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S udy o J/ψ azimu hal aniso opy a o wa d apidi y in Pb-Pb collisions a √sNN = 5.02
TeV
© Au ho s, 2019
Published e sion
ALICE Collabo a ion
ALICE Collabo a ion. (2019). S udy o J/ψ azimu hal aniso opy a o wa d apidi y in Pb-Pb
collisions a √sNN = 5.02 TeV. Jou nal o High Ene gy Physics, 2019(12), A icle 012.
h ps://doi.o g/10.1007/jhep02(2019)012
2019
JHEP02(2019)012
Published o SISSA by Sp inge
Recei ed:Decembe 16, 2018
Re ised:Janua y 18, 2019
Accep ed:Janua y 20, 2019
Published:Feb ua y 4, 2019
S udy o J/ψazimu hal aniso opy a o wa d apidi y
in Pb-Pb collisions a √sNN = 5.02 TeV
The ALICE collabo a ion
E-mail: [email p o ec ed]
Abs ac : The second ( 2) and hi d ( 3) low ha monic coe icien s o J/ψmesons a e
measu ed a o wa d apidi y (2.5< y < 4.0) in Pb-Pb collisions a √sNN = 5.02 TeV wi h
he ALICE de ec o a he LHC. Resul s a e ob ained wi h he scala p oduc me hod and
epo ed as a unc ion o ans e se momen um, pT, o a ious collision cen ali ies. A
posi i e alue o J/ψ 3is obse ed wi h 3.7σsigni icance. The measu emen s, compa ed
o hose o p omp D0mesons and cha ged pa icles a mid- apidi y, indica e an o de ing
wi h n(J/ψ)< n(D0)< n(h±) (n = 2, 3) a low and in e media e pTup o 6 GeV/c
and a con e gence wi h 2(J/ψ)≈ 2(D0)≈ 2(h±) a high pTabo e 6–8 GeV/c. In semi-
cen al collisions (5–40% and 10–50% cen ali y in e als) a in e media e pTbe ween 2 and
6 GeV/c, he a io 3/ 2o J/ψmesons is ound o be signi ican ly lowe (4.6σ) wi h espec
o ha o cha ged pa icles. In addi ion, he compa ison o he p omp D0-meson a io in
he same pTin e al sugges s an o de ing simila o ha o he 2and 3coe icien s. The
J/ψ 2coe icien is u he s udied using he E en Shape Enginee ing echnique. The
ob ained esul s a e ound o be compa ible wi h he expec ed a ia ions o he eccen ici y
o he ini ial-s a e geome y.
Keywo ds: Had on-Had on sca e ing (expe imen s)
A Xi eP in : 1811.12727
Open Access, Copy igh CERN,
o he bene i o he ALICE Collabo a ion.
A icle unded by SCOAP3.
h ps://doi.o g/10.1007/JHEP02(2019)012
JHEP02(2019)012
Con en s
1 In oduc ion 1
2 Expe imen al se up and da a sample 3
3 Analysis 4
4 Sys ema ic unce ain ies 9
5 Resul s 11
6 Conclusions 14
A Flow coe icien s o combina o ial backg ound 16
The ALICE collabo a ion 23
1 In oduc ion
The s udy o collisions o ul a- ela i is ic hea y ions aims o cha ac e ize he Qua k-
Gluon Plasma (QGP), a s ongly coupled s a e o ma e comp ising o decon ined qua ks
and gluons. One o he main ea u es o hea y-ion collisions is he aniso opic pa icle
low [1,2]. I a ises om ini ial collision geome y aniso opies being con e ed by he
p essu e g adien s o he QGP medium o inal-s a e pa icle momen um aniso opies.
The aniso opic low is desc ibed by he coe icien s no a Fou ie se ies decomposi ion o
he azimu hal dis ibu ion o he p oduced pa icles [3]
dN
dϕ∝1+2
∞
X
n=1
ncos[n(ϕ−Ψn)],(1.1)
whe e ϕis he azimu hal angle o he pa icle and Ψnis he n- h ha monic symme y plane
angle. The dominan second-o de low coe icien ( 2) is called ellip ic low and mos ly
o igina es om he almond-shaped o e lap a ea be ween he colliding nuclei in non-cen al
collisions. The hi d-o de low coe icien ( 3) is named iangula low and is gene a ed
by luc ua ions in he ini ial dis ibu ion o nucleons in he o e lap egion [4–8].
Hea y qua ks, in pa icula hei bound qua k-an iqua k s a es known as qua konia,
a e impo an p obes o he QGP. Hea y-qua k pai s a e c ea ed p io o he o ma ion
o he QGP h ough ha d pa on collisions and hus expe ience he ull e olu ion o he
sys em. Measu emen s o he J/ψnuclea modi ica ion ac o (RAA) as a unc ion o
cen ali y in Pb-Pb collisions a he LHC [9–11] a e ep oduced by anspo [12–14] and
s a is ical had oniza ion [15,16] models including pa ial o ull J/ψ( e)gene a ion by
– 1 –
JHEP02(2019)012
ecombina ion o he malized cha m qua ks. Such ( e)gene a ion componen is dominan a
low ans e se momen um (pT) as shown by he compa ison [11,17] o he RAA as unc ion
o pTwi h anspo model calcula ions. In he case o he s a is ical had oniza ion model,
he p oduced J/ψ e lec s he dynamics o he cha m qua ks a he QGP phase bounda y.
The measu ed pTspec a seem o suppo his idea [18]. Measu emen s o he azimu hal
aniso opies o J/ψp oduc ion in high-ene gy hea y-ion collisions can b ing new impo an
insigh s on he cha m qua k dynamics.
