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Aniso opic low and low luc ua ions o iden i ied had ons in Pb–Pb collisions a √sNN
= 5.02 TeV
© CERN, o he bene i o he ALICE Collabo a ion. A icle unded by SCOAP3
Published e sion
ALICE Collabo a ion
ALICE Collabo a ion. (2023). Aniso opic low and low luc ua ions o iden i ied had ons in
Pb–Pb collisions a √sNN = 5.02 TeV. Jou nal o High Ene gy Physics, 2023(5), A icle 243.
h ps://doi.o g/10.1007/JHEP05(2023)243
2023
JHEP05(2023)243
Published o SISSA by Sp inge
Recei ed:June 22, 2022
Accep ed:Sep embe 1, 2022
Published:May 31, 2023
Aniso opic low and low luc ua ions o iden i ied
had ons in Pb–Pb collisions a √sNN = 5.02 TeV
The ALICE collabo a ion
E-mail: [email p o ec ed]
Abs ac : The i s measu emen s o ellip ic low o π±, K±, p+¯p, K0
S,Λ+Λ,φ,Ξ−+Ξ+,
and Ω−+ Ω+using mul ipa icle cumulan s in Pb–Pb collisions a √sNN = 5.02 TeV a e
p esen ed. Resul s ob ained wi h wo- ( 2{2}) and ou -pa icle cumulan s ( 2{4}) a e
shown as a unc ion o ans e se momen um, pT, o a ious collision cen ali y in e -
als. Combining he da a o bo h 2{2}and 2{4}also allows us o epo he i s
measu emen s o he mean ellip ic low, ellip ic low luc ua ions, and ela i e ellip ic low
luc ua ions o a ious had on species. These obse ables p obe he e en -by-e en eccen-
ici y luc ua ions in he ini ial s a e and he con ibu ions om he dynamic e olu ion
o he expanding qua k–gluon plasma. The cha ac e is ic ea u es obse ed in p e ious
pT-di e en ial aniso opic low measu emen s o iden i ied had ons wi h wo-pa icle co -
ela ions, namely he mass o de ing a low pTand he app oxima e scaling wi h he numbe
o cons i uen qua ks a in e media e pT, a e simila ly p esen in he ou -pa icle co ela-
ions and he combina ions o 2{2}and 2{4}. In addi ion, a pa icle species dependence
o low luc ua ions is obse ed ha could indica e a signi ican con ibu ion om inal s a e
had onic in e ac ions. The compa ison be ween expe imen al measu emen s and CoLBT
model calcula ions, which combine he a ious physics p ocesses o hyd odynamics, qua k
coalescence, and je agmen a ion, illus a es hei impo ance o e a wide pT ange.
Keywo ds: Collec i e Flow, Hea y Ion Expe imen s, Pa icle Co ela ions and Fluc ua-
ions
A Xi eP in : 2206.04587
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/JHEP05(2023)243
JHEP05(2023)243
Con en s
1 In oduc ion 1
2 Expe imen al se up 3
3 Analysis p ocedu e 4
3.1 E en and ack selec ion 4
3.2 Selec ion o π±,K±, and p+p5
3.3 Recons uc ion o φmesons 5
3.4 Recons uc ion o K0
Sand Λ+Λ6
3.5 Recons uc ion o Ξ−+Ξ+and Ω−+Ω+6
3.6 Flow obse ables 7
3.7 Flow ex ac ion me hods 7
4 Sys ema ic unce ain ies 9
5 Resul s 11
5.1 Mass o de ing and scaling p ope ies 12
5.2 Resul s on low luc ua ions 14
5.3 Compa ison wi h models 16
6 Summa y 20
The ALICE collabo a ion 27
1 In oduc ion
The p ima y goal o he ul a- ela i is ic hea y-ion collision p og amme a he La ge
Had on Collide (LHC) is o s udy he p ope ies o he qua k–gluon plasma (QGP), a
no el s a e o s ongly in e ac ing ma e a high empe a u es and ene gy densi ies [1,2].
