Longitudinal and azimuthal evolution of two-particle transverse momentum correlations in Pb–Pb collisions at √sNN = 2.76 TeV
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Longi udinal and azimu hal e olu ion o wo-pa icle ans e se momen um
co ela ions in Pb–Pb collisions a √sNN = 2.76 TeV
© 2020 Conseil Eu opéen pou la Reche che Nucléai e
Published e sion
ALICE Collabo a ion
ALICE Collabo a ion. (2020). Longi udinal and azimu hal e olu ion o wo-pa icle ans e se
momen um co ela ions in Pb–Pb collisions a √sNN = 2.76 TeV. Physics Le e s B, 804, A icle
135375. h ps://doi.o g/10.1016/j.physle b.2020.135375
2020
Physics Le e s B 804 (2020) 135375
Con en s lis s a ailable a ScienceDi ec
Physics Le e s B
www.else ie .com/loca e/physle b
Longi udinal and azimu hal e olu ion o wo-pa icle ans e se
momen um co ela ions in Pb–Pb collisions a √sNN =2.76 TeV
.ALICE Collabo a ion
a i c l e i n o a b s a c
A icle his o y:
Recei ed 16 No embe 2019
Recei ed in e ised o m 21 Feb ua y 2020
Accep ed 16 Ma ch 2020
A ailable online 20 Ma ch 2020
Edi o : M. Dose
This pape p esen s he fi s measu emen s o he cha ge independen (CI) and cha ge dependen (CD)
wo-pa icle ans e se momen um co ela o s GCI
2and GCD
2in Pb–Pb collisions a
√sNN =2.76 TeV by he
ALICE collabo a ion. The wo-pa icle ans e se momen um co ela o G2was in oduced as a measu e
o he momen um cu en ans e be ween neighbo ing sys em cells. The co ela o s a e measu ed as
a unc ion o pai sepa a ion in pseudo apidi y (η) and azimu h (ϕ) and as a unc ion o collision
cen ali y. F om pe iphe al o cen al collisions, he co ela o GCI
2exhibi s a longi udinal b oadening
while unde going a mono onic azimu hal na owing. By con as , GCD
2exhibi s a na owing along bo h
dimensions. These ea u es a e no ep oduced by models such as HIJING and AMPT. Howe e , he
obse ed na owing o he co ela o s om pe iphe al o cen al collisions is expec ed o esul om
he s onge ans e se flow p ofiles p oduced in mo e cen al collisions and he longi udinal b oadening
is p edic ed o be sensi i e o momen um cu en s and he shea iscosi y pe uni o en opy densi y
η/so he ma e p oduced in he collisions. The obse ed b oadening is ound o be consis en wi h he
hypo hesized lowe bound o η/sand is in quali a i e ag eemen wi h alues ob ained om aniso opic
flow measu emen s.
©2020 Conseil Eu opéen pou la Reche che Nucléai e,. Published by Else ie B.V. This is an open access
a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3.
1. In oduc ion
Measu emen s o pa icle p oduc ion and hei co ela ions pe -
o med a he Rela i is ic Hea y Ion Collide (RHIC) and he La ge
Had on Collide (LHC) p o ide compelling e idence ha he ma -
e p oduced in hea y-ion collisions is cha ac e ized by ex emely
high empe a u es and ene gy densi ies consis en wi h a decon-
fined, bu s ongly in e ac ing Qua k–Gluon Plasma (QGP) [1–4].
Collec i e flow, which mani es s i sel by he aniso opy o pa i-
cle p oduc ion in he plane ans e se o he beam di ec ion, is
cha ac e ized by he ha monic coefficien s o a Fou ie expansion
o he azimu hal dis ibu ion o pa icles ela i e o he eac ion
plane. Compa isons o hese ha monic coefficien s wi h hyd ody-
namical model p edic ions indica e ha he ma e p oduced in
hose collisions has a shea iscosi y pe uni o en opy densi y,
η/s, ha nea ly anishes [2,5]. The shea iscosi y quan ifies he
esis ance ha any medium p esen s o i s aniso opic de o ma-
ion. I con ibu es o he ans e o momen um om one fluid
cell o i s neighbo s as well as he damping o momen um fluc-
ua ions. The each o η/se ec s is expec ed o g ow wi h he
li e ime o he sys em. Recen measu emen s o flow coefficien s
and hyd odynamical p edic ions la gely ocus on he p ecise de-
e mina ion o η/s[6–9]. Howe e , quan i a i e desc ip ions o
E-mail add ess: alice -publica ions @ce n .ch.
hea y-ion collisions wi h hyd odynamical models gene ally ely
on specific pa ame iza ions o he ini ial condi ions o colliding
sys ems, i.e., hei ini ial ene gy and en opy densi y dis ibu ion
in he ans e se plane, he magni ude o ini ial fluc ua ions, he
he maliza ion ime, and se e al model pa ame e s. I is ound ha
he p ecision o model p edic ions is hinde ed, in pa icula , by un-
ce ain ies in he ini ial s a e condi ions. Indeed, alues o shea
iscosi y ha bes ma ch he obse ed flow coefficien s a e depen-
den on he ini ial condi ions, and unless he magni ude o he
ini ial s a e fluc ua ions can be p ecisely assessed, he achie able
p ecision on η/smigh emain limi ed [10,11]. Sys ema ic s udies
o co ela ions be ween di e en o de ha monic coefficien s [12],
shown o be sensi i e o he ini ial condi ions and he empe a u e
dependence o η/s, can help o p o ide u he cons ain s o hose
condi ions and o he anspo p ope ies o he sys em. No el
app oaches based on Bayesian pa ame e es ima ion [13,14]b ing
p og ess on a simul aneous cha ac e iza ion o he ini ial condi-
ions and he QGP. Fu he mo e, i was poin ed ou [15] ha he
s eng h o momen um cu en co ela ions may be sensi i e o
η/s. I was shown, in pa icula , ha he longi udinal b oadening
o a ans e se momen um (pT) co ela o , o mally defined below
and he ea e named G2, wi h inc easing sys em li e ime is di ec ly
sensi i e o η/swhile i does no ha e any explici dependence on
he ini ial s a e fluc ua ions in he ans e se plane o he sys em.
A fi s measu emen o he b oadening o he wo-pa icle
ans e se momen um co ela o G2was epo ed by he STAR
h ps://doi.o g/10.1016/j.physle b.2020.135375
0370-2693/©2020 Conseil Eu opéen pou la Reche che Nucléai e,. Published by Else ie B.V. This is an open access a icle unde he CC BY license
(h p://c ea i ecommons.o g/licenses/by/4.0/). Funded by SCOAP3.
2ALICE Collabo a ion / Physics Le e s B 804 (2020) 135375
collabo a ion [16]. Imp o ed echniques o co ec o ins umen-
al e ec s ha e since hen been epo ed [17–19]. In his le e ,
hese echniques a e used o measu e di e en ial cha ge inde-
penden (CI) and cha ge dependen (CD) wo-pa icle ans e se
momen um co ela o s, GCI
2and GCD
2, espec i ely, as a unc ion
o pai apidi y di e ence, η, and azimu hal angle di e ence,
ϕ, o selec ed anges o Pb–Pb collision cen ali y. The shapes
o hese co ela o s a e s udied wi h a wo-componen model and
he longi udinal and azimu hal wid hs o hei nea -side peaks a e
s udied as a unc ion o he Pb–Pb collision cen ali y. The longi-
udinal b oadening o GCI
2 om pe iphe al o cen al collisions is
used o assess he magni ude o η/so he ma e p oduced in
Pb–Pb collisions while he longi udinal and azimu hal wid hs o
GCD
2a e used o assess he ole o compe ing e ec s, including a-
dial flow, di usion, and he b oadening o je s by in e ac ions wi h
he medium. In ha con ex , measu emen s o G2a e also com-
pa ed wi h p e iously epo ed measu emen s o he wo-pa icle
numbe co ela o R2and wo-pa icle ans e se momen um co -
ela o P2[18].
