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JID:PLB AID:34451 /SCO Doctopic: Experiments [m5Gv1.3; v1.252; Prn:20/02/2019; 13:17] P.1 (1-23)

Physics Letters B ••• (••••) •••–•••

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

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Observation of prompt J/ ψ meson elliptic ﬂow in high-multiplicity pPb

collisions at

√

= 8.16 TeV

.The CMS Collaboration



CERN, Switzerland

a r t i c l e i n f o a b s t r a c t

Article history:

Received

2 October 2018

Received

in revised form 14 February 2019

Accepted

14 February 2019

Available

online xxxx

Editor:

M. Doser

Keywords:

CMS

Physics

Heavy

ion

Correlation

Flow

pPb

Heavy

ﬂavor

A measurement of the elliptic ﬂow (v

) of prompt J/ ψ mesons in high-multiplicity pPb collisions

is reported using data collected by the CMS experiment at a nucleon-nucleon center-of-mass energy

√

= 8.16 TeV. Prompt J/ ψ mesons decaying into two muons are reconstructed in the rapidity region

in the nucleon-nucleon center-of-mass frame (y

), corresponding to either −2.86 < y

< −1.86 or

0.94 < y

< 1.94. The average v

result from the two rapidity ranges is reported over the transverse

momentum (p

) range from 0.2 to 10GeV. Positive v

values are observed for the prompt J/ ψ meson,

as extracted from long-range two-particle correlations with charged hadrons, for 2 < p

< 8GeV. The

prompt J/ ψ results are compared with previous CMS measurements of elliptic ﬂow for open charm

mesons (D

) and strange hadrons. From these measurements, constraints can be obtained on the

collective dynamics of charm quarks produced in high-multiplicity events arising from small systems.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Strong collective behavior is found in the azimuthal correlations

of particles emitted in relativistic nucleus-nucleus (AA) collisions

at the BNL RHIC [1–4] and at the CERN LHC [5–10]. These correla-

tions,

which are long-range in pseudorapidity (η), suggest the for-

mation

of a strongly interacting quark-gluon plasma (QGP) that ex-

hibits

nearly ideal hydrodynamic behavior [11–13]. The azimuthal

correlation structure of emitted particles is typically characterized

by its Fourier components [14]. In particular, within a hydrody-

namic

picture, the second and third Fourier anisotropy components

are known as elliptic (v

) and triangular (v

) ﬂow, respectively,

and reﬂect the QGP medium response to the initial collision ge-

ometry

and its ﬂuctuations [15–17]. In recent years, similar long-

range

collective azimuthal correlations have also been observed in

events with high ﬁnal-state particle multiplicity in proton-proton

(pp) [18–21], proton-nucleus (pA) [22–30], and lighter AA colli-

sions [31–33],

raising the question of whether a ﬂuid-like QGP is

created in these much smaller systems. While experimental mea-

surements

in these small systems are consistent with the hydrody-

namic

expansion of a tiny QGP droplet, alternative scenarios based

on gluon saturation in the initial state also claim to capture the



E-mail address: cms -publication -committee -chair @cern .ch.

main features of the correlation data (recent reviews are provided

in Refs. [34,35]).

Because of their large masses, heavy quarks (charm and bot-

tom)

are primarily produced via hard-scattering processes at a very

early stage of the collision. Thus, they are largely decoupled from

the bulk production of soft gluons and light-ﬂavor quarks at a

later stage in AA collisions, and thereby probe the properties and

dynamics of the QGP through its entire evolution [36]. A strong el-

liptic

ﬂow (v

) signal has been observed for open heavy-ﬂavor D

mesons in both AuAu collisions at RHIC [37] and PbPb collisions at

the LHC [38–40], suggesting that charm quarks may develop strong

collective ﬂow behavior. Furthermore, a recent measurement of the

elliptic ﬂow of J/ ψ mesons in PbPb collisions at

√

= 5.02 TeV

[41]has

provided additional evidence for the collective behavior of

charm quarks in the QGP.