S udies o he azimu hal aniso opy o pa icle p oduc ion ha e con ibu ed signi ican ly o
he cha ac e iza ion o he sys em c ea ed in hea y-ion collisions [3,4]. Aniso opic low
e lec s he con e sion o he ini ial s a e spa ial aniso opy in o inal s a e aniso opies in
momen um space. This ansla ion is acili a ed by in e ac ions be ween he cons i uen s
o he qua k–gluon plasma (QGP) [5–7] and a la e s ages, a e had onisa ion, be ween
he p oduced pa icles. Aniso opic low is quan i ied by s udying he azimu hal dis ibu-
ion o pa icles emi ed in he plane ans e se o he beam di ec ion [3]. This is usually
exp essed in e ms o a Fou ie se ies in he azimu hal angle ϕ[8,9] acco ding o
Ed3N
dp3=1
2π
d2N
pTdpTdη(1+2
∞
X
n=1
n(pT, η) cos[n(ϕ−Ψn)]),(1.1)
– 1 –
JHEP05(2023)243
whe e E,N,p,pT,ϕ, and ηa e he ene gy, yield, momen um, ans e se momen um,
azimu hal angle, and pseudo apidi y o pa icles, espec i ely, and Ψnis he azimu hal
angle o he symme y plane o o de n [10,11]. The ncoe icien s a e gi en by
n=hcos[n(ϕ−Ψn)]i,(1.2)
whe e hi deno e an a e age o e all pa icles in a single e en . The second Fou ie coe i-
cien , 2, is usually e e ed o as ellip ic low. I is he dominan ha monic in hea y-ion
collisions wi h la ge alues o impac pa ame e (i.e. non-cen al collisions). I s alue is
sensi i e o some o he basic anspo coe icien s o he QGP, e.g. he shea iscosi y
o e en opy densi y a io (η/s). The s udy o ellip ic low has been ins umen al in es-
ablishing he s ongly-coupled QGP pa adigm, i s in collisions a he Rela i is ic Hea y
Ion Collide (RHIC) [12–15] and, since 2010, in collisions a he La ge Had on Collide
(LHC) [16–18].
A ound he s a o he LHC hea y-ion p og am, i was ealised ha ellip ic low is also
a sensi i e p obe o he ini ial s a e o hea y-ion collisions [19]. I s magni ude luc ua es
om one e en o he o he , e lec ing he e en -by-e en luc ua ing ene gy-densi y p o-
iles o he nuclea o e lap egion p io o he o ma ion o he QGP. Ini ial e en -by-e en
geome y luc ua ions lead o he luc ua ions o e en-ha monic aniso opic low and gene -
a e non-ze o odd ha monics. In ac , he ini ial geome y luc ua ions lead o h k
ni 6=h nik
and he de elopmen o di e en o de symme y planes Ψnin di e en kinema ic egions
in pTo η[20–22]. Thus, a comp ehensi e in es iga ion o he inal s a e low luc ua ions
is c ucial o unde s anding he e en -by-e en ini ial geome y luc ua ions and hei im-
pac on he sys em dynamic e olu ion. S udies o cha ged pa icles in Pb–Pb collisions
a LHC ene gies indica ed non-Gaussian ini ial s a e luc ua ions and, consequen ly, made
i possible o cons ain hei p obabili y dis ibu ion unc ion (p.d. .) [23,24]. S udies o
low luc ua ions ha e so a been pe o med bo h expe imen ally and in heo e ical model
calcula ions o he measu emen s in eg a ed o e a la ge kinema ic ange [25–28]. On
he o he hand, a pT-di e en ial s udy, and in pa icula wi h iden i ied had ons, has no
been done be o e. These s udies can p o ide insigh s on he in e play be ween he expan-
sion o he sys em and i s la e-s age, highly-dissipa i e had onic phase, as well as pa icle
p oduc ion mechanisms.