2. The G2co ela o
The dimensionless a ian o he G2co ela o [15,20] epo ed
in his le e is defined acco ding o
G2(η1,ϕ1,η2,ϕ2)
=1
pT,1pT,2pT,1pT,2ρ2(
p1,
p2)dpT,1dpT,2
ρ1(
p1)dpT,1ρ1(
p2)dpT,2
−pT,1(η1,ϕ1)pT,2(η2,ϕ2)⎤
⎦(1)
whe e is he phase space egion in which he measu emen
is pe o med;
p1and
p2a e he h ee-momen um ec o s o
pa icles o a gi en pai ; pT,1and pT,2 hei ans e se mo-
men um componen s, espec i ely; ρ1(
pi) =d3N/dpT,idηidϕiand
ρ2(
p1,
p2) =d6N/dpT,1dη1dϕ1dpT,2dη2dϕ2 ep esen single and
pai pa icle densi ies, exp essed as unc ions o
pi, i =1, 2, and
(
p1,
p2), espec i ely; pT(ηi, ϕi)is he a e age ans e se mo-
men um o pa icles obse ed a (ηi, ϕi), wi h ηi, ϕi, i =1, 2,
e e ing o single- ack pseudo apidi y and azimu hal angle, e-
spec i ely; and pT,i =ρ1(
pi) pT,id
piis he inclusi e a e age
ans e se momen um o p oduced pa icles, i =1, 2, in he con-
side ed e en ensemble. Expe imen ally, G2is calcula ed as
G2(η1,ϕ1,η2,ϕ2)=1
pT,1pT,2SpT(η1,ϕ1,η2,ϕ2)
n1,1(η1,ϕ1)n1,2(η2,ϕ2)
−pT,1(η1,ϕ1)pT,2(η2,ϕ2)(2)
wi h
SpT(η1,ϕ1,η2,ϕ2)=n1,1
i
n1,2
j=i
pT,ipT,j(3)
whe e n1,1and n1,2a e he numbe o acks on each e en
wi hin bins cen e ed a η1, ϕ1and η2, ϕ2, and wi h ans e se
momen um pT,i, i ∈[1, n1,1], and pT,j, j = i ∈[1, n1,2], espec-
i ely. Angle b acke s, ···, e e o e en ensemble a e ages,
A =Ne en s
1A/Ne en s. The co ela o s GLS
2and GUS
2a e fi s mea-
su ed o like-sign (LS) and unlike-sign (US) pai s sepa a ely, and
combined o ob ain CI and CD co ela o s acco ding o GCI
2=
1
2GUS
2+GLS
2and GCD
2=1
2GUS
2−GLS
2, espec i ely [18]. Mea-
su emen s o G2(η1, ϕ1, η2, ϕ2)a e a e aged ac oss he longi u-
dinal and azimu hal accep ances in which he measu emen is
pe o med o ob ain G2(η, ϕ), whe e η=η1−η2and ϕ=
ϕ1−ϕ2, wi h a p ocedu e simila o ha used o R2and P2co -
ela o s [18].
3. Measu emen echniques
The esul s p esen ed in his le e a e based on 1.1 ×107se-
lec ed minimum bias (MB) Pb–Pb collisions a √sNN = 2.76 TeV
collec ed du ing he 2010 LHC hea y-ion un by he ALICE ex-
pe imen . De ailed desc ip ions o he ALICE de ec o s and hei
espec i e pe o mances a e gi en in Re s. [21,22]. The MB ig-
ge was configu ed in o de o ha e high efficiency o had onic
e en s, equi ing a leas wo ou o he ollowing h ee condi ions:
i) wo hi s in he second inne laye o he Inne T acking Sys em
(ITS), ii) a signal in he V0A de ec o , iii) a signal in he V0C de ec-
o . The ampli udes measu ed in he V0 de ec o s a e addi ionally
used o es ima e he collision cen ali y epo ed in nine classes
co esponding o 0–5% (mos cen al), 5–10%, 10–20%, ..., 70–80%
(mos pe iphe al) o he o al in e ac ion c oss sec ion [23]. The
e ex posi ion o each collision is de e mined wi h acks econ-
s uc ed in he ITS and he Time P ojec ion Chambe (TPC) and is
equi ed o be in he ange |z x| ≤7cm o he nominal in e ac ion
poin (IP). Pile-up e en s, iden ified as e en s ha ing mul iple e-
cons uc ed e ices in he ITS, a e ejec ed. Addi ionally, he ex a
ac i i y obse ed in slow esponse de ec o s (e.g., TPC) ela i e o
ha measu ed in as de ec o s (e.g., V0) o ou o bunch pile-up
e en s is used o disca d hese e en s. The emaining e en pile-
up con amina ion is es ima ed o be negligible. Longi udinally, he
ITS co e s |η| <0.9, he TPC |η| <0.9, V0A 2.8 <η<5.1 and V0C
−3.7 <η<−1.7. These ou de ec o s ea u e ull azimu hal co -
e age.
The p esen measu emen o he G2co ela o s is based on
cha ged pa icle acks measu ed wi h he TPC de ec o in he
ans e se momen um ange 0.2 ≤pT≤2.0GeV/
cand he pseu-
do apidi y ange |η| <0.8. In o de o ensu e good ack quali y
and o minimize seconda y ack con amina ion, he analysis is
es ic ed o cha ged pa icle acks in ol ing a minimum o 50
econs uc ed TPC space poin s ou o a maximum o 159, and
dis ances o closes app oach (DCA) o he econs uc ed p ima y
e ex o less han 3.2 cm and 2.4 cm in he longi udinal and a-
dial di ec ions, espec i ely. An al e na i e c i e ion, used in he
analysis o he sys ema ic unce ain ies, ha elies on acks e-
cons uc ed wi h he combina ion o he TPC and he ITS de ec o s,
hence o h called “global acks”, in ol es a minimum o 70 econ-
s uc ed TPC space poin s, hi s ei he on any o wo inne laye s
o he ITS, o in he hi d inne laye o he ITS, and a igh e DCA
selec ion c i e ion in bo h, longi udinal and adial di ec ions, he
la e one pT-dependen . Elec ons (posi ons), whose one o he
la ges sou ces a e pho on con e sions in o e+e−pai s, a e sup-
p essed disca ding e+and e−by emo ing acks wi h a specific
ene gy loss dE/dxin he TPC close han 3σdE/dx o he expec ed
median o elec ons and a leas 5σdE/dxaway om he π, Kand
pexpec a ion alues.
The single and pai efficiencies o he selec ed cha ged pa i-
cles a e es ima ed om a Mon e Ca lo (MC) simula ion using he
HIJING e en gene a o [24]wi h pa icle anspo h ough he
de ec o pe o med wi h GEANT3 [25] uned o ep oduce he de-
ec o condi ions du ing he 2010 un. Co ec ions o single ack
losses due o non-uni o m accep ance (NUA) a e ca ied ou us-
ing a weigh ing echnique [17] sepa a ely o da a and o econ-
s uc ed MC da a. Weigh s a e ex ac ed sepa a ely o posi i e and
nega i e acks, o each collision cen ali y ange, as a unc ion o
η, ϕ, pTand he longi udinal posi ion o he p ima y e ex o
each e en , z x. The pT-dependen single ack efficiency co ec-
ion is ex ac ed as he in e se o he a io o he numbe o NUA
co ec ed econs uc ed HIJING acks o gene a ed acks. Da a a e
ALICE Collabo a ion / Physics Le e s B 804 (2020) 135375 3
Fig. 1. Two-pa icle ans e se momen um co ela ions GCI
2( op) and hei longi udinal (middle) and azimu hal (bo om) p ojec ions o he mos cen al (le ), semi-cen al
(cen e ) and pe iphe al ( igh ) Pb–Pb collisions a √sNN =2.76 TeV. Ve ical ba s (mos ly smalle han he ma ke size) and shaded blue bands ep esen s a is ical and
sys ema ic unce ain ies, espec i ely. The sys ema ic unce ain y on he long- ange mean co ela o s eng h is quo ed as δBin bo h p ojec ions. Unde -co ec ed co ela o
alues a η, ϕ=0a e no shown. See ex o de ails.
