pulse height from each

calorimeter to be above a threshold set below the single neutron peak.

Table 1: Results of Glauber model evaluation of

,

, and the N

ratio, R

for each central- ity. The quoted uncertainties represent the systematic uncertainties in the Glauber calculation.

Centrality

R

0–10% 356

2 1498

133 56.7

6.2 10–20% 261

4 923

83 34.9

3.8 20–40% 158

4 441

37 16.7

1.5 40–60% 69.3

3.5 130

10 4.9

0.2 60–80% 22.6

2.3 26.5

2 1

3 Event selection and centrality

In the offline analysis, Pb+Pb collisions were required to have a primary vertex reconstructed from charged particle tracks with p

500 MeV. The tracks were reconstructed from hits in the inner de- tector using the standard track reconstruction algorithm [26] with settings optimized for the high hit density in heavy ion collisions [27]. Additional requirements of at least one hit in each MBTS counter, a time difference between the two MBTS detectors of less than 3 ns, and a ZDC coincidence were im- posed, yielding a total of 53 million minimum-bias Pb

Pb events. The combination of the MBTS, ZDC, and the primary vertex requirements eliminates e

ciently both beam-gas interactions and photo-nuclear collisions [28]. Previous studies [27] indicate that this combination of ZDC trigger and offline require- ments select minimum-bias hadronic Pb

Pb collisions with an e

ciency of 98

2%. The ine

ciency is concentrated in the very most peripheral collisions not used in this analysis.

The centrality of Pb+Pb collisions was characterized by

E

, the total transverse energy measured in the forward calorimeters (FCal). For the results presented in this note, the minimum-bias

E

distribution was divided into centrality intervals according to the following percentiles of the

E

distribution ordered from the most central to the most peripheral collisions: 0-10%, 10-20%, 20-40%, 40-60%, and 60-80%. The centrality intervals were determined after accounting for very peripheral events lost due to the minimum-bias trigger e

ciency. A standard Glauber Monte-Carlo analysis [29,30]

was used to estimate the average number of participating nucleons,

nucleon-nucleon collisions,

Pb collisions in each of the centrality bins. The results are shown in Table 1. The R

measurements presented in the note use the 60-80% centrality bin as a common peripheral reference.

The R

calculation uses the ratio R

is the average number of collisions in the 60-80% centrality bin. The R

uncertainties have been directly calculated by eval- uating the changes in R

under variations of the minimum-bias trigger efficiency, variations of the parameters of the Glauber calculation such as the nucleon-nucleon cross-section, the nuclear radius, and nuclear thickness, and variations in the modeling of the

E

distribution [27]. The R

values and uncertainties are also reported in Table 1.

4 Muon reconstruction

Muons used in this analysis were obtained by combining separate measurements of the muon trajectory in the ID and the MS using the same algorithms that were developed for p

p collisions [22]. The ID tracks were required to have a hit in the first pixel layer, at least 7 hits in the microstrip detector, no missing hits in the microstrip detector in active sensors, and a maximum of one missing hit in the pixel detector.

The tracks were also required to point to within 5 mm of the primary vertex in both the transverse and

longitudinal directions.

Table 2: Approximate number of reconstructed muon candidates in the pseudorapidity interval

1.05 in each p

and centrality bin.

Centrality [%]

p

[GeV] 0–10 10–20 20–40 40–60 60–80

4–5 49k 36k 43k 17k 4.7k

5–6 19k 15k 18k 7.4k 2.0k

6–7 8.6k 6.5k 8.2k 3.4k 0.93k 7–8 4.1k 3.1k 3.9k 1.6k 0.46k 8–9 2.2k 1.7k 2.1k 0.78k 0.21k 9–10 1.2k 0.93k 1.1k 0.46k 0.13k 10–14 1.7k 1.31k 1.5k 0.62k 0.15k