A ecen measu emen o he ellip ic low o J/ψa o wa d apidi y in cen al and semi-
cen al Pb-Pb collisions a he cen e o mass ene gy pe nucleon pai o √sNN = 5.02 TeV
indica es a signi ican posi i e 2coe icien [19]. This esul is compa ible wi h he hy-
po hesis o J/ψp oduc ion ia ecombina ion o he malized c and ¯c qua ks om he
QGP medium p edominan ly a low pT, bu he magni ude and he ans e se momen um
dependence o he 2coe icien di e signi ican ly om heo e ical calcula ions [12–14].
Mo eo e , he 2coe icien is ound o be qui e signi ican a high pT, in con as wi h
he expec a ions o small azimu hal asymme y o igina ing mainly om pa h-leng h de-
penden J/ψdissocia ion in he medium. Fu he mo e, a posi i e J/ψ 2coe icien a
in e media e and high pThas been obse ed in p-Pb collisions [20,21], in which nei he
a signi ican con ibu ion om cha m-qua k ecombina ion no sizable pa h-leng h e ec s
a e expec ed [22]. Recen measu emen s o D-meson azimu hal asymme y in Pb-Pb colli-
sions a e in e p e ed as collec i e beha io o he cha m qua ks a low pTand pa h-leng h
dependen cha m-qua k ene gy loss a high pT[23,24].
Hyd odynamic calcula ions [25] show ha n≈κnn o n = 2 and 3, whe e nis he
eccen ici y coe icien o he ini ial-s a e collision geome y. The pa ame e s κnencode
he esponse o he QGP medium and depend on he pa icle ype and mass as well as i s
ans e se momen um. A low pT, he low coe icien s o ligh - la ou ed pa icles inc ease
wi h inc easing pT[26,27]. This inc ease o ncoe icien s as a unc ion o pTdepends o
he pa icle mass and can be a ibu ed o he adial expansion o he QGP medium. A
3–4 GeV/c, he low coe icien s each a maximum. The posi ion o he maximum, di ided
by he numbe o cons i uen qua ks nq, does no dependen s ongly on he pa icle mass
as p edic ed by coalescence models [28]. Fu he mo e, he n alues a he maximum,
di ided by nq, a e simila o all measu ed ligh - la ou ed pa icles, wi h de ia ions o up
o ±20% be ween mesons and ba yons [27]. A high pTabo e 6–8 GeV/c, he obse ed
azimu hal aniso opy o he inal-s a e pa icles is belie ed o come om pa h-leng h de-
penden pa on ene gy loss inside he QGP. Calcula ions [29] show ha he co esponding
2and 3coe icien s exhibi app oxima ely linea dependence on 2and 3, espec i ely.
Ne e heless, he co ela ion be ween he low coe icien s and he ini ial-s a e eccen ici ies
is weake wi h espec o he hyd odynamic case, especially be ween 3and 3. In e es -
ingly, he pa icle-mass dependence o 2and 3appea s o be s ongly educed in he
a io 3/ 2in semi-cen al collisions o ligh - la o ed pa icles [27]. Whe he he abo e
conside a ions also hold o hea y qua ks and qua konia is an open ques ion whose answe
could help o unde s and he o igin o cha m qua k azimu hal aniso opies and cha ac e ize
hei in e ac ions wi h he lowing medium.
– 2 –
JHEP02(2019)012
In he p esen analysis, he J/ψ 2and 3coe icien s as well as he a io 3/ 2as a
unc ion o he ans e se momen um and he collision cen ali y a e measu ed. Whe e e
possible, he da a a e compa ed o exis ing mid- apidi y cha ged-pa icle (p edominan ly
π±) and p omp D0-meson esul s. In addi ion, he dependence o he J/ψ 2coe icien
on he ini ial-s a e condi ions is s udied wi h he E en Shape Enginee ing (ESE) ech-
nique [30]. Fluc ua ions in he ini ial-s a e ene gy densi y dis ibu ion lead o e en -by-
e en a ia ions o he low obse ed a a gi en cen ali y [31]. The ESE echnique consis s
o selec ing e en s wi h he same cen ali y bu di e en low and he e o e ini ial-s a e
geome y eccen ici y [32,33]. Recen ly, he ESE echnique has been applied o he mea-
su emen o mid- apidi y D-meson p oduc ion in Pb-Pb collisions a √sNN = 5.02 TeV [34].
The ob ained esul s indica e a co ela ion be ween he D-meson azimu hal aniso opy and
he low o ligh - la ou ed pa icles.
The J/ψmesons a e econs uc ed a o wa d apidi y (2.5< y < 4.0) ia hei µ+µ−
decay channel. The measu ed J/ψmesons o igina e om bo h p omp J/ψ(di ec and
om decays o highe -mass cha monium s a es) and non-p omp J/ψ( eed down om
b-had on decays) p oduc ion.
This le e is o ganized as ollows. A b ie desc ip ion o he ALICE appa a us and he
da a sample used is gi en in sec ion 2. Sec ion 3ou lines he employed analysis echnique.
The e alua ion o he sys ema ic unce ain ies is discussed in sec ion 4, while he esul s
a e epo ed in sec ion 5. Finally, conclusions a e p esen ed in sec ion 6.
2 Expe imen al se up and da a sample
The ALICE de ec o s essen ial o he p esen analysis a e b ie ly desc ibed below. A
ull o e iew o he ALICE appa a us and i s pe o mance can be ound in e s. [35,36].
The muon spec ome e , which co e s he pseudo apidi y ange -4 < η < -2.5, is used o
econs uc muon acks. The spec ome e consis s o a on abso be ollowed by i e
acking s a ions. The hi d s a ion is placed inside a dipole magne . The acking s a ions
a e complemen ed by wo igge s a ions loca ed downs eam behind an i on wall. The
Silicon Pixel De ec o (SPD) [37] is employed o econs uc he posi ion o he p ima y
e ex and o de e mine he low di ec ion. The SPD consis s o wo cylind ical laye s
co e ing |η|<2.0 and |η|<1.4, espec i ely. I is placed in he cen al ba el o ALICE.