subsequen ly co ec ed wi h NUA and single ack efficiency co -
ec ions. Pai losses due o ack me ging o c ossing a e co ec ed
in pa based on he echnique desc ibed in [18] and in pa based
on he a io o he a e age numbe o econs uc ed HIJING pai s
ela i e o he gene a ed numbe o pai s. Co ec ions o pTde-
penden pai losses a e no included in he epo ed esul s gi en
hey ha e a la ge (>20%) sys ema ic unce ain y. Co ela o alues
a |η| <0.05, |ϕ| <0.04 ad., le unde -co ec ed by his las
ac , a e no epo ed in his wo k. Howe e , his does no impac
he shape and wid h o he G2co ela o , which a e o in e es o
he de e mina ion o he iscous b oadening. No fil e s a e used o
supp ess like-sign (LS) pa icle co ela ions esul ing om Hanbu y
B own and Twiss (HBT) e ec s. Fo pions, which domina e he pa -
icle p oduc ion, HBT p oduces a peak cen e ed a η, ϕ=0in
GLS
2. The wid h o his peak dec eases in in e se p opo ion o he
size o he collision sys em. Gi en he numbe o HBT pai s is el-
a i ely small compa ed o he o al numbe o pai s accoun ed o
in GLS
2, he implied educ ion o he longi udinal b oadening is el-
a i ely modes and hus no conside ed in his analysis.
4. S a is ical and sys ema ic unce ain ies
S a is ical unce ain ies on he s eng h o G2a e ex ac ed
using he sub-sample me hod wi h en sub-samples. Sys ema ic
unce ain ies a e de e mined by epea ing he analysis unde di -
e en e en and ack selec ion condi ions. De ia ions om he
nominal esul s a e conside ed significan and assessed as sys-
ema ic unce ain ies based on a s a is ical es [26]. The impac
o po en ial TPC e ec s sensi i e o he magne ic field pola i y is
assessed by spli ing he whole da a sample in o posi i e and nega-
i e magne ic field configu a ions, whe eas unce ain ies associa ed
wi h he collision cen ali y es ima ion a e s udied by compa ing
nominal esul s, based on he V0 de ec o , wi h hose ob ained
wi h an al e na i e cen ali y measu e based on hi mul iplici y
on he wo inne laye s o he ITS. E ec s o he kinema ic ac-
cep ance in which he measu emen is pe o med a e in es iga ed
by epea ing he analysis wi h e en s in he ange |z x| <3cm o
he nominal IP. The p esence o biases caused by seconda y pa i-
cles is checked using he “global acks” selec ion c i e ion. Biases
associa ed wi h pai losses a e s udied based on pai efficiency
co ec ions ob ained wi h HIJING/GEANT3 simula ions. The la ges
sys ema ic unce ain y amoun s o a global shi in G2(η, ϕ)
co ela o s eng h which is independen o ηand ϕand is
epo ed as δB. This shi a ec s he magni ude o he p ojec-
ions on o ηand ϕbu no he shapes o he nea -side peak,
|ϕ| <π/2, o G2along hese coo dina es. Sys ema ic unce ain-
ies in he shape o he nea -side peak o GCI
2and GCD
2a e mainly
due o he p esence o seconda y pa icles. O e all, sys ema ic
unce ain ies on he shapes o he p ojec ions o GCI
2and GCD
2
along he longi udinal (azimu hal) dimension amoun o 4%(5%)
and 5%(10%), espec i ely, wi h dec easing alues owa ds pe iph-
e al e en s.
5. Resul s
Fig. 1p esen s he co ela o s GCI
2(η, ϕ)measu ed in 0–5%,
30–40%, 70–80% Pb–Pb collisions, and hei espec i e p ojec ions
along he ηand ϕaxes. The GCI
2co ela o s ea u e sizable
4ALICE Collabo a ion / Physics Le e s B 804 (2020) 135375
ϕmodula ions, domina ed in mid-cen al collisions by a s ong
ellip ic flow (cos(2ϕ)) componen . On he nea -side, a op he az-
imu hal modula ion, he GCI
2co ela o s ea u e a nea -side peak
whose ampli ude mono onically dec eases om pe iphe al o cen-
al collisions while i s longi udinal wid h sys ema ically b oadens.
Quali a i ely simila ends we e obse ed o he R2and P2co e-
la o s epo ed by ALICE [18] and he GCI
2co ela o ( he e named
C) epo ed by STAR [16]. In mos cen al collisions, he ampli ude
o he ϕmodula ions associa ed wi h collec i e flow dec eases
bu he longi udinal b oadening emains. Addi ionally, a deple ion
cen e ed a (η, ϕ) =(0, 0)consis en wi h p e ious ALICE e-
sul s [27,28]can
be seen.
In o de o s udy he cen ali y e olu ion o he nea -side peak
o he GCI
2and GCD
2co ela o s independen ly o he unde ly-
ing collec i e azimu hal beha io , hey a e sepa a ely pa ame ized
wi h a wo-componen model defined as
F(η,ϕ)=B+
6
n=2
an×cos(nϕ)
+A×γη
2ωη1
γηe−
η
ωη
γη
×γϕ
2ωϕ1
γϕe−
ϕ
ωϕ
γϕ
,(4)
whe e Band ana e in ended o desc ibe he long- ange mean
co ela ion s eng h and azimu hal aniso opy, while he bidimen-
sional gene alized Gaussian, defined by he pa ame e s A, ωη,
ωϕ, γηand γϕ, is in ended o model he signal o in e es . The
(η, ϕ) =(0, 0)deple ion p esen in he GCI
2co ela o is no
p ope ly modeled by Eq. (4) and he deple ion a ea, |η| <0.31
and |ϕ| <0.26 ad., is excluded om he fi . Bidimensional fi s
a e ca ied ou conside ing only s a is ical unce ain ies. In he
case o he GCI
2co ela o he χ2/nd alues o semi-cen al o
pe iphe al collisions a e ound in he ange 1–2; o cen al col-
lisions hey inc ease o 4. The a ea which con ibu es he mos
o he inc ease o he χ2/nd is he egion be ween he gene al-
ized Gaussian and he Fou ie expansion. Excluding his a ea he
χ2/nd alues ob ained in cen al collisions a e wi hin he ange
1–2.3. Fi s o GCD
2gi e χ2/nd o he o de o uni y o pe iph-
e al o semi-cen al collisions and in he ange 2–3.5 o cen al
collisions. La ge χ2/nd alues obse ed in cen al collisions ise
because he nea side peak s a s o depa om he gene alized
Gaussian desc ip ion. The ac ual ocus is on he e olu ion o he
wid hs. The longi udinal and azimu hal wid hs o he co ela o s,
deno ed σηand σϕ, espec i ely, a e hen ex ac ed as he s an-
da d de ia ion o he gene alized Gaussian
ση(ϕ)=
ω2
η(ϕ)(3/γη(ϕ))
(1/γη(ϕ)),(5)
and plo ed as a unc ion o collision cen ali y in he op panels o
Fig. 2 o bo h GCI
2and GCD
2co ela o s. The global shi o he co -
ela o s eng h, quo ed as a sys ema ic unce ain y in he p ojec-
ions o he co ela o s, does no a ec he shape o he nea -side
peak o G2. Acco dingly, he wid hs a e no a ec ed ei he . Co e-
la ions be ween he con ibu o s o he longi udinal wid h and he
ha monic pa ame e s o he GCI
2co ela o a e ound as ollows:
a2and a4a e an i-co ela ed wi h ωηwi h alues in he anges
−0.8 o −0.4 and −0.5–0, espec i ely, while a3is co ela ed wi h
alues 0–0.4. On he o he hand, a2and a4a e co ela ed wi h
Fig. 2. Top panels: collision cen ali y e olu ion o he longi udinal (le ) and az-
imu hal ( igh ) wid hs o he G2CD and CI co ela o s measu ed in Pb–Pb col-
lisions a √sNN =2.76 TeV. Cen al and bo om panels: wid h e olu ion ela i e
o he alue in he mos pe iphe al collisions o he wo-pa icle ans e se mo-
men um co ela ions GCI
2(cen al) and GCD
2(bo om) along he longi udinal (le )
and azimu hal ( igh ) dimensions. Da a a e compa ed wi h HIJING and AMPT model
expec a ions. In da a, e ical ba s and shaded bands ep esen s a is ical and sys-
ema ic unce ain ies, espec i ely. Fo models, shaded bands ep esen s a is ical
unce ain ies.