Simila s udies in he pas o a ious low coe icien s ha e been pi o al in es ablish-
ing he need o include iscous co ec ions in hyd odynamic models and, consequen ly, in
cons aining he alue o η/s o be e y close o he conjec u ed lowe limi o 1/4πcalcu-
la ed o in ini ely s ongly coupled gauge heo ies ia he AdS/CFT co espondence [29].
De ailed s udies o how aniso opic low de elops o di e en pa icle species as a unc-
ion o pT o a ious cen ali y in e als (i.e. an es ima e o he deg ee o o e lap be ween
he wo colliding nuclei) o Pb–Pb collisions a LHC ene gies [26–28] con i med a numbe
o quali a i e ea u es al eady obse ed a RHIC [12–15]: he mass o de ing o na low
pTand he pa icle ype (i.e. mesons e sus ba yons) g ouping a in e media e pT. The
o me o igina es om he in e play be ween adial low and he aniso opic expansion o
he sys em because o a he malized expanding sou ce wi h a common low eloci y o he
p oduced pa icles [30], while he la e is in e p e ed as an indica ion o had on o ma ion
– 2 –
JHEP05(2023)243
ia qua k coalescence in his momen um ange [31,32]. These s udies also e ealed, o he
i s ime, simila quali a i e ea u es in he 1% mos cen al Pb–Pb collisions [27], a ca -
ego y o e en s known as ul acen al wi h no p e ailing ellipsoidal geome y. In addi ion,
new esul s on he non-linea low modes o highe ha monics [33] illus a ed unambigu-
ously ha he a o emen ioned ea u es can s ill be obse ed a e he non-linea esponse
o he sys em, he la e being p opo ional o he p oduc o lowe -o de ini ial spa ial
aniso opies [34–37].
All hese s udies elied on measu ing a ious low ha monics using a ia ions o wo-
pa icle co ela ion echniques. One o he disad an ages o such app oaches is ha hey a e
sensi i e o non- low e ec s, i.e. co ela ions be ween (mainly wo) pa icles no associa ed
wi h he common symme y plane. In o de o supp ess such con ibu ions, one could
measu e mul ipa icle cumulan s which need a la ge da a sample o each he same le el
o unce ain ies as o hei wo-pa icle coun e pa measu emen s. This is possible now
by combining he en i e da a se o Pb–Pb collisions a he cen e-o -mass ene gy pe
nucleon pai √sNN = 5.02 TeV om he LHC Run 2. Fu he mo e, he usage o highe -
o de cumulan s opens up he possibili y o s udy, o he i s ime, he pa icle species
dependence o low luc ua ions.
The i s measu emen s o ellip ic low and low luc ua ions using wo- and ou -pa icle
cumulan s o π±,K±, p+p,K0
S,Λ+Λ,φ,Ξ−+Ξ+, and Ω−+Ω+in Pb–Pb collisions a
√sNN = 5.02 TeV a e p esen ed in his a icle. Resul s ob ained wi h he gene ic ame-
wo k [38–40], which co ec s de ec o ine iciencies and non-uni o mi ies in he azimu hal
accep ance, a e epo ed o a wide ange o ans e se momen a (0.2< pT<6 GeV/c)
in he 10–60% cen ali y in e al. Cen ali y is exp essed as pe cen iles o he inelas ic
had onic c oss sec ion, wi h low pe cen age alues co esponding o head-on collisions.
The s udies a e pe o med sepa a ely o pa icles and an ipa icles, and he esul s a e
compa ible wi hin he s a is ical unce ain ies. The e o e, 2is he a e age be ween e-
sul s o pa icles and an ipa icles which o he es o he a icle will be deno ed as π±,
K±, p+p, e c.