The cen al ba el is ope a ed inside a solenoidal magne ic ield pa allel o he beam line.
The SPD is also used o econs uc he so-called ackle s, ack segmen s o med by he
clus e s in he wo SPD laye s and he p ima y e ex [38]. The V0 de ec o [39] consis s
o wo a ays o 32 scin illa o coun e s each, co e ing 2.8 < η < 5.1 (V0A) and -3.7 < η <
-1.7 (V0C), espec i ely. I p o ides he minimum-bias (MB) igge and is used o e en
selec ion and de e mina ion o collision cen ali y [40]. In addi ion, wo ungs en-qua z
neu on Ze o Deg ee Calo ime e s (ZDCs), ins alled 112.5 me e s om he in e ac ion poin
along he beam line on each side, a e used o e en selec ion.
The p esen analysis is based on he da a sample o Pb-Pb collisions collec ed by ALICE
in 2015 a √sNN = 5.02 TeV. The igge equi ed coincidence o MB and dimuon igge s.
The MB igge was p o ided by he V0 de ec o eques ing signals in bo h V0A and
– 3 –

JHEP02(2019)012
V0C a ays. The dimuon unlike-sign igge equi ed a leas a pai o opposi e-sign ack
segmen s in he muon igge s a ions. The ans e se momen um h eshold o he igge
algo i hm was se such ha he e iciency o muon acks wi h pT= 1 GeV/cis 50%. The
sample o single muons o like-sign dimuons we e collec ed using he same igge algo i hm,
bu equi ing a leas one ack segmen o a leas a pai o like-sign ack segmen s,
espec i ely. The in eg a ed luminosi y o he analyzed da a sample is abou 225 µb−1.
The beam-induced backg ound is il e ed ou o line by applying a selec ion based
on he V0 and he ZDC iming in o ma ion [41]. The in e ac ion pile-up is emo ed by
exploi ing he co ela ions be ween he numbe o clus e s in he SPD, he numbe o
econs uc ed SPD ackle s and he o al signal in he V0A and V0C de ec o s. The
p ima y e ex posi ion is equi ed o be wi hin ±10 cm om he nominal in e ac ion
poin along he beam di ec ion. The da a a e spli in in e als o collision cen ali y, which
is ob ained based on he o al signal in he V0A and V0C de ec o s [40].
The muon selec ion is iden ical o ha used in e . [20]. The dimuons a e econs uc ed
in he accep ance o he muon spec ome e (2.5< y < 4.0) and a e equi ed o ha e a
ans e se momen um be ween 0 and 12 GeV/c.
3 Analysis
The low coe icien s no he selec ed dimuons a e measu ed using he scala p oduc (SP)
me hod [2,42], in which hey a e calcula ed om he exp ession
n{SP}=hhunQSPD∗
nii
Rn
,
Rn=shQSPD
nQV0A∗
nihQSPD
nQV0C∗
ni
hQV0A
nQV0C∗
ni,
(3.1)
whe e un= exp(inϕ) is he uni low ec o o he dimuon, QSPD
n,QV0A
nand QV0C
na e he
e en low ec o s measu ed in he SPD, V0A and V0C de ec o s, espec i ely, and nis he
ha monic numbe . The b acke s h···ideno e an a e age o e all e en s, he double b acke s
hh···ii an a e age o e all pa icles in all e en s, and ∗ he complex conjuga e. The SPD
e en low ec o QSPD
nis calcula ed om he azimu hal dis ibu ion o he econs uc ed
SPD ackle s. The V0A and V0C e en low ec o s QV0A
nand QV0C
na e calcula ed om
he azimu hal dis ibu ion o he signal in he V0 de ec o . The componen s o all h ee
e en low ec o s a e co ec ed o non-uni o m de ec o accep ance and e iciency using
a ecen e ing p ocedu e (i.e. by sub ac ing o he Qn- ec o a e aged o e many e en s
om he Qn- ec o o each e en ) [43]. The denomina o Rnin he abo e equa ion is called
esolu ion and is ob ained as a unc ion o collision cen ali y. The gap in pseudo apidi y
be ween unand QSPD
n(|∆η|>1.0) supp esses sho - ange co ela ions (“non- low”), which
a e un ela ed o he azimu hal asymme y in he ini ial geome y and come om je s and
esonance decays [19]. In he ollowing, he n{SP}coe icien s a e deno ed as n.
The J/ψ low coe icien s a e ex ac ed by a i o he supe posi ion o he J/ψsignal
and he backg ound o he dimuon low coe icien s as a unc ion o he dimuon in a ian
– 4 –
JHEP02(2019)012
mass [44]
n(Mµµ) = NJ/ψ
NJ/ψ +NB
+−
J/ψ
n+NB
+−
NJ/ψ +NB
+−
B
n(Mµµ),(3.2)
whe e J/ψ
nis he low coe icien o he signal and B
nis he Mµµ-dependen low coe icien
o he backg ound. The NJ/ψ and NB
+−a e he signal and he backg ound dimuon yields,
espec i ely, as a unc ion o Mµµ. They a e ob ained by i ing he Mµµ dis ibu ion wi h
a mix u e o an ex ended C ys al Ball (CB2) unc ion o he J/ψsignal and a Va iable-
Wid h Gaussian (VWG) unc ion o he backg ound [45]. The J/ψpeak posi ion and wid h
a e le ee, while he CB2 ail pa ame e s a e ixed o he alues epo ed in e . [46].
The s a is ical unce ain ies o NJ/ψ and NB
+−a e no conside ed in he i o n(Mµµ),
gi en hei negligible con ibu ion o he s a is ical unce ain y o he J/ψ
ncoe icien . The
ψ(2S) signal is no included in he i o n(Mµµ) because o i s ex emely low signi icance
in cen al and semi-cen al collisions.