γηwi h alues wi hin 0.4–0.8 and 0–0.5, espec i ely, while a3
is an i-co ela ed wi h alues in he ange −0.5–0. a2co ela-
ions show no cen ali y dependence while he absolu e alue o
a3and a4co ela ions dec eases om cen al o pe iphe al colli-
sions. In he case o he con ibu o s o he azimu hal wid h, a2
and a4a e co ela ed wi h ωϕand wi h γϕwi h alues in he
anges 0.5–0.8 and 0.6–0.9, and 0.6–0.9 and 0.7–0.9, espec i ely,
while a3is an i-co ela ed wi h bo h wi h alues wi hin −0.8 o
−0.5 and −0.9 o −0.7. On he azimu hal dimension he absolu e
alue o he ha monic coefficien s co ela ions dec eases owa ds
pe iphe al collisions. Sys ema ic unce ain ies in he wid hs o he
nea -side peak o GCI
2and GCD
2a e mainly due o he p esence o
seconda y pa icles. Wi h he al e na i e ack selec ion c i e ion,
sys ema ic unce ain ies on he longi udinal and azimu hal wid hs
o he nea -side peak a e es ima ed o be 2% and 3%, espec i ely,
o bo h GCI
2and GCD
2, o mos cen al e en s, wi h dec easing
alues owa ds pe iphe al collisions. Unce ain y con ibu ions on
he wid hs a e no co ela ed wi h cen ali y and a e ages along
cen ali y classes a e conside ed. O e all, maximum sys ema ic un-
ce ain ies o 4%(2%) and 3.5%(3%) a e assigned o he GCI
2and GCD
2
wid hs, espec i ely, along he longi udinal (azimu hal) dimension.
The impac o he size o he a ea excluded om he fi on he
wid h o he GCI
2co ela o is e alua ed enla ging he a ea in bo h
dimensions. Only semi-cen al o cen al cen ali y classes ha e
hei co esponding longi udinal wid hs modified. The e ec is a
b oadening om 1.5% in he 30–40% class up o a b oadening o
20% in he 0–5% class inco po a ed as an addi ional asymme ic
sys ema ic unce ain y on he wid hs o GCI
2. On he azimu hal
wid hs he impac is educed o a 2% na owing.
6. Discussion
B oadening and na owing a e he ea e in ended as he beha -
io o he co ela ion unc ion, measu ed by i s wid hs, when going
om pe iphe al collisions, high alues o cen ali y pe cen ile, o
cen al collisions, lowe alues o cen ali y pe cen ile. The GCI
2co -
ela o b oadens longi udinally bu na ows in azimu h, whe eas
he GCD
2co ela o na ows bo h longi udinally and azimu hally.
As shown in Fig. 3, hese dependencies a e quali a i ely consis-
ALICE Collabo a ion / Physics Le e s B 804 (2020) 135375 5
Fig. 3. Le panel: collision cen ali y e olu ion o he longi udinal wid h o numbe co ela o RCD
2and ans e se momen um co ela o s PCD
2and GCD
2. Cen al panel: idem
o he azimu hal wid h o RCD
2, PCD
2and GCD
2. Righ panel: collision cen ali y e olu ion o he longi udinal wid h o RCI
2, PCI
2, and GCI
2. Da a o R2and P2a e om [18].
Ve ical ba s and shaded bands ep esen s a is ical and sys ema ic unce ain ies, espec i ely.
en wi h hose o R2and P2co ela o s measu ed in he same
kinema ic ange by he ALICE collabo a ion [18]. No e ha he G2
co ela o is sensi i e o ans e se momen um and numbe den-
si y fluc ua ions since bo h a ec he momen um cu en densi y.
In con as , R2is sensi i e o numbe densi y fluc ua ions and P2,
sensi i e o ans e se momen um fluc ua ions, is designed o min-
imize he con ibu ion o hose numbe densi y fluc ua ions [29].
In ac [29]
(P2+1)(R2+1)=(G2+1)(6)
so, he inc ease in ans e se momen um cu en s could be due o
ei he he inc ease in mul iplici y o he inc ease o ans e se mo-
men um. The GCD
2and PCD
2co ela o s ea u e app oxima ely equal
wid hs while RCD
2is app oxima ely 30% wide h oughou i s cen-
ali y e olu ion. The cen ali y dependence o GCD
2is quali a i ely
consis en wi h ha o balance unc ion (BF) obse a ions [30,31].
Phenomenological analyses o he BFs sugges ha hei na ow-
ing wi h cen ali y is la gely due o he p esence o s ong adial
flow and delayed had oniza ion in Pb–Pb collisions [30]. I is hus
easonable o in e ha adial flow and la ge pT, in mo e cen-
al collisions, also p oduce he obse ed na owing o GCD
2. This
conjec u e is suppo ed by calcula ions o he collision cen ali y
dependence o GCD
2azimu hal wid hs wi h he HIJING and AMPT
models shown in he bo om igh panel o Fig. 2. Radial flow
migh also explain he obse ed azimu hal na owing o he GCI
2
co ela o wi h cen ali y, which is easonably well ep oduced by
calcula ions wi h AMPT wi h s ing mel ing, bu no by HIJING
o AMPT calcula ions wi h only had onic esca e ing as shown in
cen al igh panel o Fig. 2.
The b oadening o he longi udinal wid h o he GCI
2co ela-
o is o pa icula in e es gi en p edic ions ha i should g ow
in p opo ion o η/so he ma e p oduced in he collisions [15].
As expec ed o a sys em wi h fini e iscosi y, i is ound ha GCI
2
b oadens significan ly wi h inc easing collision cen ali y, while by
con as , GCD
2exhibi s a sligh bu dis inc na owing. This GCD
2
longi udinal na owing is expec ed om a boos o pa icle pai s
by adial flow bu is no p ope ly accoun ed o by AMPT cal-
cula ions shown in he bo om le panel o Fig. 2. Radial flow
should also p oduce a na owing o he GCI
2co ela o in he lon-
gi udinal di ec ion. Howe e compe ing e ec s, possibly associa ed
wi h he fini e shea iscosi y o he sys em, a e ins ead p oducing
a significan b oadening al hough eaching wha seems a sa u a-
ion le el a semi-cen al collisions. No e ha HIJING and AMPT,
wi h he had onic esca e ing enabled, g ossly ail o ep oduce
he obse ed b oadening and ins ead p edic a sligh na owing
(Fig. 2cen al le panel). AMPT wi h s ing mel ing and wi hou
he had onic esca e ing phase quali a i ely ep oduces he longi-
udinal b oadening o GCI
2, e en i s sa u a ion, bu g ossly miss he
na owing o GCD
2along ha dimension and hus canno be con-
side ed eliable in his con ex .
Fig. 4. Two-pa icle ans e se momen um co ela ion GCI
2longi udinal wid h e o-
lu ion wi h he numbe o pa icipan s in Au–Au collisions a
√sNN =200 GeV [16]
and in Pb–Pb collisions a √sNN =2.76 TeV, measu ed in his wo k, using he
bi-dimensional fi desc ibed in he ex (2D) and he me hod used by he STAR
expe imen [16](1D). Fo comple eness, STAR RMS low limi [16]is also shown.