This a icle is o ganized as ollows: he expe imen al se up is p esen ed in sec ion 2,
while he analysis p ocedu e, pa icle iden i ica ion (PID), econs uc ion me hods, and
low measu emen echniques a e desc ibed in sec ion 3. Sec ion 4ou lines he e alua ion
o sys ema ic unce ain ies. The 2o π±,K±, p+p,K0
S,Λ+Λ,φ,Ξ−+Ξ+, and Ω−+Ω+
and he co esponding low luc ua ions a e epo ed and compa ed o hyd odynamic cal-
cula ions in sec ion 5. The a icle concludes wi h a summa y in sec ion 6.
2 Expe imen al se up
The ALICE de ec o [41,42] has been designed o allow de ailed physics s udies unde
he ex eme condi ions c ea ed in hea y-ion collisions. ALICE consis s o a cen al ba el
ha con ains se e al de ec o s wi h ull o limi ed azimu hal co e age and a se o o wa d
de ec o s. The cen al egion is loca ed in a solenoid magne which gene a es up o a 0.5T
ield pa allel o he beam di ec ion.
– 3 –

JHEP05(2023)243
The main acking de ec o s, posi ioned in he cen al ba el, a e he Inne T acking
Sys em (ITS) [41] and he Time P ojec ion Chambe (TPC) [43]. The ITS consis s o six
laye s o silicon de ec o s employing h ee di e en echnologies. The wo inne mos laye s
a e Silicon Pixel De ec o s (SPD), ollowed by wo laye s o Silicon D i De ec o s (SDD).
Finally, he wo ou e mos laye s a e double-sided Silicon S ip De ec o s (SSD). The SPD
is also used o e en selec ion and e ex econs uc ion. The TPC su ounds he ITS and
is also employed o p ecise acking o cha ged pa icles and o pa icle iden i ica ion ia
he speci ic ene gy loss, dE/dx. The dE/dxis ex ac ed using a unca ed-mean p ocedu e,
esul ing in a dE/dx esolu ion o he 5%mos cen al Pb–Pb collisions o a ound 6.5%,
which imp o es o mo e pe iphe al collisions [42]. The de ec o p o ides a sepa a ion by a
leas 2 s anda d de ia ions (σ) o π±,K±, and p+pa pT<0.7 GeV/c and he possibili y
o iden i y pa icles on a s a is ical basis o pT>2 GeV/c [42]. The Time o Fligh de ec o
(TOF) [44] is loca ed a ound he TPC and is used o pa icle iden i ica ion by measu ing
he ligh ime o pa icles om he collision poin wi h a esolu ion o abou 80 ps [42]. The
s a ime o he TOF measu emen is p o ided by he T0 de ec o wi h a esolu ion o
abou 25 ps [42,45], wo a ays o Che enko coun e s co e ing he pseudo apidi y anges
−3.3< η < −3.0(T0C) and 4.6< η < 4.9(T0A), o om a combina o ial algo i hm
ha uses he pa icle a i al imes a he TOF de ec o i sel [42,44]. Bo h me hods o
es ima ing he s a ime a e ully e icien o he 60%mos cen al Pb–Pb collisions. The
TOF p o ides a 3σsepa a ion be ween π±–K±and K±–p+pup o pT= 2.5 GeV/c and
pT= 4 GeV/c, espec i ely [42]. The ITS, TPC, and TOF de ec o s co e he ull azimu h
wi hin |η|<0.9.
In he o wa d egion, wo scin illa o a ays (V0) [46] a e used o igge ing, e en
selec ion, and he de e mina ion o he collision cen ali y [47]. The V0 consis s o wo
sys ems, he V0C and V0A, posi ioned a −3.7< η < −1.7and 2.8< η < 5.1, espec i ely.
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 on each side, a e used o e en selec ion.
Mo e de ails on he ALICE se up and he pe o mance o he de ec o s can be ound
in e s. [41,42].
3 Analysis p ocedu e
3.1 E en and ack selec ion
The da a sample used in his analysis consis s o Pb–Pb collisions a √sNN = 5.02 TeV
eco ded by he ALICE de ec o in he yea s 2015 and 2018 LHC da a- aking campaigns.