The reconstructed muon momenta were obtained from a combined fit to the muon trajectories in the ID and MS. The results presented here use muons having 4

p

14 GeV and

1.05. The lower limit of the p

range was chosen to be near the plateau of the muon e

ciency curve. The upper p

limit results both from the limited statistics of the data and the desire to limit this measurement to a muon p

range where the contribution of W decays to the muon spectrum is less than 1% [22, 31]. The muon

interval was chosen to avoid transitional regions in calorimeter coverage where the muon performance is degraded. The momentum resolution is 5% over the measured p

range. The number of reconstructed muons passing the described cuts in each p

and centrality bin are listed in Table 2.

The performance of the ATLAS detector and o

ine analysis in measuring muons in Pb

Pb colli- sions was evaluated using a Monte Carlo (MC) data set [32] originally prepared for studies of jet perfor- mance. The sample also provides enough events containing high-p

muons from heavy flavour decays and background sources for the purposes of this analysis. The MC data set was obtained by overlaying GEANT4-simulated [33]

s

2.76 TeV p

p dijet events on to 1 million GEANT4-simulated minimum- bias Pb+Pb events obtained from version 1.38b of the HIJING event generator [34]. HIJING was run with default parameters, except for the disabling of jet quenching. To simulate the effects of elliptic flow [27] in Pb

Pb collisions, a parameterized cos 2φ modulation that varies with centrality,

and p

as determined by previous ATLAS measurements [27] was imposed on the particles after generation [35].

The p

p events were obtained from the ATLAS MC09 tune [36] of the PYTHIA event generator [37].

One million PYTHIA hard scattering events were generated for each of five intervals of ˆ p

, the trans- verse momentum of outgoing partons in the 2

2 hard scattering, with boundaries 17, 35, 70, 140, 280 and 560 GeV. The p

p events for each ˆ p

interval were overlaid on the same sample of HIJING events.

The e

ciency for reconstructing muons associated with heavy flavour decays was evaluated using

the MC sample described above for different bins in collision centrality. Figure 1 shows the fraction

of muons from semi-leptonic charm and bottom decays reconstructed as a function of muon p

,

p

),

for a subset of the centrality bins: 0-10%, 20-40%, and 60-80%. For p

5 GeV, the reconstruction

efficiency is found to be constant within the statistical uncertainties. The

p

) values for each centrality

bin were fit to a constant over the range 5

p

14 GeV to estimate the “plateau” efficiency. The

results for all centrality bins were consistent with

0.80

0.02. For 4

p

5 GeV, a statistically

significant variation of

with centrality is observed and the efficiencies were taken directly from the

results shown in Fig. 1. Those vary between 0.67

0.02 in peripheral collisions (60-80%) to 0.64

0.02

in central collisions (0-10%).

[GeV]

p

0 2 4 6 8 10 12 14 16

ε

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0-10%

20-40%

60-80%

Simulation

| < 1.05

|η

Preliminary ATLAS

Figure 1: E

ciency (ε) for reconstructing heavy flavour semi-leptonic decay muons as a function of muon p

for three collision centrality bins. The efficiency is shown over a wider p

range than that used in the analysis. The dotted line indicates the plateau efficiency value,

0.8.

5 Muon signal extraction

The measured muons consist of both “signal” muons and background muons. The signal muons are those that originate directly from the Pb+Pb collision, from vector meson decays, and from heavy quark decays. The background muons arise from pion and kaon decays, muons produced in hadronic show- ers in the calorimeters, and mis-associations of MS and ID tracks. Previous studies have shown that the signal and background contributions to the reconstructed muon sample can be discriminated sta- tistically [22, 38]. For this analysis a weighted combination of two discriminant quantities has been used [38]. The fractional momentum imbalance,

p

p

, quantifies the difference between the ID and MS measurements of the muon momentum after accounting for the energy loss of the muon in the calorimeters [39]. It is defined as:

∆

p

p

p

p

p

( p, η, φ)

p

(3)

where p

and p

represent the reconstructed muon momenta from the ID and MS, respectively and

∆

p

represents a momentum and angle-dependent average energy loss of muons in the calorimeter ob- tained from MC simulations. The “scattering significance”, S , characterizes deflections in the trajectory resulting from (e.g.) decays in flight. For each measurement along the muon trajectory, i, the deviation in azimuthal angle of the measured hit position from the fitted trajectory,

, was calculated and compared to the expected deviation from multiple scattering,

, to obtain the signed quantity s

q

, where q represents the track charge. The TRT measurements were not used when calculating s

due to the high occupancy of the TRT in Pb

Pb collisions. Then, the scattering significance at the kth layer, S (k), was calculated according to:

S (k)

1

√

n











k

X

i=1

s

n

X

j=k+1

s











.

(4)

C 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

C d dP

0 1 2 3 4 5 6 7 8 9 10

Signal, 0-80%

Signal, 0-10%

Signal, 60-80%

Background, 0-80%

Background, 0-10%

Background, 60-80%

Simulation < 6 GeV 5 < p

| < 1.05

| η

ATLAS Preliminary

Figure 2: Simulated C distributions, dP/dC, for signal and background muons for the full (0-80%)

centrality range and for the 0-10% and 60-80% centrality bins for muons in the momentum range of 5 –

6 GeV.

Here n represents the total number of measurements of the muon trajectory; typically n

16. S (k) yields a statistically significant value when the muon is deflected between measurements k and k

1. An overall scattering significance, S , was obtained from the maximum value of S (k):

S

max

(k)|, k

1, 2, ...}. (5)

The effectiveness of

p

and S in discriminating between signal and background muons varies with momentum in a complementary manner. S is more e

ective at lower muon momenta where the deflections resulting from (e.g.) in-flight decays are greater.

p

is more e

ective at larger muon momenta where in-flight decays are less important and a larger fraction of the muons are generated in hadronic showers. To take advantage of the complementarity of the two discriminants, a “composite”

discriminant was formed [38] according to:

C

∆

p

p

+

rS (6)

where r is a parameter that controls the relative contribution of the two discriminants to C. MC studies indicate that r

0.07 provides optimal separation between signal and background muons over the muon momentum range studied here [38].

Distributions for C were obtained from the PYTHIA

HIJING Monte Carlo sample for the di

erent centrality and muon p

bins used in this analysis. The C distributions were obtained separately for signal muons from charm and bottom decays and for background muons generated by pions and kaons.

Figure 2 shows the resulting C distributions for muons with 5

p

6 GeV in the 0-10% and 60-80%

centrality bins. As demonstrated by the figure, the signal and background C distributions were found to vary only weakly with collision centrality. As a result, for the template fitting procedure described below, the analysis was carried out using centrality-integrated (0-80%) signal and background C distributions which are also shown in Fig. 2.

The MC signal and background C distributions were used to perform a template fit to the C distri- butions in the data. Specifically, a hypothetical probability density distribution for C, dP/dC is formed assuming that a fraction, f

, of the measured muons is signal,

dP

dC

f

dP dC

_S+

(1

f

) dP dC

,

(7)

where dP/dC|

and dP/dC|

represent the Monte Carlo C distributions from signal and background sources, respectively.

To account for possible di

erences in the C distribution between data and MC due to (e.g.) in- accuracies in the MC description of multiple scattering, the fits allow for limited adaptation of the MC templates to the data. In particular, the fit allows a shift and re-scaling of the C distribution, C

a

b (C

is the usual mean of the C distribution. In addition, a Gaus- sian smearing of the MC C distribution was included such that the data C distribution was fit to

dP

dC

f

dP dC

_S+

(1

f

) dP dC

!