Pa icles p oduced by je agmen a ion a e also known o ex-
hibi co ela ions and je -medium in e ac ions can b oaden such
co ela ions. Two-pa icle co ela ion measu emen s, o pa icles
associa ed wi h high-pTje s, indeed show subs an ial b oaden-
ing o low pTpa icle co ela ions ela i e o co ela ion unc ions
measu ed in pp collisions [27,28,32]. This b oadening, howe e , is
obse ed in bo h he longi udinal and azimu hal di ec ions in s a k
con as wi h he beha io o he inclusi e GCI
2co ela o mea-
su ed in his wo k which exhibi s a significan na owing in he
azimu hal di ec ion. Addi ionally, he numbe o pa icles om je s
is ela i ely small compa ed o he numbe om he bulk. The e-
o e, al hough je agmen a ion may con ibu e o he b oadening
obse ed in he longi udinal di ec ion, i is unlikely o amoun o
a significan con ibu ion gi en he obse ed na owing in he ϕ
di ec ion and he ela i ely low impac o co ela ions om je pa -
icles.
Fig. 4compa es esul s om his analysis wi h hose epo ed
by he STAR collabo a ion [16]. Fo p ope compa ison, Fig. 4
p esen s oo mean squa e (RMS) wid hs o ηp ojec ions o GCI
2
calcula ed abo e a long ange baseline as in he STAR analysis [16].
Al hough STAR epo ed esul s a e based on he dimensional e -
sion o GCI
2, he same exp ession as in Eq. (1)bu wi hou he no -
maliza ion pT,1pT,2, he co ela o wid hs epo ed in his le e
a e iden ical o bo h, he dimensional and dimensionless e sions
o he G2co ela o . The longi udinal b oadening measu ed in his
analysis, using he 1D RMS me hod, amoun s o 36% while ha
obse ed by STAR eaches 74% showing also a sa u a ion a semi-
cen al collisions. I was e ified ha he smalle b oadening seen
in his analysis is no a esul o he sligh ly na owe longi udinal
accep ance o he ALICE expe imen by es ing he analysis me hod
wi h Mon e Ca lo models ep oducing he app oxima e shape and
s eng h o he measu ed co ela ion unc ions. The longi udinal
6ALICE Collabo a ion / Physics Le e s B 804 (2020) 135375
Fig. 5. Expec ed longi udinal wid hs o he mos cen al collisions o he wo-
pa icle ans e se momen um co ela ion GCI
2 o di e en alues o η/sby using
he exp ession sugges ed in [15]. Da a poin e o ba s ep esen o al unce ain ies
ob ained by adding in quad a u e s a is ical and sys ema ic unce ain ies. In he o -
mula σcis he longi udinal wid h o he mos cen al collisions in e ed by using
his exp ession and ep esen ed o each o he η/s alues by he colo discon in-
uous bands (con inuous o η/s =1/4π) a he highes numbe o pa icipan s, σ0
is he longi udinal wid h o he mos pe iphe al collisions (only wo pa icipan s)
which is ob ained by ex apola ing he fi , Tcis he c i ical empe a u e, τ0is he
o ma ion ime and τc, he eeze-ou ime. E o caps in he same colo as he
discon inuous bands, ep esen unce ain ies o he in e ed longi udinal wid hs o
he mos cen al collisions (see ex o de ails).
b oadening o GCI
2and i s obse ed sa u a ion hus appea s o be
po en ially dependen on he beam ene gy.
In e p e ing he longi udinal b oadening o GCI
2as o igina ing
exclusi ely om iscous e ec s, an es ima e o he shea iscosi y
pe uni o en opy densi y, η/s, o he ma e p oduced in hea y-
ion collisions can be ex ac ed [16]using he exp ession
σ2
c−σ2
0=4
Tc
η
s1
τ0−1
τc, (7)
de i ed in [15]. In Eq. (7)σcis he longi udinal wid h o he
mos cen al collisions (ideally 0% cen ali y), σ0is he longi udinal
wid h o he mos pe iphe al collisions (ideally 100% cen ali y),
Tcis he c i ical empe a u e, τ0is he o ma ion ime and τc, he
eeze-ou ime. The co ela o wid h o he mos pe iphe al Pb–
Pb collisions a √sNN =2.76 TeV is es ima ed based on a powe
law ex apola ion o he measu ed alues, shown in Fig. 5, down
o Npa =2. Canonical alues a e used o he c i ical empe a-
u e, Tc=160 MeV [33], he o ma ion ime τ0=1 m/c[33], and
he eeze-ou ime, τc, =10.5 m/c[34]. Wi h hese inpu s in
Eq. (7), GCI
2longi udinal wid hs o he mos cen al collisions a e
calcula ed o se e al alues o η/s =0.06, 1/4π, 0.14 and 0.22
and also shown in Fig. 5as colo discon inuous (con inuous o
η/s =1/4π) bands a he highes numbe o pa icipan s. Consid-
e ing 2%, 30%, and 3% unce ain ies o Tc(155 <Tc<165 TeV),
τ0, and τc, (10 <τc, <11 m) espec i ely, he unce ain ies o
he ou ob ained GCI
2longi udinal wid hs o he mos cen al col-
lisions each 9%, 10%, 12%, and 14%, espec i ely, also shown in
Fig. 5as e o caps in he same colo as he discon inuous bands.
The GCI
2co ela o wid h measu ed in cen al collisions hus a o s
a he small alues o η/s, close o he KSS limi o 1/4π[35].
The au ho s o Re . [15]ob ain he co ela o wid h alues, o
Au–Au collisions a √sNN =200 GeV, wi hou an ac ual measu e-
men o GCI
2 om he only a ailable wo-pa icle ans e se mo-
men um co ela o which in i s u n was in e ed om e en -wise
mean ans e se momen um fluc ua ions [36] and on i s ene gy
dependence [37]. They cons ain η/s o a ela i ely wide in e al
0.08–0.30. The p ecision o he STAR measu emen is limi ed by
he ela i e unce ain y o he GCI
2co ela o wid hs o Au–Au col-
lisions a √sNN =200 GeV; η/s =0.06–0.21 was epo ed in [16].
7. Conclusions
Measu emen s o cha ge dependen (CD) and cha ge indepen-
den (CI) ans e se momen um co ela o s G2in Pb–Pb collisions
a
√sNN =2.76 TeV we e p esen ed aiming a he de e mina ion o
he shea iscosi y pe uni o en opy densi y, η/s, o he ma e
o med in such collisions. The nea -side peak o he GCD
2co e-
la o is obse ed o significan ly na ow wi h collision cen ali y
bo h in he longi udinal and azimu hal di ec ions. This beha io is
ound o be simila o ha o he cha ge balance unc ion as a e-
sul , mos likely, o an inc ease o he a e age adial flow eloci y
om pe iphe al o cen al collisions. By con as , he GCI
2co ela o
is ound o na ow only in he azimu hal di ec ion wi h collision
cen ali y and ea u es a sizable b oadening in he longi udinal di-
ec ion. The obse ed b oadening along he longi udinal di ec ion
is expec ed based on ic ion o ces associa ed wi h he fini e shea
iscosi y o he sys em. Taking he model p oposed in [15], an es-
ima e o he alue o η/so o de 1/4π, in quali a i e ag eemen
wi h alues ob ained om o he me hods [14,38], is ob ained.
S ing mel ing AMPT wi hou he had onic esca e ing phase has
been ound o quali a i ely ep oduce he longi udinal b oadening
o GCI
2bu g ossly misses he na owing o GCD
2along ha dimen-
sion. The obse ed sa u a ion in he longi udinal b oadening and
he sizable di e ence in b oadening ela i e o ha obse ed by
STAR may esul om he in e play o iscous o ces and kinema ic
na owing associa ed o adial flow. In he la e case, he di e -
ence compa ed o he STAR esul s due o a possible dependence
on he beam ene gy could be be e es ablished wi h expanded
expe imen al measu emen s o ene gies in he beam ene gy scan
(BES) a RHIC o a 5.02 TeV a he LHC.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing finan-
cial in e es s o pe sonal ela ionships ha could ha e appea ed o
influence he wo k epo ed in his pape .