In the study of collectivity in small systems, such as that oc-

curring

in pp or pPb collisions, a key open question is whether

the strong collective behavior observed for bulk constituents in

high-multiplicity events also extends to charm and bottom quarks.

Long-range correlations involving inclusive muons at high trans-

verse

momentum (p

) reveal a hint of heavy-ﬂavor quark collec-

tivity

in pPb collisions [42]. Furthermore, the recent observation

of a signiﬁcant elliptic ﬂow signal for prompt D

mesons in pPb

collisions

has provided evidence for charm quark collectivity in a

small system [43]. The v

signal for D

mesons is found to be

smaller than that of light-ﬂavor mesons at a given p

, indicating

https://doi.org/10.1016/j.physletb.2019.02.018

0370-2693/

SCOAP

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that in these small systems there is a weaker collective motion for

charm quarks, as compared to that of the bulk medium. However,

as the D

meson carries both a light and a charm quark, the rela-

tive

contribution of these different ﬂavor quarks to the observed v

signal is not fully constrained. Without detailed theoretical model-

ing,

a scenario is not excluded where the D

meson v

signal is

entirely carried by the light-ﬂavor quark. The observation of an el-

liptic

ﬂow signal for J/ ψ mesons in a small system could provide

more direct evidence of charm quark collectivity and could impose

new constraints on the collective dynamics of heavy-quark produc-

tion

in such collisions. Furthermore, heavy-quark collectivity may

also provide a hint of how, in small systems, hard probes inter-

act

with the QGP [36], assuming this is formed. First measurement

of inclusive J/ ψ (combined charmonia and J/ ψ mesons from de-

cay

of open beauty hadrons) v

in pPb collisions was reported in

Ref. [44], where positive v

coeﬃcients were found in the range

of 3 < p

< 6 GeV with center-of-mass rapidities −4.46 < y

−

2.96 or 2.03 < y

< 3.53. A recent model calculation of J/ ψ v

in pPb collisions suggests little v

signal arising from ﬁnal-state

interactions between charm quarks and the QGP medium [45].

This Letter presents the ﬁrst measurement of prompt J/ ψ me-

son

elliptic ﬂow (excluding contributions from b hadron decays)

from long-range two-particle correlations in very high multiplicity

pPb collisions at

√

= 8.16 TeV. The v

harmonics for prompt

J/ ψ mesons in the ranges −2.86 < y

< −1.86 and 0.94 < y

1.94 are determined over a wide p

range from 0.2 to 10 GeV. To

estimate the possible residual contribution from back-to-back jet-

correlations, the v

values are also presented after subtracting

correlations obtained from low-multiplicity pPb events (denoted as

sub

), where jet-like correlations are assumed to dominate. The re-

sults

are compared to those of the light strange-ﬂavor K

and 

hadrons, and the open heavy-ﬂavor prompt D

meson, which were

previously reported by CMS [43]in the same p

range but in a

different rapidity range of −1.46 < y

< 0.54. In order to explore

possible collectivity at the partonic level, a comparison is also pre-

sented

in terms of the transverse kinetic energy per constituent

quark (KE

, where KE



+ p

−m, and n

is the number

of constituent quarks).

2. The CMS detector

The central feature of the CMS apparatus is a superconduct-

ing

solenoid of 6 m internal diameter, providing a magnetic ﬁeld

of 3.8 T. Within the solenoid volume, there are four primary sub-

detectors

including a silicon pixel and strip tracker detector, a lead

tungstate crystal electromagnetic calorimeter, and a brass and scin-

tillator

hadron calorimeter, each composed of a barrel and two

endcap sections. Iron and quartz-ﬁber Cherenkov hadron forward

(HF) calorimeters cover the range 3.0 < |η| < 5.2. Muons are mea-

sured

in the range |η| < 2.4in gas-ionization detectors embedded

in the steel ﬂux-return yoke outside the solenoid, with detection

planes made using three technologies: drift tubes, cathode strip

chambers, and resistive-plate chambers. The silicon tracker mea-

sures

charged particles within the range |η| < 2.5. For charged

particles with 1 < p

< 10 GeV and |η| < 1.4, the track resolutions

are typically 1.5% in p

and 25–90 (45–150) μm in the transverse

(longitudinal) impact parameter [46]. A detailed description of the

CMS detector, together with a deﬁnition of the coordinate sys-

tem

used and the relevant kinematic variables, can be found in

Ref. [47].