In p e ious measu emen s [19,20], he Mµµ dependence o he backg ound low coe -
icien s was pa ame e ized by an a bi a y unc ion. This app oach leads o an inc ease
o he s a is ical unce ain y o he J/ψ low coe icien s, because he pa ame e s o he
unc ion a e no ixed. Mo eo e , an addi ional sys ema ic unce ain y a ises om he
ac ha he unc ional o m o he backg ound dis ibu ion is unknown. In he p esen
analysis, we adop a di e en app oach. I is known ha , in collisions o hea y ions, he
dimuon backg ound in he icini y o he J/ψis mos ly combina o ial and can be desc ibed
sa is ac o ily wi h he e en -mixing echnique [9,17]. This echnique consis s in o ming
dimuons by combining muons om wo di e en e en s ha ing simila collision cen ali y.
The low coe icien s o he combina o ial backg ound a e ully de e mined by he low coe -
icien s o he single muons om which he backg ound dimuons a e o med. One can show
ha o any gi en kinema ical con igu a ion o he backg ound dimuon, i s low coe icien s
can be exp essed as
B
n(Mµµ) = h (1)
n(p(1)
T, η1) cos[n(ϕ1−ϕ)] + (2)
n(p(2)
T, η2) cos[n(ϕ2−ϕ)]iMµµ
h1+2
∞
P
m=1
(1)
m(p(1)
T, η1) (2)
m(p(2)
T, η2) cos[m(ϕ1−ϕ2)]iMµµ
,(3.3)
whe e (1)
n(p(1)
T, η1) and (2)
n(p(2)
T, η2) a e he low coe icien s o he wo muons as a unc ion
o hei ans e se momen a and pseudo apidi ies, ϕ1and ϕ2a e he azimu hal angles o
he wo muons and ϕis he azimu hal angle o he dimuon. The b acke s h···iMµµ deno e
an a e age o e all dimuons (p(1)
T,p(2)
T,η1,η2,ϕ1,ϕ2) ha belong o any gi en Mµµ
in e al. The de ails on he de i a ion o eq. (3.3) a e gi en in appendix A. In case o he
e en mixing, he nume a o in eq. (3.3) is calcula ed as
Du(1)
nQ(1),SPD
n
R(1)
n
cos(n(ϕ1−ϕ)) + u(2)
nQ(2),SPD
n
R(2)
n
cos(n(ϕ2−ϕ))EMµµ
,(3.4)
whe e u(1)
nand u(2)
na e he uni ec o o he wo muons, Q(1)
nand Q(2)
na e he SPD low
ec o s o he e en s con aining he wo muons, and R(1)
nand R(2)
na e hei esolu ions.
– 5 –
JHEP02(2019)012
The b acke s h···iMµµ deno e an a e age o e all mixed-e en dimuons belonging o any
gi en Mµµ in e al. The denomina o in eq. (3.3) e lec s he modi ica ion o he dimuon
yield due o he low o single muons. Since he e en low ec o s o he wo mixed e en s
a e no co ela ed, he mixed-e en dimuon yield is no modi ied by he single muon low.
Thus, he denomina o is ob ained di ec ly as he a io NB
+−/Nmix
+−, whe e Nmix
+−is he
numbe o mixed-e en unlike-sign dimuons as a unc ion o Mµµ. The a io is calcula ed
a e a p ope no maliza ion o Nmix
+−using he like-sign dimuons om he same and mixed
e en s. The no maliza ion ac o is ob ained as [17]
R
Mµµ
Nmix
+− Nsame
++ Nsame
−−
Nmix
++ Nmix
−−
dMµµ
R
Mµµ
Nmix
+−dMµµ
,(3.5)
whe e Nsame
++ (Nsame
−− ) and Nmix
++ (Nmix
−− ) a e he numbe s o like-sign (posi i e and nega i e
cha ges) same-e en and mixed-e en dimuons, espec i ely. The in eg al is calcula ed in
he in a ian mass in e al be ween 2.2 and 4.5 GeV/c2. Assuming a pu ely combina o ial
backg ound, he B
n(Mµµ) coe icien , ob ained wi h he e en -mixing p ocedu e desc ibed
abo e, is used di ec ly in o de o ix he backg ound e m o he i om eq. (3.2). All he
analysis s eps discussed in his sec ion a e pe o med sepa a ely in each conside ed dimuon
ans e se momen um and cen ali y in e al. The e en mixing and he no maliza ion o
Nmix
+−a e done in 5%-wide collision cen ali y in e als.
Examples o he Mµµ i and he mixed-e en dis ibu ion Nmix
+−as a unc ion o Mµµ
in se e al cen ali y and pTin e als a e shown in igu e 1. A low and in e media e pT,
he mixed-e en dis ibu ion desc ibes he dimuon backg ound on a pe cen le el wi h a
esidual di e ence p esumably o igina ing om he single muon low. Howe e , a high pT,
his di e ence becomes much la ge (up o ≈35% in he icini y o he J/ψmass in 8 <
pT<12 GeV/cand 30–50% cen ali y in e al) and goes beyond a possible single muon
low con ibu ion. This poin s o he p esence o a co ela ed dimuon backg ound. Such
a backg ound is belie ed o o igina e om p oduc ion o hea y- la o qua k pai s and o
become signi ican in semi-cen al and pe iphe al collisions a high pT[47,48].
Examples o he 2(Mµµ) i based on he analysis app oach desc ibed abo e a e p e-
sen ed in igu e 2. As can be seen, he i pe o ms qui e sa is ac o ily, wi h he mixed-e en
2coe icien being able o desc ibe he shape and ampli ude o he backg ound 2in he
en i e conside ed in a ian mass in e al om 1.5 o 4.5 GeV/c2. This is no su p ising
a low and in e media e pT, whe e he mixed-e en dimuon dis ibu ion desc ibes a he
p ecisely he backg ound dimuon dis ibu ion ( op and middle panels in igu es 1and 2).