Acknowledgemen s
Au ho s hank D . Sean Ga in and D . Geo ge Moschelli o
ui ul discussions.
The ALICE Collabo a ion would like o hank all i s enginee s
and echnicians o hei in aluable con ibu ions o he cons uc-
ion o he expe imen and he CERN accele a o eams o he ou -
s anding pe o mance o he LHC complex. The ALICE Collabo a ion
g a e ully acknowledges he esou ces and suppo p o ided by
all G id cen es and he Wo ldwide LHC Compu ing G id (WLCG)
collabo a ion. The ALICE Collabo a ion acknowledges he ollow-
ing unding agencies o hei suppo in building and unning he
ALICE de ec o : A. I. Alikhanyan Na ional Science Labo a o y (Ye e-
an Physics Ins i u e) Founda ion (ANSL), S a e Commi ee o Sci-
ence and Wo ld Fede a ion o Scien is s (WFS), A menia; Aus ian
Academy o Sciences, Aus ian Science Fund (FWF): [M 2467-N36]
and Na ionals i ung ü Fo schung, Technologie und En wicklung,
Aus ia; Minis y o Communica ions and High Technologies, Na-
ional Nuclea Resea ch Cen e , Aze baijan; Conselho Nacional de
Desen ol imen o Cien ífico e Tecnológico (CNPq), Financiado a de
Es udos e P oje os (Finep), Fundação de Ampa o à Pesquisa do
Es ado de São Paulo (FAPESP) and Uni e sidade Fede al do Rio
G ande do Sul (UFRGS), B azil; Minis y o Educa ion o China
(MOEC), Minis y o Science & Technology o China (MSTC) and
Na ional Na u al Science Founda ion o China (NSFC), China; Min-
is y o Science and Educa ion and C oa ian Science Founda ion,
C oa ia; Cen o de Aplicaciones Tecnológicas y Desa ollo Nuclea
(CEADEN), Cubaene gía, Cuba; Minis y o Educa ion, You h and
Spo s o he Czech Republic, Czech Republic; The Danish Council
ALICE Collabo a ion / Physics Le e s B 804 (2020) 135375 7
o Independen Resea ch|Na u al Sciences, he Villum Fonden and
Danish Na ional Resea ch Founda ion (DNRF), Denma k; Helsinki
Ins i u e o Physics (HIP), Finland; Commissa ia à l’Ene gie A om-
ique (CEA), Ins i u Na ional de Physique Nucléai e e de Physique
des Pa icules (IN2P3) and Cen e Na ional de la Reche che Scien-
ifique (CNRS) and Région des Pays de la Loi e, F ance; Bundesmin-
is e ium ü Bildung und Fo schung (BMBF) and GSI Helmhol zzen-
um ü Schwe ionen o schung GmbH, Ge many; Gene al Sec e-
a ia o Resea ch and Technology, Minis y o Educa ion, Resea ch
and Religions, G eece; Na ional Resea ch, De elopmen and Inno-
a ion Office, Hunga y; Depa men o A omic Ene gy, Go e nmen
o India (DAE), Depa men o Science and Technology, Go e nmen
o India (DST), Uni e si y G an s Commission, Go e nmen o In-
dia (UGC) and Council o Scien ific and Indus ial Resea ch (CSIR),
India; Indonesian Ins i u e o Science, Indonesia; Cen o Fe mi -
Museo S o ico della Fisica e Cen o S udi e Rice che En ico Fe mi
and Ins i u o Nazionale di Fisica Nuclea e (INFN), I aly; Ins i u e
o Inno a i e Science and Technology, Nagasaki Ins i u e o Ap-
plied Science (IIST), Japanese Minis y o Educa ion, Cul u e, Spo s,
Science and Technology (MEXT) and Japan Socie y o he P omo-
ion o Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia
(CONACYT) y Tecnología, h ough Fondo de Coope ación In e na-
cional en Ciencia y Tecnología (FONCICYT) and Di ección Gene al
de Asun os del Pe sonal Academico (DGAPA), Mexico; Nede landse
O ganisa ie oo We enschappelijk Onde zoek (NWO), Ne he lands;
The Resea ch Council o No way, No way; Commission on Science
and Technology o Sus ainable De elopmen in he Sou h (COM-
SATS), Pakis an; Pon ificia Uni e sidad Ca ólica del Pe ú, Pe u; Min-
is y o Science and Highe Educa ion and Na ional Science Cen e,
Poland; Ko ea Ins i u e o Science and Technology In o ma ion and
Na ional Resea ch Founda ion o Ko ea (NRF), Republic o Ko ea;
Minis y o Educa ion and Scien ific Resea ch, Ins i u e o A omic
Physics and Minis y o Resea ch and Inno a ion and Ins i u e
o A omic Physics, Romania; Join Ins i u e o Nuclea Resea ch
(JINR), Minis y o Educa ion and Science o he Russian Fede a-
ion, Na ional Resea ch Cen e Ku cha o Ins i u e, Russian Science
Founda ion and Russian Founda ion o Basic Resea ch, Russia;
Minis y o Educa ion, Science, Resea ch and Spo o he Slo ak
Republic, Slo akia; Na ional Resea ch Founda ion o Sou h A ica,
Sou h A ica; Swedish Resea ch Council (VR) and Knu & Alice
Wallenbe g Founda ion (KAW), Sweden; Eu opean O ganiza ion o
Nuclea Resea ch, Swi ze land; Su ana ee Uni e si y o Technology
(SUT), Na ional Science and Technology De elopmen Agency (NS-
DTA) and Office o he Highe Educa ion Commission unde NRU
p ojec o Thailand, Thailand; Tu kish A omic Ene gy Au ho i y
(TAEK), Tu key; Na ional Academy o Sciences o Uk aine, Uk aine;
Science and Technology Facili ies Council (STFC), Uni ed Kingdom;
Na ional Science Founda ion o he Uni ed S a es o Ame ica (NSF)
and Uni ed S a es Depa men o Ene gy, Office o Nuclea Physics
(DOE NP), Uni ed S a es o Ame ica.
Re e ences
[1] STAR Collabo a ion, J. Adams, e al., Expe imen al and heo e ical challenges in
he sea ch o he qua k gluon plasma: he STAR Collabo a ion’s c i ical assess-
men o he e idence om RHIC collisions, Nucl. Phys. A 757 (2005) 102–183,
a Xi :nucl -ex /0501009 [nucl -ex].
[2] PHENIX Collabo a ion, K. Adcox, e al., Fo ma ion o dense pa onic ma e
in ela i is ic nucleus-nucleus collisions a RHIC: expe imen al e alua ion by
he PHENIX Collabo a ion, Nucl. Phys. A 757 (2005) 184–283, a Xi :nucl -ex /
0410003 [nucl -ex].
[3] BRAHMS Collabo a ion, I. A sene, e al., Qua k gluon plasma and colo glass
condensa e a RHIC? The pe spec i e om he BRAHMS expe imen , Nucl.
Phys. A 757 (12) (2005) 1–27, h p://www.sciencedi ec .com /science /a icle /pii /
S0375947405002770, Fi s Th ee Yea s o Ope a ion o RHIC.
[4] PHOBOS Collabo a ion, B.B. Back, e al., The PHOBOS pe spec i e on disco e ies
a RHIC, Nucl. Phys. A 757 (2005) 28–101, a Xi :nucl -ex /0410022 [nucl -ex].
[5] U. Heinz, C. Shen, H. Song, The iscosi y o qua k-gluon plasma a RHIC and
he LHC, AIP Con . P oc. 1441 (1) (2012) 766–770, a Xi :1108 .5323 [nucl - h].
[6] STAR Collabo a ion, J. Adams, e al., Azimu hal aniso opy in Au+Au collisions a
√sNN =200 GeV, Phys. Re . C 72 (2005) 014904, a Xi :nucl -ex /0409033 [nucl -
ex].
[7] ALICE Collabo a ion, K. Aamod , e al., Ha monic decomposi ion o wo-pa icle
angula co ela ions in Pb–Pb collisions a
√sNN =2.76 TeV, Phys. Le . B 708
(2012) 249–264, a Xi :1109 .2501 [nucl -ex].