3. Data selection and J/ ψ meson reconstruction

The pPb data at

√

= 8.16 TeV used in this analysis were

collected in 2016, and correspond to an integrated luminosity

of 186 nb

−1

. The beam energies are 6.5 TeV for the protons and

2.56 TeV per nucleon for the lead nuclei. Because of the asym-

metric

beam conditions, particles selected in the laboratory rapid-

ity

range of 1.4 < y

lab

< 2.4(−2.4 < y

lab

< −1.4) have a corre-

sponding

nucleon-nucleon center-of-mass frame rapidity range of

0.94 < y

< 1.94 (−2.86 < y

< −1.86), with positive rapid-

ity

deﬁned in the proton beam direction. To minimize statistical

uncertainties, the quoted J/ ψ meson v

results combine the indi-

vidual

values obtained for the proton and lead beam directions.

The

pPb data are analyzed in different ranges of N

oﬄine

trk

, where

oﬄine

trk

is the number of primary charged particle tracks [46]with

|η| < 2.4 and p

> 0.4 GeV. The main results are obtained with

events in the high-multiplicity range 185 ≤ N

oﬄine

trk

< 250. To select

these events, dedicated triggers were developed, as discussed in

Refs. [48,49]. Events with N

oﬄine

trk

< 35 are also used to estimate

the possible contribution of residual back-to-back jet-like corre-

lations.

These lower-multiplicity events are selected online with

a hardware-based trigger requiring two muon candidates in the

muon detectors with no explicit momentum or rapidity thresh-

old [50].

In the oﬄine analysis, hadronic collisions are selected by

requiring at least one HF calorimeter tower with more than 3GeV

total energy in each of the two HF detectors. Events must con-

tain

a primary vertex close to the nominal interaction point of the

beams, within 15 cm along the beam direction, and 0.2 cm in the

plane transverse to beam direction. The N

oﬄine

trk

range limits cor-

respond

to fractional inelastic cross sections from 100 to 57% for

oﬄine

trk

< 35, and from 0.33 to 0.01% for 185 ≤ N

oﬄine

trk

< 250, re-

spectively.

The

oﬄine muon reconstruction algorithm starts either by ﬁnd-

ing

tracks in the muon detectors, which are then ﬁtted together

with tracks reconstructed in the silicon tracker (global muons), or

by extrapolating tracks from the silicon tracker to match a hit on

at least one segment of the muon detectors (tracker muons). The

muon candidates are required to pass the identiﬁcation criteria

of the particle-ﬂow algorithm [51], which suppresses contamina-

tion

of “punch-through” hadrons misidentiﬁed as muons, based on

energy deposition in the calorimeters. The soft muon selection cri-

teria

are also imposed, as deﬁned in Ref. [52], to further improve

the purity of muons.

The

J/ ψ meson candidates are formed from pairs of oppo-

sitely

charged muons, originating from a common vertex. Based

on the vertex probability distributions for signal and background

candidates, the probability that the dimuon pair shares a common

vertex is required to be larger than 1%, lowering the background

from random combinations as well as from semileptonic decays

of bottom and charm hadrons. Because of the long lifetime of

b hadrons compared to that of J/ ψ mesons, the nonprompt J/ ψ

meson component can be reduced by placing constraints on the

pseudo-proper decay length [53]. This is deﬁned by



/ψ

= L

xyz

J/ψ

μμ

(1)

where L

xyz

is the distance between the primary and dimuon ver-

tices,

J/ψ

is the Particle Data Group [54]world average value of

the J/ ψ meson mass (assumed for all dimuon candidates), and p

μμ

is the dimuon momentum. The upper limit (decreasing as a func-

tion

of p

) imposed on the 

/ψ

value is based on Monte Carlo

(MC) studies with simulated event samples of pythia 8.209 [55,56],

and found to reject 75–90% (from low to high p

) of nonprompt

J/ ψ mesons, largely independent of multiplicity. The residual non-

prompt

J/ ψ meson fraction in the data is estimated to be approx-

imately

5% across the full p

range, and its effect on the v

mea-

surement

is propagated as a systematic uncertainty, as described

in Section 5.