Rema kably, howe e , he mixed-e en app oach pe o ms sa is ac o ily also a high pT
in semi-cen al collisions, whe e he con ibu ion o he co ela ed backg ound is signi i-
can (bo om igh panels in igu es 1and 2). Gi en ha he denomina o in eq. (3.3)
is ob ained as he a io NB
+−/Nmix
+−, his means ha he low coe icien o he co ela ed
backg ound is signi ican ly lowe han ha o he combina o ial one. The sys ema ic e ec
a ising om he p esence o he co ela ed backg ound and he co esponding unce ain ies
a e discussed in sec ion 4. The app oach desc ibed abo e pe o ms equally well also in case
– 6 –
JHEP02(2019)012
1.5 2 2.5 3 3.5 4 4.5
2
cCoun s / 50 MeV/
50
100
150
200
250
300
350
400
450
3
10×
Da a
To al i
Signal i
Backg ound i
E en mixing
= 5.02 TeV
NN
sALICE Pb-Pb 0-10%
<4.0y2.5< c<2 GeV/
T
p0<
)
2
c (GeV/
µµ
M
1.5 2 2.5 3 3.5 4 4.5
Ra io
0.96
0.98
1
1.02
Da a / To al i
Da a / E en mixing Backg ound i / E en mixing
1.5 2 2.5 3 3.5 4 4.5
2
cCoun s / 50 MeV/
50
100
150
200
250
3
10×
10-50%
c<2 GeV/
T
p0<
)
2
c (GeV/
µµ
M
1.5 2 2.5 3 3.5 4 4.5
Ra io
0.9
0.95
1
1.05
1.5 2 2.5 3 3.5 4 4.5
2
cCoun s / 50 MeV/
20
40
60
80
100
120
140
160
3
10×
0-10%
c<6 GeV/
T
p2<
)
2
c (GeV/
µµ
M
1.5 2 2.5 3 3.5 4 4.5
Ra io
0.96
0.98
1
1.02
1.04
1.5 2 2.5 3 3.5 4 4.5
2
cCoun s / 50 MeV/
20
40
60
80
100
3
10×
10-50%
c<6 GeV/
T
p2<
)
2
c (GeV/
µµ
M
1.5 2 2.5 3 3.5 4 4.5
Ra io
0.95
1
1.05
1.5 2 2.5 3 3.5 4 4.5
2
cCoun s / 50 MeV/
200
400
600
800
1000
1200
1400
1600 0-10%
c<12 GeV/
T
p6<
)
2
c (GeV/
µµ
M
1.5 2 2.5 3 3.5 4 4.5
Ra io
0.9
1
1.1
1.2
1.5 2 2.5 3 3.5 4 4.5
2
cCoun s / 50 MeV/
500
1000
1500
2000
2500 10-50%
c<12 GeV/
T
p6<
)
2
c (GeV/
µµ
M
1.5 2 2.5 3 3.5 4 4.5
Ra io
1
1.2
1.4
Figu e 1. (Colo online) The Mµµ dis ibu ion in low ( op panels), in e media e (middle panels)
and high (bo om panels) pTin e als o cen al (le panels) and semi-cen al ( igh panels)
collisions. The da a a e i ed o a combina ion o an ex ended C ys al Ball (CB2) unc ion o
he signal and a Va iable-Wid h Gaussian (VWG) unc ion o he backg ound. The dis ibu ions
a e compa ed o he ones ob ained wi h he e en -mixing echnique (see ex o de ails). Only
s a is ical unce ain ies a e shown.
– 7 –
JHEP02(2019)012
)c (GeV/
T
p
2 4 6 8 10
2
0
0.05
0.1
0.15
0.2 Unbiased
V0A
2
q20% low-
V0A
2
q20% high-
= 5.02 TeV
NN
sALICE Pb-Pb
<4.0y, 2.5<ψInclusi e J/
5-40%
)c (GeV/
T
p
2 4 6 8 10
(unbiased)
2
)/
V0A
2
q(low/high-
2
1−
0
1
2
V0A
2
low-qψJ/
V0A
2
high-qψJ/
σ1±: Fi
V0A
2
low-qψJ/
σ1±: Fi
V0A
2
high-qψJ/
V0A
2
low-q
±
µ
V0A
2
high-q
±
µ
= 5.02 TeV
NN
sALICE Pb-Pb
<4.0y2.5<
5-40%
Figu e 7. (Colo online) Le : he J/ψ 2as a unc ion o pT o shape selec ed and unbiased
samples in he 5–40% cen ali y in e al in Pb-Pb collisions a √sNN = 5.02 TeV. Poin s a e sligh ly
shi ed along he ho izon al axis o be e isibili y. S a is ical and sys ema ic unce ain ies a e
shown as ba s and boxes, espec i ely. Righ : a io o he J/ψ 2in lowes and highes qV0A
2e en -
shape classes and he unbiased sample. The shaded bands ep esen he esul wi h a cons an
unc ion ±1σ. The J/ψ esul s a e compa ed o he a ios o he single muons 2ob ained wi h
he same e en -shape classes.
6 Conclusions
In summa y, he ellip ic and iangula low coe icien s o inclusi e J/ψmesons a o wa d
apidi y ha e been measu ed in Pb-Pb collisions a √sNN = 5.02 TeV o e a b oad ange
o ans e se momen um and in a ious cen ali y in e als. This is he i s measu emen
o he 3coe icien o inclusi e J/ψp oduc ion, indica ing a posi i e alue wi h 3.7σ
signi icance o 0 < pT<12 GeV/c.