[8] U. Heinz, R. Snellings, Collec i e flow and iscosi y in ela i is ic hea y-ion col-
lisions, Annu. Re . Nucl. Pa . Sci. 63 (2013) 123–151, a Xi :1301.2826 [nucl - h].
[9] ALICE Collabo a ion, K. Aamod , e al., Ellip ic flow o cha ged pa icles in Pb–
Pb collisions a 2.76 TeV, Phys. Re . Le . 105 (2010) 252302, a Xi :1011.3914
[nucl -ex].
[10] H. Song, S.A. Bass, U. Heinz, T. Hi ano, C. Shen, 200 A GeV Au+Au collisions
se e a nea ly pe ec qua k-gluon liquid, Phys. Re . Le . 106 (2011) 192301,
a Xi :1011.2783, E a um: Phys. Re . Le . 109 (2012) 139904.
[11] C. Shen, U. Heinz, Collision ene gy dependence o iscous hyd odynamic flow
in ela i is ic hea y-ion collisions, Phys. Re . C 85 (2012) 054902, a Xi :1202 .
6620 [nucl - h], E a um: Phys. Re . C 86 (2012) 049903.
[12] ALICE Collabo a ion, S. Acha ya, e al., Sys ema ic s udies o co ela ions be-
ween di e en o de flow ha monics in Pb–Pb collisions a
√sNN = 2.76 TeV,
Phys. Re . C 97 (2) (2018) 024906, a Xi :1709 .01127 [nucl -ex].
[13] J. Au inen, J.E. Be nha d, S.A. Bass, I. Ka penko, In es iga ing he collision
ene gy dependence o η/sin he beam ene gy scan a he BNL ela i is ic
hea y ion collide using Bayesian s a is ics, Phys. Re . C 97 (Ap 2018) 044905,
h ps://link.aps .o g /doi /10 .1103 /PhysRe C .97.044905.
[14] J.E. Be nha d, J.S. Mo eland, S.A. Bass, J. Liu, U. Heinz, Applying Bayesian pa-
ame e es ima ion o ela i is ic hea y-ion collisions: simul aneous cha ac e -
iza ion o he ini ial s a e and qua k-gluon plasma medium, Phys. Re . C 94 (2)
(2016) 024907, a Xi :1605 .03954 [nucl - h].
[15] S. Ga in, M. Abdel-Aziz, Measu ing shea iscosi y using ans e se momen um
co ela ions in ela i is ic nuclea collisions, Phys. Re . Le . 97 (2006) 162302,
a Xi :nucl - h /0606061 [nucl - h].
[16] STAR Collabo a ion, G. Agakishie , e al., E olu ion o he di e en ial ans e se
momen um co ela ion unc ion wi h cen ali y in Au+Au collisions a
√sNN =
200 GeV, Phys. Le . B 704 (2011) 467–473, a Xi :1106 .4334 [nucl -ex].
[17] S. Ra an, P. Pujaha i, S. P asad, C.A. P uneau, Co ec ing co ela ion unc ion
measu emen s, Phys. Re . C 89 (2) (2014) 024906, a Xi :1311.3915 [nucl -ex].
[18] ALICE Collabo a ion, S. Acha ya, e al., Two-pa icle di e en ial ans e se mo-
men um and numbe densi y co ela ions in p–Pb and Pb–Pb a he LHC, Phys.
Re . C 100 (Oc 2019) 044903, a Xi :1805 .04422 [nucl -ex].
[19] V. Gonzalez, A. Ma in, P. Lad on De Gue a a, J. Pan, S. Basu, C. P uneau, E ec
o cen ali y bin wid h co ec ions on wo-pa icle numbe and ans e se mo-
men um di e en ial co ela ion unc ions, Phys. Re . C 99 (3) (2019) 034907,
a Xi :1809 .04962 [physics .da a -an].
[20] M. Sha ma, C.A. P uneau, Me hods o he s udy o ans e se momen um di -
e en ial co ela ions, Phys. Re . C 79 (2009) 024905, a Xi :0810 .0716 [nucl -
ex].
[21] ALICE Collabo a ion, K. Aamod , e al., The Alice expe imen a he CERN
LHC, J. Ins um. 3(08) (2008), S08002,
h p://s acks .iop .o g /1748 -0221 /3 /i =08 /
a =S08002.
[22] ALICE Collabo a ion, B. Abele , e al., Pe o mance o he Alice expe imen a
he CERN LHC, In . J. Mod. Phys. A 29 (2014) 1430044, a Xi :1402 .4476 [nucl -
ex].
[23] ALICE Collabo a ion, B. Abele , e al., Cen ali y de e mina ion o Pb–Pb col-
lisions a √sNN = 2.76 TeV wi h Alice, Phys. Re . C 88 (4) (2013) 044909,
a Xi :1301.4361 [nucl -ex].
[24] X.-N. Wang, M. Gyulassy, HIJING: a Mon e Ca lo model o mul iple je p oduc-
ion in p p, p A and A A collisions, Phys. Re . D 44 (1991) 3501–3516.
[25] R. B un, F. B uyan , F. Ca mina i, S. Giani, M. Mai e, A. McPhe son, G. Pa ick,
L. U ban, GEANT: De ec o Desc ip ion and Simula ion Tool, Oc 1994, CERN
P og am Lib a y, CERN, Gene a, 1993,
h p://cds .ce n .ch / eco d /1082634, Long
W i eup W5013.
[26] R. Ba low, Sys ema ic e o s: ac s and fic ions, in: Ad anced S a is ical Tech-
niques in Pa icle Physics, P oceedings, Con e ence, Du ham, UK, Ma ch 18-22,
2002, 2002, pp. 134–144, a Xi :hep -ex /0207026 [hep -ex], h p://www.ippp .du .
ac .uk /Wo kshops /02 /s a is ics /p oceedings //ba low.pd .
[27] ALICE Collabo a ion, J. Adam, e al., Anomalous e olu ion o he nea -side je
peak shape in Pb–Pb collisions a √sNN = 2.76 TeV, Phys. Re . Le . 119 (10)
(2017) 102301, a Xi :1609 .06643 [nucl -ex].
[28] ALICE Collabo a ion, J. Adam, e al., E olu ion o he longi udinal and azimu hal
s uc u e o he nea -side je peak in Pb–Pb collisions a √sNN =2.76 TeV,
Phys. Re . C 96 (3) (2017) 034904, a Xi :1609 .06667 [nucl -ex].
[29] S. Ga in, G. Moschelli, Viscosi y and he so idge a RHIC, J. Phys. G 35 (2008)
104084, a Xi :0806 .4366 [nucl - h].
[30] ALICE Collabo a ion, B. Abele , e al., Cha ge co ela ions using he balance
unc ion in Pb–Pb collisions a √sNN = 2.76 TeV, Phys. Le . B 723 (2013)
267–279, a Xi :1301.3756 [nucl -ex].
[31] ALICE Collabo a ion, J. Adam, e al., Mul iplici y and ans e se momen um
e olu ion o cha ge-dependen co ela ions in pp, p–Pb, and Pb–Pb collisions
a he LHC, Eu . Phys. J. C 76 (2) (2016) 86, a Xi :1509 .07255 [nucl -ex].
8ALICE Collabo a ion / Physics Le e s B 804 (2020) 135375
[32] CMS Collabo a ion, S. Cha chyan, e al., Measu emen o je agmen a ion in
PbPb and pp collisions a
√sNN =2.76 TeV, Phys. Re . C 90 (2) (2014) 024908,
a Xi :1406 .0932 [nucl -ex].
[33] F. Beca ini, The qua k gluon plasma and ela i is ic hea y ion collisions in he
LHC e a, J. Phys. Con . Se . 527 (2014) 012012.
[34] ALICE Collabo a ion, K. Aamod , e al., Two-pion Bose-Eins ein co ela ions in
cen al Pb–Pb collisions a
√sNN = 2.76 TeV, Phys. Le . B 696 (2011) 328–337,
a Xi :1012 .4035 [nucl -ex].