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Fig. 1. Example of ﬁts to the invariant mass spectrum (left) and the v

S+B

inv

) distribution (right) in the p

interval 6.0–8.0 GeV for pPb events with 185 ≤ N

oﬄine

trk

< 250.

4. Analysis technique

The azimuthal anisotropy of J/ ψ mesons is extracted from the

long-range (|η| > 1) two-particle azimuthal correlations, follow-

ing

an identical procedure to that described in Refs. [21,27,43].

A two-dimensional (2D) correlation function is constructed by pair-

ing

each J/ ψ candidate with reference primary charged-particle

tracks with 0.3 < p

< 3 GeV and |η| < 2.4(denoted as “ref” parti-

cles),

and calculating

J/ψ

pair

dη dφ

B(0, 0)

S(η, φ)

B(η, φ)

(2)

where η and φ are the differences in η and in the azimuthal

angle (φ) of the pair. The same-event pair distribution, S(η, φ),

represents the yield of particle pairs normalized by the number of

J/ ψ candidates from the same event. The mixed-event pair yield

distribution, B(η, φ), is constructed by pairing J/ ψ candidates

in each event with the reference primary charged-particle tracks

from 20 different randomly selected events, from the same N

oﬄine

trk

range and having a primary vertex falling in the same 2cm wide

range of reconstructed longitudinal, z coordinate. The analysis pro-

cedure

is performed in each p

and invariant mass (m

inv

) range of

J/ ψ candidates. A correction for the acceptance and eﬃciency of

the J/ ψ meson yields is applied, but found to have a negligible ef-

fect

on the measurements. The φ correlation functions averaged

over |η| > 1(to remove short-range correlations, such as jet frag-

mentation)

are then obtained from the 2D distributions and ﬁtted

by the ﬁrst three terms of a Fourier series (including additional

terms has a negligible effect on the ﬁt results):

J/ψ

pair

dφ

assoc

2π



1 +



n=1

n

cos(nφ)



. (3)

Here, V

n

are the Fourier coeﬃcients and N

assoc

represents the

total number of same-event pairs per J/ ψ candidate for a given

invariant mass interval. By assuming that V

n

is the prod-

uct

of single-particle anisotropies of J/ ψ mesons and reference

charged particles [57], V

n

(J/ ψ, ref) = v

(J/ ψ) × v

(ref), the v

anisotropy harmonics for J/ ψ candidates can be extracted as a

function of invariant mass, v

(J/ ψ) = V

n

(J/ ψ, ref)/

√

n

(ref, ref).

The V

n

(ref, ref) represents the Fourier coeﬃcients extracted by

correlating two reference charged particles. With the current data,

only the second order (n = 2) elliptic anisotropy harmonic can be

measured with meaningful statistical precision.

To extract the genuine v

values of the J/ ψ meson signal (v

the contribution from background candidates (v

) has to be sub-

tracted

from the v

values of all J/ ψ meson candidates, as obtained

in the previous step. The procedure is to ﬁrst ﬁt the dimuon mass

spectrum with a function composed of three components: two

Crystal Ball functions [58]with different widths but common mean

and tail parameters for the J/ ψ signal (the tail parameters are ﬁxed

to the values obtained from simulation), S(m

inv

), and an exponen-

tial

function to model the background, B(m

inv

). Then, the signal

plus background v

S+B

inv

) distribution is ﬁtted with:

S+B

inv

) = α(m

inv

+[1 − α(m

inv

)]v

inv

), (4)

where

α(m

inv

) =

S(m

inv

)

S(m

inv

) + B(m

inv

)

(5)