A minimum bias igge was p o ided by equi ing signals in bo h V0A and V0C scin illa o
a ays. In addi ion, he sample o semi-cen al collisions was enhanced by an online selec-
ion based on he V0 signal ampli udes. Beam-induced backg ound e en s (i.e. beam–gas
in e ac ions) we e emo ed o line u ilizing he V0 and ZDC iming in o ma ion. Pileup o
collisions om di e en bunch c ossings in he TPC was ejec ed by compa ing mul iplici y
es ima es om he V0 de ec o o hose o acking de ec o s a mid apidi y, exploi ing he
di e ence in eadou imes be ween he sys ems. The p ima y e ex posi ion, de e mined
om acks econs uc ed in he ITS and TPC, was equi ed o be wi hin ±10 cm om he
– 4 –
JHEP05(2023)243
nominal in e ac ion poin along he beam di ec ion. These selec ion c i e ia we e me by
app oxima ely 245 million e en s in he 10–60% cen ali y in e al. The collision cen ali y
was es ima ed om he ampli udes o he signals measu ed in he V0 de ec o [47].
Cha ged-pa icle acks, used o measu e he 2o π±,K±, p+p,φ-mesons, and in-
clusi e cha ged pa icles, we e econs uc ed using he ITS and TPC wi hin |η|<0.8and
0.2< pT<10 GeV/c. Each ack was equi ed o ha e a minimum numbe o 70 TPC
space poin s (ou o a maximum o 159) wi h a χ2pe TPC space poin lowe han 4
and a leas 2 hi s in he ITS wi h a χ2pe ITS hi smalle han 36. Mo eo e , acks
wi h a dis ance o closes app oach (DCA) la ge han 2 cm in he longi udinal di ec-
ion we e ejec ed. In he ans e se plane, a pT-dependen DCA selec ion o he o m
0.0105+0.0350 p−1.1
Tcm was applied. These selec ion c i e ia lead o an e iciency o abou
80% o p ima y acks a pT>0.5 GeV/c and con amina ion om ake acks ( andom
associa ions o space poin s) and seconda y cha ged pa icles (i.e. pa icles o igina ing om
weak decays, con e sions, and seconda y had onic in e ac ions in he de ec o ma e ial) o
abou 5% a pT≈1 GeV/c.
3.2 Selec ion o π±,K±, and p+p
Pa icle iden i ica ion o π±,K±, and p+pis pe o med using he dE/dx om he TPC
and he ime o ligh om he TOF sys em, i a ailable. The iden i ica ion is based on
he no malised di e ence be ween he measu ed and he expec ed signal o a gi en species
(σTPC and σTOF, espec i ely). I uses he co ela ion be ween nσTPC and nσTOF in a
Bayesian app oach [48], whe e he signals con e ed in o p obabili ies a e olded wi h he
expec ed abundances (p io s) o each pa icle species. The minimal p obabili y h eshold
has been se o 0.95 o π±and 0.85 o K±and p+p. In addi ion, pa icles a e selec ed
by equi ing |nσTPC|<3and |nσTOF|<3 o each species in he whole pT ange. This
p ocedu e ensu es a high pu i y o he s udied sample, hus educing he unce ain ies
due o pa icle misiden i ica ion. The esul ing pu i y, es ima ed using Mon e Ca lo (MC)
simula ions, is highe han 95% o π± o 0.2< pT<10 GeV/c, abo e 80% o K± o
0.3< pT<6 GeV/c, and eaches alues la ge han 90% o p+p o 0.5< pT<6 GeV/c.