⊗

e

√

2πσ (8)

A kernel estimation method [40] was used to produce the unbinned probability density distribution,

dP

from the MC signal and background samples. The signal fraction, f

, was then evaluated for

each centrality and muon p

bin using unbinned maximum likelihood fits with four free parameters, f

,

a, b, and

RooFit [42]. Examples of

the resulting template fits are shown in Fig. 3 for the 0-10% and 60-80% centrality bins and for two muon

p

intervals. Typical fitted values for the a, b, and

parameters in Eq. 8 are, a

0.02, b

0.95

1.05,

C

0 0.2 0.4 0.6 0.8 1

Counts

0 20 40 60 80 100 120

= 2.76 TeV) sNN

Pb+Pb ( Best-fit template Signal Background

| < 1.05 η

|

< 14 GeV 10 < pT

0-10%

b-1

µ L dt = 7

∫

ATLAS Preliminary

0 0.2 0.4 0.6 0.8 1

Counts

0 200 400 600 800

1000

Best-fit template Signal Background

| < 1.05 η

|

< 6 GeV 5 < pT

0-10%

C

0 0.2 0.4 0.6 0.8 1

Counts

0 2 4 6 8 10 12 14

16

Best-fit template Signal Background

| < 1.05 η

|

< 14 GeV 10 < pT

60-80%

0 0.2 0.4 0.6 0.8 1

Counts

0 20 40 60 80 100

= 2.76 TeV) sNN

Pb+Pb ( Best-fit template Signal Background

| < 1.05 η

|

< 6 GeV 5 < pT

60-80%

Figure 3: Examples of the template fits to measured C distributions (see text) in 0-10% (left) and 60- 80% (right) centrality bins for two p

intervals: 5

p

6 GeV (top) and 10

p

14 GeV (bottom).

The curves show the contributions of signal and background sources based on the corresponding C

distributions obtained from MC including the shift, re-scaling, and smearing modifications (see text).

and

0.002. The combination of the MC signal and background C distributions are found to describe well the measured C distributions. The description remains good even if the adaptation of the template described in Eq. 8 is removed, though the fit results may change (see below).

The signal muon fractions extracted from the template fits for all p

and centrality bins are shown in Fig. 4. The statistical uncertainties on f

from the fits represent 1σ confidence intervals that account for the limited statistics in the data C distributions and correlations between the fit parameters. The uncertainties in the fit results due to the finite MC statistics were evaluated using a pseudo-experiment technique in which new pseudo-MC C distributions with the same number of counts as the original MC C distributions were obtained by statistically sampling the MC distributions. The resulting pseudo-MC distributions were then used to perform template fits. The procedure was repeated eight times for each p

and centrality bin and the standard deviation of the resulting f

values in each bin was combined in quadrature with the statistical uncertainty from the original fit to produce a combined statistical uncer- tainty on f

. The fractional uncertainties on f

due to MC statistics are found to be below 2% and are typically much smaller than the uncertainties from the template fits.

The sensitivity of the measured f

values to the adaptation of the MC C distributions to the data was evaluated by performing the fits fixing the a and

parameters to zero and b to one. Those fits yielded systematically lower f

values than the values obtained from the default fits. The reductions varied from as much as 18% for the 60-80%, 4–5 GeV bin to about 3% for the highest p

bins. The di

erences between the two values for each centrality and p

bin were used to estimate systematic uncertainties on the fit due to data-MC matching of the C distributions. Typically, those errors are largest for the lowest p

bin and decrease with increasing p

, but the 6–7 GeV and 7–8 GeV bins also show enhanced sensitivity to the template adaptation. That is particularly true for the 60-80% 7–8 GeV p

bin which suffers from low statistics.

The use of the centrality-integrated MC C distributions in the template fitting provides another po- tential source of data-MC mismatch. To evaluate the impact of this choice, the analysis was performed using centrality-selected MC C distributions. The reduction in template statistics worsened the statistical accuracy of the fits, particularly for the most peripheral bin. However, in all cases the di

erences from the default results were within the uncertainty estimates described in the preceding paragraph. Based on that observation and the judgment that the adaptation of the template distribution can likely account for the small centrality di

erences observed in the C distributions, no additional systematic error is assigned to account for the use of the centrality-integrated templates.