Here, v

inv

) for the background J/ ψ candidates is modeled as

an exponential function of the invariant mass, and α(m

inv

) is the

J/ ψ signal fraction obtained from the mass spectrum ﬁt. An exam-

ple

of ﬁts to the mass spectrum and v

S+B

inv

) in the p

interval

6.0–8.0 GeV for the multiplicity range 185 ≤ N

oﬄine

trk

< 250 is shown

in Fig. 1. The residual contribution of back-to-back dijets to the

measured v

results is estimated from low-multiplicity pPb events

and is removed from the signal after accounting for the jet yield

ratio of the selected events, following a jet subtraction procedure

similar to that established in Refs. [21,43,57]. The Fourier coeﬃ-

cients,

n

, extracted from Eq. (3)for N

oﬄine

trk

< 35, are subtracted

from the V

n

coeﬃcients obtained in the high-multiplicity region,

with

sub



n

− V

n

oﬄine

trk

< 35)

assoc

oﬄine

trk

< 35)

assoc

jet

oﬄine

trk

< 35)

(6)

Here, Y

jet

represents the jet yield obtained by integrating the

difference of the short-range (|η| < 1) and long-range event-

normalized

associated yields for each multiplicity class. The ratio,

jet

oﬄine

trk

< 35), is introduced to account for the enhanced

jet correlations resulting from the selection of higher-multiplicity

events. For p

(J/ ψ) < 4.5 GeV, the jet yield ratio cannot be directly

estimated from the two-particle azimuthal correlations, as the J/ ψ

candidates tend to have larger η values than the acceptance for

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charged particles. Therefore, the value is assumed to be the same

as that for the high-p

region, where no p

dependence has been

observed. It was also previously observed that the values of jet

yield ratio for D

and strange particle species show little depen-

dence

on p

over the full p

range [43].

5. Systematic uncertainties

Sources of systematic uncertainties on the prompt J/ ψ me-

son

measurement include the J/ ψ meson yield correction (ac-

ceptance

and eﬃciency correction derived from pythia simula-

tion),

the nonprompt J/ ψ meson contamination, the background

inv

) functional form, the signal and background invariant

mass PDF, the jet subtraction procedure, the contamination of

events containing more than one pPb interaction (pileup), and the

trigger bias. In this Letter, the quoted uncertainties in v

are ab-

solute

values, and are found to have no dependence on p

, except

those for the jet subtraction procedure. Systematic uncertainties

originating from different sources are added in quadrature to ob-

tain

the overall systematic uncertainty shown as boxes in the ﬁg-

ures.

evaluate the uncertainties arising from the eﬃciency cor-

rection

to the J/ ψ meson yield, the v

values are compared to

the uncorrected ones, yielding an uncertainty of 0.008. The ef-

fect

on the measured v

due to the residual contribution from

nonprompt J/ ψ mesons is evaluated by varying the 

/ψ

require-

ment

such that the nonprompt J/ ψ meson yield is doubled. The

values are found not to change by more than ±0.004, which

is assigned as the systematic uncertainty due to the J/ ψ meson

yield correction. Possible differences in the rejection eﬃciency of

nonprompt J/ ψ mesons between data and simulation are investi-

gated

and found to be negligible. The systematic uncertainties from

the background v

functional form are evaluated by comparing

inv

) values based on ﬁrst-, second-, and third-order polyno-

mial

ﬁts to the background distribution. The resulting J/ ψ signal

values are found to vary by less than 0.009. Systematic effects

related to signal invariant mass PDF are found to be negligible by

releasing, one at a time, the ﬁxed tail parameters of the Crystal

Ball functions. The variation of v

, while changing the background

invariant mass PDF to a second- or third-order polynomial func-

tion

is also found to be negligible. In the jet subtraction procedure,

the statistical precision of the jet yield ratio is limited. The v

sub

results are found to be consistent within ±0.002 to ±0.014 (in-

creasing

with p

) when varying the jet yield ratio by its statistical

uncertainty. The systematic uncertainties from the potential pileup

effect and the trigger bias are taken to be the same as for inclusive

charged particles in Ref. [49], where they can be established with

good statistical precision. The pileup and trigger bias uncertainties

are negligible compared to the other sources of systematic uncer-

tainties,

as the fraction of residual pileup events is only a few %

and the trigger eﬃciency is close to 100%.