3.3 Recons uc ion o φmesons
The φmeson is econs uc ed in he decay channel φ→K++ K−wi h a b anching
a io o 49.2% [49]. I s decay p oduc s a e selec ed using he same c i e ia o p ima y
K±(see sec ion 3.2). The φmeson yield is ob ained om he in a ian mass (MK+K−)
econs uc ed om all possible K±pai s a e sub ac ing he combina o ial backg ound
e alua ed using he like-sign kaon pai s in each pTand cen ali y in e al. The esul ing
MK+K−dis ibu ion is pa ame ised as a sum o a B ei –Wigne (BW) dis ibu ion and
a hi d-o de polynomial unc ion ha accoun s o esidual con amina ion wi hin he
in a ian mass ange o 0.99 < MK+K−<1.07 GeV/c2. The pT-di e en ial yield o φ
mesons is ex ac ed by in eg a ion o he BW dis ibu ion and used o he 2ex ac ion
oge he wi h he backg ound yield (see eq. 3.14). The p ocedu e o he econs uc ion o
φmeson is iden ical o he p e ious measu emen s [28], while he ex ac ion o 2{4}(pT)
is sligh ly di e en and explained in sec ion 3.7.
– 5 –
JHEP05(2023)243
3.4 Recons uc ion o K0
Sand Λ+Λ
The econs uc ion o K0
Sand Λ+Λis based on iden i ying hei seconda y e ices called
V0s in he decay channels K0
S→π++π−and Λ→p + π−(Λ→p + π+) wi h b anching
a ios o 69.2% and 63.9% [49], espec i ely. Selec ion c i e ia ela ed o he dis inc i e V-
shaped decay opology and equi emen s on he cha ac e is ics o he daugh e pa icles a e
applied o supp ess he la ge combina o ial backg ound. The in a ian mass is calcula ed
assuming ha he daugh e pa icles, iden i ied using he TPC (|nσTPC|<3) o e he en i e
pT ange, a e ei he a π+π−pai o a pπ−(pπ+) pai . The V0candida es a e selec ed wi h
an in a ian mass be ween 0.4 and 0.6 GeV/c2 o K0
Sand 1.08 and 1.16 GeV/c2 o Λ+Λ.
The daugh e acks a e econs uc ed wi hin |η|<0.8using he same TPC ack quali y
equi emen s desc ibed in sec ion 3.1 o cha ged acks. In addi ion, he a io be ween he
numbe o space poin s and he numbe o c ossed ows in he TPC is equi ed o be la ge
han 0.8, he minimum DCA o daugh e acks o he p ima y e ex is 0.1 cm, and he
maximum DCA o daugh e acks o he seconda y e ex is 0.5 cm. Only V0candida es
p oduced a a adial dis ance be ween 5 and 100 cm om he beam line and wi h a cosine o
he poin ing angle ( he angle be ween he line connec ing he p ima y and V0 e ices and
he V0momen um ec o ) la ge han 0.998 a e accep ed. To educe he con amina ion
om Λ+Λand elec on–posi on pai s coming om γcon e sions, an addi ional selec ion
is applied in he A men e os–Podolanski a iables [50] o he K0
Scandida es, simila o
wha is done in e . [28]. To ob ain he pT-di e en ial yield o K0
Sand Λ+Λ, he in a ian
mass dis ibu ions in a ious pTin e als a e pa ame ised as a sum o wo Gaussian
dis ibu ions wi h he same mean and a hi d-o de polynomial unc ion which accoun s
o esidual backg ound. The K0
Sand Λ+Λyields a e ex ac ed by in eg a ion o he
Gaussian dis ibu ions and a e no co ec ed o eed-down om highe mass ba yons (e.g.
Ξ±,Ω±), bu hese ha e a negligible e ec on 2[26].
3.5 Recons uc ion o Ξ−+Ξ+and Ω−+Ω+
The Ξ−+Ξ+and Ω−+Ω+a e econs uc ed h ough he cascade opology o he ollowing
weak decays: Ξ−→Λ + π−(Ξ+→Λ + π+) and Ω−→Λ+K−(Ω+→Λ + K+) wi h
b anching a ios o 99.9% and 67.8% [49], espec i ely, wi h a subsequen Λ(Λ) decay.