The MC background C distributions depend on the primary hadron composition, particularly the relative proportions of kaons and pions (K/π) which may di

er from that in the data. To test the sensitiv- ity of the results to such a difference, new MC background C distributions were obtained by separately doubling the

and K contributions. The new C

distributions were used in the template fits and the resulting di

erences in extracted f

used to estimate the K/π systematic uncertainties on the f

values.

The resulting (fractional) uncertainties are typically of order 1%, but they can be as large as 5% in the lowest p

bin.

Potential systematic uncertainties resulting from the template fitting procedure were evaluated using a simple cut procedure applied to the C distributions. For a given centrality and p

bin, a cut was applied at a chosen value of C, C

, and the fraction of muons in the data below the cut, f

was calculated. For an appropriate choice of cut, that fraction represents most of the signal muons with a modest contamination of background muons. The MC signal and background C distributions were used to evaluate the fraction of the signal (background) muons below the cut, f

( f

). Then, the fraction of signal muons evaluated using this cut method, f

(C

), was estimated:

f

(C

)

f

f

f

f

(9)

[GeV]

p

4 6 8 10 12 14

S

f

0 0.2 0.4 0.6

60-80%

S

f

0 0.2 0.4 0.6

40-60%

S

f

0 0.2 0.4 0.6

20-40%

S

f

0 0.2 0.4 0.6

10-20%

ATLAS Preliminary

S

f

0 0.2 0.4

0.6

0-10%

=2.76 TeV sNN

Pb+Pb, b-1

µ L dt = 7

∫

Figure 4: Fractions of signal muons, f

, in the measured muon yields as a function of muon p

in dif-

ferent bins of collision centrality. The points are shown at the mean transverse momentum of the muons

in the given p

bin. The shaded boxes indicate systematic errors (see text) due to possible data-MC tem-

plate matches and the template fitting (i.e. combination of dP/dC and “Fit” entries in Table 3), which

can vary from point-to-point. The error bars show combined statistical and total systematic uncertainties

including the e

ciency and hadron composition (K/π), some of which are also too small to be visible.

[GeV]

pT

4 5 6 7 8 9 10 11 12 13 14

ηd T dp TpN2 d evtN1

10-7

10-6

10-5

10-4

10-3

Pb+Pb

= 2.76 TeV sNN

| < 1.05 η

|

b-1

L dt = 7 µ

∫

ATLAS

0-10%

10-20%

20-40%

40-60%

60-80%

Preliminary

Figure 5: Invariant differential muon per-event yields calculated according to Eq. 10 as a function of muon p

for di

erent bins in collision centrality. The points are shown at the mean transverse momentum of the muons in the given p

bin. The statistical errors are smaller than the sizes of the points in all bins and are not shown. The error bars indicate combined statistical and systematic errors (see text).

f

values were obtained using C

values of 0.15, 0.2, and 0.25. The results from the three C

values agree typically to within a few %. The averages of the three f

values for each p

and centrality bin were compared to the results of the template fit where the adaptation was disabled. These two different estimates of the signal fraction agreed typically to better than 1%, but di

erences as large as 5% were observed for the 60-80% centrality bin. These differences were used to establish systematic uncertainties associated with the template fitting procedure.

Table 3 summarizes the contributions to the systematic error in the determination of the signal frac- tion, f

, for three sample p

bins in 0-10% and 60-80% centrality bins.

6 Results

The invariant di

erential per-event muon yields for a given centrality bin were obtained according to 1

N

d

N p

d p

dη

_cent

=

1

N

N

( p

)

ε^cent

( p

) p

p

(10)

where N

is the number of sampled Pb

Pb collisions in the centrality interval, N

is the number of signal muons in the centrality bin and

is the muon reconstruction efficiency discussed in the previous section. Figure 5 shows the resulting distributions for the five centrality bins included in this analysis.