The ob ained inclusi e J/ψ 2and 3coe icien s as well as he a io 3/ 2a e compa ed
o he esul s o cha ged pa icles and p omp D0mesons a mid- apidi y. A low and
in e media e pT, he 2and 3 esul s exhibi an o de ing wi h he cha ged pa icles ha ing
la ges alues, ollowed by he p omp D0mesons and inally he J/ψha ing he smalles
alues. In semi-cen al collisions a in e media e pT, he J/ψ 3/ 2 a io is ound o be
signi ican ly lowe compa ed o ha o cha ged pa icles. Despi e he la ge unce ain ies,
he alues o he p omp D0 a io a e somewha lowe han he cha ged pa icles and highe
han he J/ψmesons, hin ing a a possible o de ing simila o ha obse ed o he 2and
3coe icien s.
A high pT, he 2o he cha ged pa icles, he p omp D0mesons and he J/ψseem
o con e ge o simila alues. The unce ain ies o he 3coe icien s do no allow one o
d aw i m conclusions abou hei con e gence, al hough he cen ali y- and pT-in eg a ed
J/ψ 3is compa ible wi h ha o high-pTcha ged pa icles.
The analysis using E en Shape Enginee ing echnique shows ha he J/ψ 2coe i-
cien s inc ease (dec ease) o classes o e en s wi h high (low) educed e en low ec o .
– 14 –

JHEP02(2019)012
Compa ed o single muons econs uc ed in he same apidi y in e al, he J/ψ esul s
a e ound compa ible wi h he expec ed a ia ions o he eccen ici y o he ini ial-s a e
geome y.
Acknowledgmen s
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 Collab-
o 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 Collab-
o a ion acknowledges he ollowing 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 Science and Wo ld Fede a-
ion o Scien is s (WFS), A menia; Aus ian Academy o Sciences and Na ionals i ung
¨u 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 ´ı ico e Tecnol´ogico (CNPq), Uni e sidade Fede al do Rio G ande
do Sul (UFRGS), Financiado a de Es udos e P oje os (Finep) and Funda¸c˜ao de Ampa o
`a Pesquisa do Es ado de S˜ao Paulo (FAPESP), B azil; Minis y o Science & Technology
o China (MSTC), Na ional Na u al Science Founda ion o China (NSFC) and Minis y o
Educa ion o China (MOEC) , China; Minis y o Science and Educa ion, C oa ia; Cen o
de Aplicaciones Tecnol´ogicas y Desa ollo Nuclea (CEADEN), Cubaene g´ıa, Cuba; Min-
is y o Educa ion, You h and Spo s o he Czech Republic, Czech Republic; The Danish
Council o Independen Resea ch — Na u al Sciences, he Ca lsbe g Founda ion and Dan-
ish Na ional Resea ch Founda ion (DNRF), Denma k; Helsinki Ins i u e o Physics (HIP),
Finland; Commissa ia `a l’Ene gie A omique (CEA) and Ins i u Na ional de Physique
Nucl´eai e e de Physique des Pa icules (IN2P3) and Cen e Na ional de la Reche che Sci-
en i ique (CNRS), F ance; Bundesminis e ium ¨u Bildung, Wissenscha , Fo schung und
Technologie (BMBF) and GSI Helmhol zzen um ¨u 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 O ice, 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
India (UGC) and Council o Scien i ic 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 Is 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 Applied Science (IIST),
Japan Socie y o he P omo ion o Science (JSPS) KAKENHI and Japanese Minis y o
Educa ion, Cul u e, Spo s, Science and Technology (MEXT), Japan; Consejo Nacional de
Ciencia (CONACYT) y Tecnolog´ıa, h ough Fondo de Coope aci´on In e nacional en Cien-
cia y Tecnolog´ıa (FONCICYT) and Di ecci´on Gene al de Asun os del Pe sonal Academico
(DGAPA), Mexico; Nede landse O ganisa ie oo We enschappelijk Onde zoek (NWO),
– 15 –
JHEP02(2019)012
Ne he lands; The Resea ch Council o No way, No way; Commission on Science and Tech-
nology o Sus ainable De elopmen in he Sou h (COMSATS), Pakis an; Pon i icia Uni-
e sidad Ca ´olica del Pe ´u, Pe u; Minis 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 i ic Resea ch, Ins i u e o A omic Physics and Romanian Na ional Agency o Sci-
ence, Technology and Inno a ion, 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 Re-
sea 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 ga-
niza ion o Nuclea Resea ch, Swi ze land; Na ional Science and Technology De elopmen
Agency (NSDTA), Su ana ee Uni e si y o Technology (SUT) and O ice o he Highe
Educa ion Commission unde NRU p ojec o Thailand, Thailand; Tu kish A omic Ene gy
Agency (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, O ice o
Nuclea Physics (DOE NP), Uni ed S a es o Ame ica.
A Flow coe icien s o combina o ial backg ound
The azimu hal dis ibu ion o he combina o ial backg ound dNB/dϕis a p oduc o he
azimu hal dis ibu ions o he single muons om which he backg ound dimuons a e o med.
Thus, using eq. (1.1) one ob ains
dNB
dϕ∝ 1+2
∞
X
n=1
(1)
n(p(1)
T,η1)cos[n(ϕ1−Ψn)]! 1+2
∞
X
m=1
(2)
m(p(2)
T,η2)cos[m(ϕ2−Ψm)]!
∝1+2
∞
X
n=1
(1)
n(p(1)
T,η1)cos[n(∆ϕ1+ϕ−Ψn)]
+2
∞
X
m=1
(2)
m(p(2)
T,η2)cos[m(∆ϕ2+ϕ−Ψm)] (A.1)
+4
∞
X
n=1
∞
X
m=1
(1)
n(p(1)
T,η1) (2)
m(p(2)
T,η2)cos[n(∆ϕ1+ϕ−Ψn)]cos[m(∆ϕ2+ϕ−Ψm)],
whe e (1)
n(p(1)
T, η1) and (2)
m(p(2)
T, η2) a e he low coe icien s o he wo muons as a unc ion
o hei ans e se momen a and pseudo apidi ies, ϕ1and ϕ2a e he azimu hal angles o
he wo muons, ϕis he azimu hal angle o he dimuon and ∆ϕ1,2=ϕ1,2−ϕ.