6. Results

Fig. 2 shows the v

results of prompt J/ ψ mesons at for-

ward

rapidities (−2.86 < y

< −1.86 or 0.94 < y

< 1.94) for

high-multiplicity (185 ≤ N

oﬄine

trk

< 250) pPb collisions, covering a

range from 0.2 to 10 GeV. Results obtained separately for J/ ψ

meson rapidity in the Pb- and p-going direction are compared,

and found to be consistent within statistical uncertainties. Thus,

as mentioned earlier, combined v

values are presented for the

best statistical precision. The v

results for K

and  hadrons

(light, strange-ﬂavor), and prompt D

mesons (open heavy-ﬂavor),

reported in a previous CMS publication [43]for the midrapidity

region −1.46 < y

< 0.54, are also shown for comparison.

Fig. 2. The v

results of the prompt J/ ψ mesons at forward rapidities (−2.86 <

< −1.86 or 0.94 < y

< 1.94), as a function of p

in the multiplicity range

185 ≤ N

oﬄine

trk

< 250 for pPb collisions at

√

= 8.16 TeV. Data for K

and 

hadrons, and prompt D

mesons at midrapidity (−1.46 < y

< 0.54) from previous

CMS measurements [43]are also shown for comparison. The error bars correspond

to statistical uncertainties, while the shaded areas denote the systematic uncertain-

ties.

Positive prompt J/ ψ meson v

values are observed over a wide

range from about 2 to 8GeV. The prompt J/ ψ meson v

re-

sults

show a trend of ﬁrst increasing up to p

∼ 4 GeV and then

decreasing toward higher p

. This observed trend appears to be in

common with the other hadron species shown. In the p

range

below 5GeV, the v

values for J/ ψ and D

mesons are consis-

tent

with each other within the uncertainties, while an indication

of smaller v

values for J/ ψ mesons than that for D

mesons

is seen for p

> 5GeV, although the difference is not signiﬁcant

within current experimental uncertainties. Over the full p

range,

the v

signal values for both J/ ψ and D

hadrons are smaller than

those for K

and  hadrons. This observation is consistent with

the earlier conclusion that charm quarks develop a weaker col-

lective

dynamics than light quarks in small systems [43]. Because

of experimental limitation, v

values for the prompt J/ ψ meson

and the other meson species are not compared within the same

rapidity range, possibly affecting their comparison. The rapidity

dependence of v

values for charged particles in pPb collisions

has been measured [59,60], suggesting up to around 15% variation

from |y

lab

| ∼ 0to 2.4.

better study the elliptic ﬂow signal coming purely from long-

range

collective correlations, the J/ ψ v

results are corrected for

residual jet correlations. The resulting (v

sub

) values are shown in

Fig. 3 (upper) for prompt J/ ψ mesons as a function of p

with

185 ≤ N

oﬄine

trk

< 250, and compared to similarly corrected K

, ,

and D

hadron results [43]. The effect of the correction for all par-

ticle

species is most noticeable at very high p

, while the overall

dependence of the v

data remains unchanged. The K

mesons

have a larger correction applied to their v

values (possibly be-

cause

mesons are more correlated with the bulk multiplicity,

and thus are biased toward stronger jet correlations due to the

selection of high multiplicities) and their v

sub

values after the

correction tend to converge to those of the prompt J/ ψ and D

mesons at high p

recent model calculation of J/ ψ v

in minimum bias pPb col-

lisions,

based on ﬁnal-state interactions between produced charm

quarks and a QGP medium, suggests a very small v

signal of less

than 0.01 [45]. This calculation indicates that additional contribu-

tions,

e.g., those from initial-state interactions, may be needed to

account for the observed v

signal of prompt J/ ψ mesons for high-

multiplicity

pPb events reported in this Letter.

Motivated

by the possible formation of a hydrodynamically

expanding QGP medium in small systems, the elliptic ﬂow sig-

nals

for K

, , J/ ψ and D

hadrons are compared as a function

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