The yields increase by more than an order of magnitude between peripheral and central collisions as expected from the geometric enhancement of hard scattering rates.

The muon R

is calculated from the ratio of the invariant differential yields between a given cen- trality bin and the 60-80% bin multiplied by 1/R

. Since the kinematic and phase space factors cancel between the numerator and denominator, the R

calculation reduces to

R

(p

)|

1 R























1 N

N

1

N

N

ε⁶⁰⁻⁸⁰























.

(11)

Table 3: Systematic uncertainty contributions from different sources for sample p

bins in 0-10% and 60-80% centrality bins. “dP/dC” represents the systematic uncertainties due to potential data-MC mis- matches in the template, “Fit” represents the estimated systematic on the fitting procedure evaluated using the cut method. “K/π” represents the uncertainty due to the hadron composition and “ε” represents the uncertainty on the efficiency estimation.

Centrality p

Uncertainty [%]

[%] [GeV] dP/dC Fit K/π ε Total

0-10

4–5 4 0 5 3 7

7–8 5 0.5 0.5 2 5.5

10–14 4 1 1 2 5

60-80

4–5 18 1 5 3 19

7–8 14 5 0.5 2 15

10–14 4 4 2 2 6

The resulting R

values are shown in Fig. 6. The R

values vary weakly with p

and the points for each centrality interval are consistent with a p

-independent R

within the uncertainties on the points.

The R

varies strongly with centrality, increasing from about 0.4 in the 0-10% centrality bin to about 0.85 in the 40-60% bin.

One disadvantage of R

is the poor statistics in peripheral bins, which have small geometric en- hancement of hard scattering processes compared to central collisions. Statistical errors in the reference peripheral p

bin then influence the R

results for that bin for all centralities. Such an effect can be observed in Fig. 6 for the 7–8 GeV p

bin. Alternatively, the centrality variation can be characterized by comparing different centrality bins to the most central bin which has the highest statistics producing a peripheral-to-central ratio, R

. The R

is defined analogously to Eq. 11 but with the 60-80% reference replaced by the 0-10% centrality bin. Figure 7 shows the resulting R

values as a function of p

for dif- ferent collision centralities. The figure provides similar insights as Fig. 6, but the R

allows a stronger statement about the p

dependence of the suppression. Namely, the shape of the muon spectra in the 0-10%, 10-20%, 20-40% and 40-60% centrality bins remains the same, within uncertainties, while over those centrality bins the suppression is changing by a factor of nearly 2.

The variation of R

with centrality as characterized by the average number of participants,

is shown in Fig. 8 for the di

erent p

bins included in the analysis. The R

decreases smoothly from peripheral to central collisions. The centrality dependence is observed to be the same for all p

bins within the experimental uncertainties.

7 Discussion

CMS has previously reported measurements of R

for non-prompt J/ψ produced in b decays in

s

2.76 TeV Pb

Pb collisions [23]. The R

in the 0-20% centrality bin (hN

308) is consistent with

the 0-10% (hN

356) muon R

presented here in the 10

p

14 GeV bin, for which the muon

yield is expected to be dominated by b decay contributions. However, the R

reported by CMS in

the 20-100% bin (hN

64) falls well below the R

measurements presented here. Since the CMS

results are in terms of R

and this analysis uses centrality 60-80% as the peripheral reference, we have

[GeV]

pT

0 2 4 6 8 10 12 14

CPMuon R

0 0.2 0.4 0.6 0.8 1 1.2

0-10% / 60-80%

10-20% / 60-80%

20-40% / 60-80%

40-60% / 60-80%

Pb+Pb

= 2.76 TeV sNN

| < 1.05 η

|

b-1

µ L dt = 7

∫

Figure 6: Muon R

as a function of p

calculated according to Eq. 11 for di

erent centrality bins. The points are shown at the mean transverse momentum of the muons in the given p

bin. The error bars include both statistical and systematic uncertainties. The contribution of the systematic uncertainties from R

and

p

bins, are indicated by the shaded boxes.