– 16 –
JHEP02(2019)012
The n- h o de low coe icien o he backg ound dimuon is hen calcula ed as
B
n(p(1)
T, p(2)
T, η1, η2, ϕ1, ϕ2) = hcos[n(ϕ−Ψn)]i=
2π
R0
dNB
dϕcos[n(ϕ−Ψn)]dϕ
2π
R0
dNB
dϕdϕ
.(A.2)
The denomina o in eq. (A.2) is ob ained as
2π+ 2
∞
X
n=1
(1)
n(p(1)
T, η1)In(∆ϕ1)+2
∞
X
m=1
(2)
m(p(2)
T, η2)Im(∆ϕ2)
+ 4
∞
X
n=1
∞
X
m=1
(1)
n(p(1)
T, η1) (2)
m(p(2)
T, η2)Inm(∆ϕ1,∆ϕ2),
(A.3)
whe e
In(∆ϕ1,2) =
2π
Z
0
cos[n(∆ϕ1,2+ϕ−Ψn)]dϕ= 0,(A.4)
Imn(∆ϕ1,∆ϕ2) =
2π
Z
0
cos[n(∆ϕ1+ϕ−Ψn)] cos[m(∆ϕ2+ϕ−Ψm)]dϕ
=(0,n6= m
πcos[n(∆ϕ1−∆ϕ2)],n=m.(A.5)
The nume a o in eq. (A.2) is ob ained as
2
∞
X
k=1
(1)
k(p(1)
T, η1)Jkn(∆ϕ1)+2
∞
X
m=1
(2)
m(p(2)
T, η2)Jmn(∆ϕ2)
+ 4
∞
X
k=1
∞
X
m=1
(1)
k(p(1)
T, η1) (2)
m(p(2)
T, η2)Jkmn(∆ϕ1,∆ϕ2),
(A.6)
whe e
Jkn(∆ϕ1,2) =
2π
Z
0
cos[k(∆ϕ1,2+ϕ−Ψk)] cos[n(ϕ−Ψn)]dϕ
=(0,k6= n
πcos[n∆ϕ1,2],k=n,(A.7)
Jkmn(∆ϕ1,∆ϕ2) =
2π
Z
0
cos[k(∆ϕ1+ϕ−Ψk)] cos[m(∆ϕ2+ϕ−Ψm)]
×cos[n(ϕ−Ψn)]dϕ= 0.(A.8)
– 17 –
JHEP02(2019)012
Combining eq. (A.2)–(A.8) yields
B
n(p(1)
T, p(2)
T, η1, η2, ϕ1, ϕ2) = (1)
n(p(1)
T, η1) cos[n(ϕ1−ϕ)] + (2)
n(p(2)
T, η2) cos[n(ϕ2−ϕ)]
1+2
∞
P
m=1
(1)
m(p(1)
T, η1) (2)
m(p(2)
T, η2) cos[m(ϕ1−ϕ2)]
.
(A.9)
Finally, he B
nas a unc ion o Mµµ is ob ained by a e aging he nume a o and
denomina o in eq. (A.9) o e all dimuons, which belong o a gi en Mµµ in e al:
B
n(Mµµ) = h (1)
n(p(1)
T, η1) cos[n(ϕ1−ϕ)] + (2)
n(p(2)
T, η2) cos[n(ϕ2−ϕ)]iMµµ
h1+2
∞
P
m=1
(1)
m(p(1)
T, η1) (2)
m(p(2)
T, η2) cos[m(ϕ1−ϕ2)]iMµµ
.(A.10)
The eq. (A.8) is de i ed assuming no co ela ion be ween di e en ha monic symme y
plane angles Ψ. While his is in gene al he case, he e a e some no iceable excep ions [59].
In ac , he signi ican co ela ion be ween he Ψ2and Ψ4angles leads o non-ze o J422. The
co esponding con ibu ion o he nume a o o eq. (A.10) o B
2is gi en app oxima ely by
1
2hcos[4(Ψ4−Ψ2)]ih (1)
4(p(1)
T, η1) (2)
2(p(2)
T, η2) cos[4(ϕ1−ϕ)−2(ϕ2−ϕ)]
+ (2)
4(p(2)
T, η2) (1)
2(p(1)
T, η1) cos[4(ϕ2−ϕ)−2(ϕ1−ϕ)]iMµµ ,
(A.11)
whe e he b acke s h···i deno e an a e age o e all e en s. The con ibu ion is es ima ed
as desc ibed in he ollowing. Fi s , he 2and 4coe icien s o single muons a e measu ed
wi h he SP me hod, a e aged o e pseudo apidi y and pa ame e ized as a unc ion o pT.
The ob ained pa ame e iza ions 2,4(pT) a e hen combined wi h opposi e-sign dimuons
(p(1)
T, p(2)
T, η1, η2, ϕ1, ϕ2) in he da a ou side he J/ψmass peak. The alues o hcos[4(Ψ4−
Ψ2)]i, which anges om 0 in cen al collisions o abou 0.8 in pe iphe al collisions, a e
aken om e . [59]. Finally, he magni ude o he e ec is calcula ed ia in e pola ion o
he esul s a he J/ψmass peak. In gene al, he magni ude is ound o be a he o de o
10−4, eaching a mos 7 ×10−4 o 0 < pT<2 GeV/cand he 30–50% cen ali y in e al.
A simila e ec is p esen in he nume a o o eq. (A.10) o B
3, due o he co ela ion
o he Ψ3and Ψ6angles. In p ac ice, howe e , his con ibu ion can be ce ainly neglec ed,
because o he small magni ude o he 6coe icien .
Open Access. This a icle is dis ibu ed unde he e ms o he C ea i e Commons
A ibu ion License (CC-BY 4.0), which pe mi s any use, dis ibu ion and ep oduc ion in
any medium, p o ided he o iginal au ho (s) and sou ce a e c edi ed.