Candida es a e ound by applying opological and kinema ic c i e ia i s o selec he V0
wi h an in a ian mass be ween 1.08 and 1.16 GeV/c2and hen o ma ch i wi h one o
he emaining seconda y acks. They a e selec ed by equi ing he DCA be ween he V0
and he ack o be less han 0.3 cm, he cosine o he poin ing angle o be a leas 0.999
and 0.998 o he cascade and V0, espec i ely, he DCA be ween he V0and p ima y
e ex o be la ge han 0.05 cm, he minimum DCA o V0daugh e acks o he p ima y
e ex o be 0.1 cm, he maximum DCA o V0daugh e acks o be 1.0 cm, and he
minimum DCA o he daugh e ack o he p ima y e ex o be 0.03 cm. Only Ξ−+Ξ+
and Ω−+Ω+candida es p oduced a a adial dis ance be ween 0.9 and 100 cm om he
beam line wi h he same adial dis ance epo ed in sec ion 3.4 o V0a e accep ed. Each
o he h ee daugh e acks is also equi ed o ha e pT>0.15 GeV/c wi hin |η|<0.8and
o pass he TPC ack quali y c i e ia de ailed abo e o cha ged acks. In addi ion, he
– 6 –
JHEP05(2023)243
daugh e acks a e checked o compa ibili y wi h he pion, kaon, o p o on hypo heses by
selec ing pa icles wi h |nσTPC|<3 o each species. The pT-di e en ial yield o Ξ−+Ξ+
and Ω−+Ω+is ob ained by i ing he in a ian mass dis ibu ions wi h a sum o wo
Gaussian dis ibu ions wi h he same mean and a hi d-o de polynomial unc ion ha
desc ibe he signal and he backg ound, espec i ely.
3.6 Flow obse ables
A common app oach o s udy he e en -by-e en low luc ua ions o a gi en low coe icien
is by using he wo- and mul ipa icle cumulan s [51,52], which ha e di e en sensi i i ies
o e ec s s emming om non- low and low luc ua ions,
n{2}=h 2
ni1/2+δn,(3.1)
n{4}=h2h 2
ni2−h 4
nii1/4,(3.2)
whe e δndeno es he wo-pa icle non- low e ec s.
Assuming ha low luc ua ion σ nis ela i ely small compa ed o n, which was
ound o be ue o non-cen al hea y-ion collisions a he LHC [53–55], and also assuming
ha non- low e ec s can be expe imen ally emo ed (o la gely supp essed, e.g. by using
app op ia e ηgaps) in wo-pa icle co ela ion measu emen s, he ncan be w i en as [56]
2
n{2}=h ni2+σ2
n,(3.3)
2
n{4} ≈ h ni2−σ2
n,(3.4)
whe e h niand σ na e he mean and luc ua ions o he aniso opic low coe icien , e-
spec i ely. These wo quan i ies co espond o he i s and second momen s o he e en -
by-e en ndis ibu ion. The obse able h niis expec ed o be ee om low luc ua ions
and o only e lec he ue ellip ic low om he low symme y plane.