[35] P. Ko un, D.T. Son, A.O. S a ine s, Viscosi y in s ongly in e ac ing quan um
field heo ies om black hole physics, Phys. Re . Le . 94 (2005) 111601, a Xi :
hep - h /0405231 [hep - h].
[36] STAR Collabo a ion, J. Adams, e al., T ans e se-momen um pTco ela ions on
(η, ϕ) om mean-pTfluc ua ions in Au–Au collisions a √sNN =200 GeV, J.
Phys. G 32 (2006) L37–L48, a Xi :nucl -ex /0509030 [nucl -ex].
[37] STAR Collabo a ion, J. Adams, e al., The ene gy dependence o pTangula co -
ela ions in e ed om mean-pTfluc ua ion scale dependence in hea y ion
collisions a he SPS and RHIC, J. Phys. G 34 (2007) 451–466, a Xi :nucl -ex /
0605021 [nucl -ex].
[38] J.S. Mo eland, J.E. Be nha d, S.A. Bass, Es ima ing ini ial s a e and qua k-gluon
plasma medium p ope ies using a hyb id model wi h nucleon subs uc u e
calib a ed o p-Pb and Pb–Pb collisions a
√sNN =5.02 TeV, a Xi :1808 .02106
[nucl - h].
ALICE Collabo a ion
S. Acha ya141, D. Adamo á94, A. Adle 74, J. Adol sson80, M.M. Agga wal 99, G. Aglie i Rinella33,
M. Agnello30, N. Ag awal 10,53, Z. Ahammed141, S. Ahmad16, S.U. Ahn76, A. Akindino 91,
M. Al-Tu any106, S.N. Alam141, D.S.D. Albuque que122, D. Aleksand o 87, B. Alessand o58,
H.M. Al anda6, R. Al a o Molina71, B. Ali 16, Y. Ali 14, A. Alici 10,26,53, A. Alkin2, J. Alme21, T. Al 68,
L. Al enkampe 21, I. Al sybee 112, M.N. Anaam 6, C. And ei47, D. And eou33, H.A. And ews110,
A. And onic144, M. Angele i33, V. Anguelo 103, C. Anson15, T. An iˇ
ci´
c107, F. An ino i56, P. An onioli 53,
R. Anwa 125, N. Apadula 79, L. Aphece che114, H. Appelshäuse 68, S. A celli26, R. A naldi58, M. A a ia 79,
I.C. A sene20, M. A slandok103, A. Augus inus33, R. A e beck 106, S. Aziz 61, M.D. Azmi16, A. Badalà55,
Y.W. Baek 40, S. Bagnasco 58, X. Bai 106, R. Bailhache68, R. Bala 100, A. Baldisse i137, M. Ball 42,
S. Balouza104, R. Ba be a 27, L. Ba ioglio25, G.G. Ba na öldi 145, L.S. Ba nby93, V. Ba e 134, P. Ba alini6,
K. Ba h33, E. Ba sch68, F. Ba u aldi 28, N. Bas id134, S. Basu 143, G. Ba igne114, B. Ba yunya75,
D. Bau i48, J.L. Bazo Alba 111, I.G. Bea den88, C. Bedda63, N.K. Behe a60, I. Beliko 136,
A.D.C. Bell Hecha a ia144, F. Bellini33, R. Bellwied125, V. Belyae 92, G. Bencedi 145, S. Beole25,
A. Be cuci47, Y. Be dniko 97, D. Be enyi145, R.A. Be ens130, D. Be zano 58, M.G. Besoiu67, L. Be e 33,
A. Bhasin100, I.R. Bha 100, M.A. Bha 3, H. Bha 48, B. Bha acha jee41, A. Bianchi25, L. Bianchi25,
N. Bianchi51, J. Bielˇ
cík36, J. Bielˇ
cíko á94, A. Bilandzic104,117, G. Bi o145, R. Biswas3, S. Biswas3,
J.T. Blai 119, D. Blau87, C. Blume68, G. Boca 139, F. Bock 33,95, A. Bogdano 92, S. Boi 23, L. Boldizsá 145,
A. Bolozdynya92, M. Bomba a37, G. Bonomi140, H. Bo el137, A. Bo isso 92,144, H. Bossi 146, E. Bo a25,
L. B a ud68, P. B aun-Munzinge 106, M. B egan 121, M. B oz36, E.J. B ucken43, E. B una58,
G.E. B uno105, M.D. Buckland127, D. Budniko 108, H. Buesching68, S. Bu alino30, O. Bugnon 114,
P. Buhle 113, P. Buncic 33, Z. Bu helezi72,131, J.B. Bu 14, J.T. Bux on96, S.A. Bysiak118, D. Ca a i89,
A. Cali a106, E. Cal o Villa 111, R.S. Camacho44, P. Came ini24, A.A. Capon113, F. Ca nesecchi10,26,
R. Ca on137, J. Cas illo Cas ellanos137, A.J. Cas o130, E.A.R. Casula 54, F. Ca alano 30,
C. Ceballos Sanchez52, P. Chak abo y 48, S. Chand a141, W. Chang 6, S. Chapeland33, M. Cha ie 127,
S. Cha opadhyay141, S. Cha opadhyay109, A. Chau in23, C. Cheshko 135, B. Cheynis135,
V. Chiban e Ba oso 33, D.D. Chinella o122, S. Cho60, P. Chochula 33, T. Chowdhu y 134, P. Ch is akoglou 89,
C.H. Ch is ensen 88, P. Ch is iansen80, T. Chujo 133, C. Cicalo 54, L. Ci a elli10,26, F. Cindolo 53,
J. Cleymans124, F. Colama ia 52, D. Colella 52, A. Collu79, M. Colocci 26, M. Concas58,ii,
G. Conesa Balbas e 78, Z. Conesa del Valle 61, G. Con in24,127, J.G. Con e as36, T.M. Co mie 95,
Y. Co ales Mo ales25, P. Co ese 31, M.R. Cosen ino123, F. Cos a 33, S. Cos anza139, P. C oche 134,
E. Cuau le69, P. Cui 6, L. Cunquei o95, D. Dab owski142, T. Dahms 104,117, A. Dainese 56,
F.P.A. Damas 114,137, M.C. Danisch103, A. Danu67, D. Das109, I. Das 109, P. Das 85, P. Das 3, S. Das3,
A. Dash85, S. Dash48, S. De 85, A. De Ca o29, G. de Ca aldo52, J. de Cu eland38, A. De Falco23,
D. De G u ola10, N. De Ma co58, S. De Pasquale 29, S. Deb 49, B. Debjani3, H.F. Degenha d 121,
K.R. Deja142, A. Delo 84, S. Delsan o25,131, D. De e ak106, P. Dhankhe 48, D. Di Ba i 32, A. Di Mau o 33,
R.A. Diaz8, T. Die el 124, P. Dillensege 68, Y. Ding 6, R. Di ià 33, D.U. Dixi 19, Ø. Dju sland21,
U. Dmi ie a62, A. Dob in33,67, B. Dönigus68, O. Do dic20, A.K. Dubey141, A. Dubla106, S. Dudi 99,
M. Dukhishyam85, P. Dupieux134, R.J. Ehle s 146, V.N. Eikeland21, D. Elia 52, H. Engel74, E. Epple 146,
B. E azmus114, F. E ha d 98, A. E okhin112, M.R. E sdal21, B. Espagnon 61, G. Eulisse33, D. E ans 110,
S. E dokimo 90, L. Fabbie i104,117, M. Faggin 28, J. Fai e78, F. Fan 6, A. Fan oni51, M. Fasel 95,
P. Fecchio 30, A. Feliciello58, G. Feofilo 112, A. Fe nández Téllez44, A. Fe e o137, A. Fe e i25,
A. Fes an i33, V.J.G. Feuilla d103, J. Figiel118, S. Filchagin108, D. Finogee 62, F.M. Fionda 21, G. Fio enza 52,