[GeV]

pT

0 2 4 6 8 10 12 14

PCMuon R

0 0.5 1 1.5 2 2.5 3 3.5 4

10-20% / 0-10%

20-40% / 0-10%

40-60% / 0-10%

60-80% / 0-10%

Pb+Pb

= 2.76 TeV sNN

| < 1.05 η

|

b-1

µ L dt = 7

∫

Figure 7: Muon peripheral to central ratio, R

, as a function of p

calculated according to Eq. 11 for

di

erent centrality bins. The points are shown at the mean transverse momentum of the muons in the

given p

bin. The error bars include both statistical and systematic uncertainties. The contribution of the

systematic uncertainties from R

and

p

bins, are indicated by

the shaded boxes.

part>

<N

0 50 100 150 200 250 300 350 400

CPMuon R

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Pb+Pb

= 2.76 TeV sNN

| < 1.05 η

| b-1

µ L dt = 7

∫

< 5 GeV 4 < pT

< 7 GeV 6 < pT

< 9 GeV 8 < pT

< 14 GeV 10 < pT

Preliminary

Figure 8: Muon R

as a function of

calculated according to Eq. 11 for di

erent bins in muon p

. The error bars show combined statistical and systematic uncertainties. The sets of points for the different

p

bins are successively displaced by

N

6 for clarity of presentation.

di

er appreciably from measurements of single hadron suppression at the LHC at comparable transverse momenta [20, 21, 43]. The single hadron R

reported by CMS [20] in the 0-5% centrality bin relative to the 50-90% centrality interval is a factor of approximately two smaller than the 0-10% muon R

value reported here, while that in the 5-10% centrality bin is lower by about 50%. The single hadron R

is also observed to vary much more rapidly with p

than the muon R

shown in Fig. 6. Interpretation of this difference may be complicated by the indirect relationship between the transverse momentum of the observed particle and the parent parton for both the hadrons and the muons. Nonetheless, the clear difference between semi-leptonic muon and charged hadron suppression at the LHC should be contrasted with the situation at RHIC where the experimental data do not indicate such a difference [10].

PHENIX has reported a semi-leptonic electron R

for p

4 GeV in the 0-10% centrality bin of 0.30

0.02(stat)

0.04(syst) [11]. STAR has reported similar results for R

( p

) [10]. The RHIC semi- leptonic electron results show more suppression than the measurements reported here, while the natural expectation would be that the suppression would be greater in Pb

Pb collisions at the LHC due to the higher initial energy densities [44].

8 Conclusions

This note has presented ATLAS measurements of muon production and suppression in

s

2.76 TeV

Pb+Pb collisions in a transverse momentum range dominated by heavy flavor decays, 4

p

14 GeV,

and over the pseudo-rapidity range

1.05. The fraction of prompt muons was estimated using

template fits to the distribution of a quantity capable of distinguishing statistically between signal and

background. The p

spectra of signal muons were evaluated in five centrality bins: 0-10%, 10-20%,

(0-10%) collisions compared to the most peripheral collisions included in the analysis (60-80%). No significant variation of R

with muon p

is observed. The R

decreases smoothly from peripheral to central collisions. The central muon R

for 10

p

14 GeV agrees with the central (0-10%) non-prompt J/ψ R

measured by CMS. The central R

is 1.5-2 times larger than that measured for charged hadrons in a comparable p

range and using comparable, though not identical, centrality ranges.

The central R

indicates weaker suppression than observed in the semi-leptonic electron R

measured over the same p

range in

s

200 GeV Au+Au collisions at RHIC.

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