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JHEP02(2019)012
The ALICE collabo a ion
S. Acha ya139, F.T.-. Acos a20, D. Adamo ´a93, A. Adle 74, J. Adol sson80, M.M. Agga wal98,
G. Aglie i Rinella34, M. Agnello31, N. Ag awal48, Z. Ahammed139, S.U. Ahn76, S. Aiola144,
A. Akindino 64, M. Al-Tu any104, S.N. Alam139, D.S.D. Albuque que121, D. Aleksand o 87,
B. Alessand o58, H.M. Al anda6, R. Al a o Molina72, Y. Ali15, A. Alici10,27,53, A. Alkin2,
J. Alme22, T. Al 69, L. Al enkampe 22, I. Al sybee 111, M.N. Anaam6, C. And ei47,
D. And eou34, H.A. And ews108, A. And onic142,104, M. Angele i34, V. Anguelo 102, C. Anson16,
T. An iˇci´c105, F. An ino i56, P. An onioli53, R. Anwa 125, N. Apadula79, L. Aphece che113,
H. Appelsh¨ause 69, S. A celli27, R. A naldi58, I.C. A sene21, M. A slandok102, A. Augus inus34,
R. A e beck104, M.D. Azmi17, A. Badal`a55, Y.W. Baek60,40, S. Bagnasco58, R. Bailhache69,
R. Bala99, A. Baldisse i135, M. Ball42, R.C. Ba al85, A.M. Ba bano26, R. Ba be a28, F. Ba ile52,
L. Ba ioglio26, G.G. Ba na ¨oldi143, L.S. Ba nby92, V. Ba e 132, P. Ba alini6, K. Ba h34,
E. Ba sch69, N. Bas id132, S. Basu141, G. Ba igne113, B. Ba yunya75, P.C. Ba zing21,
J.L. Bazo Alba109, I.G. Bea den88, H. Beck102, C. Bedda63, N.K. Behe a60, I. Beliko 134,
F. Bellini34, H. Bello Ma inez44, R. Bellwied125, L.G.E. Bel an119, V. Belyae 91, G. Bencedi143,
S. Beole26, A. Be cuci47, Y. Be dniko 96, D. Be enyi143, R.A. Be ens128, D. Be zano58,34,
L. Be e 34, P.P. Bhadu i139, A. Bhasin99, I.R. Bha 99, H. Bha 48, B. Bha acha jee41,
J. Bhom117, A. Bianchi26, L. Bianchi125, N. Bianchi51, J. Bielˇc´ık37, J. Bielˇc´ıko ´a93,
A. Bilandzic103,116, G. Bi o143, R. Biswas3, S. Biswas3, J.T. Blai 118, D. Blau87, C. Blume69,
G. Boca137, F. Bock34, A. Bogdano 91, L. Boldizs´a 143, A. Bolozdynya91, M. Bomba a38,
G. Bonomi138, M. Bono a34, H. Bo el135, A. Bo isso 142,102, M. Bo i127, E. Bo a26,
C. Bou jau88, L. B a ud69, P. B aun-Munzinge 104, M. B egan 120, T.A. B oke 69, M. B oz37,
E.J. B ucken43, E. B una58, G.E. B uno34,33, D. Budniko 106, H. Buesching69, S. Bu alino31,
P. Buhle 112, P. Buncic34, O. Busch131,i, Z. Bu helezi73, J.B. Bu 15, J.T. Bux on95, J. Cabala115,
D. Ca a i89, H. Caines144, A. Cali a104, E. Cal o Villa 109, R.S. Camacho44, P. Came ini25,
A.A. Capon112, W. Ca ena34, F. Ca nesecchi10,27, J. Cas illo Cas ellanos135, A.J. Cas o128,
E.A.R. Casula54, C. Ceballos Sanchez8, S. Chand a139, B. Chang126, W. Chang6, S. Chapeland34,
M. Cha ie 127, S. Cha opadhyay139, S. Cha opadhyay107, A. Chau in24, C. Cheshko 133,
B. Cheynis133, V. Chiban e Ba oso34, D.D. Chinella o121, S. Cho60, P. Chochula34,
T. Chowdhu y132, P. Ch is akoglou89, C.H. Ch is ensen88, P. Ch is iansen80, T. Chujo131,
S.U. Chung18, C. Cicalo54, L. Ci a elli10,27, F. Cindolo53, J. Cleymans124, F. Colama ia52,
D. Colella52, A. Collu79, M. Colocci27, M. Concas58,ii, G. Conesa Balbas e78, Z. Conesa del
Valle61, J.G. Con e as37, T.M. Co mie 94, Y. Co ales Mo ales58, P. Co ese32,
M.R. Cosen ino122, F. Cos a34, S. Cos anza137, J. C ko sk´a61, P. C oche 132, E. Cuau le70,
L. Cunquei o94,142, T. Dahms103,116, A. Dainese56, F.P.A. Damas113,135, S. Dani66,
M.C. Danisch102, A. Danu68, D. Das107, I. Das107, S. Das3, A. Dash85, S. Dash48, S. De49, A. De
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N. De Ma co58, S. De Pasquale30, R.D. De Souza121, H.F. Degenha d 120, A. Deis ing104,102,
A. Delo 84, S. Delsan o26, C. Deplano89, P. Dhankhe 48, D. Di Ba i33, A. Di Mau o34, B. Di
Ruzza56, R.A. Diaz8, T. Die el124, P. Dillensege 69, Y. Ding6, R. Di i`a34, Ø. Dju sland22,
A. Dob in34, D. Domenicis Gimenez120, B. D¨onigus69, O. Do dic21, A.K. Dubey139, A. Dubla104,
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M.A.S. Figue edo120, S. Filchagin106, D. Finogee 62, F.M. Fionda22, G. Fio enza52, F. Flo 125,
– 23 –