Bo h h niand σ ncan be calcula ed using he measu ed n{2}and n{4}as
h ni ≈ s 2
n{2}+ 2
n{4}
2,(3.5)
σ n≈s 2
n{2}− 2
n{4}
2.(3.6)
Fu he mo e, he ela i e low luc ua ions F( n)a e de ined as
F( n) = σ n
h ni.(3.7)
3.7 Flow ex ac ion me hods
The measu emen o he pT-di e en ial ncoe icien s o iden i ied had ons is pe o med
using wo- and ou -pa icle cumulan me hod [51], acco ding o
n{2}(pT) = dn{2}
pcn{2},(3.8)
n{4}(pT) = −dn{4}
(−cn{4})3/4.(3.9)
– 7 –
JHEP05(2023)243
0 1 2 3 4 5
0
0.05
0.1
q
n / {4}
2
20%−10
0 1 2 3 4 5
0
0.05
0.1
30%−20
0 1 2 3 4 5
) c (GeV/
q
n /
T
p
0
0.05
0.1
q
n / {4}
2
40%−30
0 1 2 3 4 5
) c (GeV/
q
n /
T
p
0
0.05
0.1 50%−40
0 1 2 3 4 5
) c (GeV/
q
n /
T
p
0
0.05
0.1 60%−50
0 1 2 3 4 5
0
0.05
0.1
±
π
±
K
S
0
K
)p p(
±
π
±
K
S
0
K
)p p(
)Λ(Λ
φ
)Ξ(Ξ
)Ω(Ω
)Λ(Λ
φ
)Ξ(Ξ
)Ω(Ω
ALICE
= 5.02 TeV
NN
s
Pb −Pb
| < 0.8η|
Figu e 4. The dependence o 2{4}/nqon pT/nq, whe e nqis he numbe o cons i uen s qua ks,
o di e en pa icle species and cen ali ies in Pb–Pb collisions a √sNN = 5.02 TeV. The e ical
e o ba s and he illed boxes ep esen s a is ical and sys ema ic unce ain ies, espec i ely.
0 2 4 6 8 10
0
0.1
0.2
0.3
>
2
<
20%−10
0 2 4 6 8 10
0
0.1
0.2
0.3
30%−20
0 2 4 6 8 10
)c (GeV/
T
p
0
0.1
0.2
0.3
>
2
<
40%−30
0 2 4 6 8 10
)c (GeV/
T
p
0
0.1
0.2
0.3 50%−40
0 2 4 6 8 10
)c (GeV/
T
p
0
0.1
0.2
0.3 60%−50
0 2 4 6 8 10
0
0.1
0.2
0.3
±
h
±
π
±
K
S
0
K
±
h
±
π
±
K
S
0
K
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
ALICE
= 5.02 TeV
NN
s
Pb −Pb
| < 0.8η|
Figu e 5. The dependence o he mean alue o 2(h 2i) on pT o di e en pa icle species and
cen ali ies in Pb–Pb collisions a √sNN = 5.02 TeV. The e ical e o ba s and he illed boxes
ep esen s a is ical and sys ema ic unce ain ies, espec i ely.
5.2 Resul s on low luc ua ions
The measu emen s o 2wi h wo- and ou -pa icle cumulan s p o ide he i s oppo uni y
o in es iga e he i s momen s o he 2dis ibu ion o di e en pa icle species. Figu e 5
p esen s he mean alue o 2, deno ed as h 2i, as a unc ion o pT o he same combina ion
– 14 –

JHEP05(2023)243
0 2 4 6 8 10
0
0.05
0.1
0.15
2
σ
20%−10
0 2 4 6 8 10
0
0.05
0.1
0.15
30%−20
0 2 4 6 8 10
)c (GeV/
T
p
0
0.05
0.1
0.15
2
σ
40%−30
0 2 4 6 8 10
)c (GeV/
T
p
0
0.05
0.1
0.15 50%−40
0 2 4 6 8 10
)c (GeV/
T
p
0
0.05
0.1
0.15 60%−50
0 2 4 6 8 10
0
0.05
0.1
0.15
±
h
±
π
±
K
S
0
K
±
h
±
π
±
K
S
0
K
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
ALICE
= 5.02 TeV
NN
s
Pb −Pb
| < 0.8η|
Figu e 6. The pTdependence o he s anda d de ia ion o 2(σ 2) o di e en pa icle species
and cen ali ies in Pb–Pb collisions a √sNN = 5.02 TeV. The e ical e o ba s and he illed boxes
ep esen s a is ical and sys ema ic unce ain ies, espec i ely.
0 2 4 6 8 10
0
0.2
0.4
0.6
)
2
F(
20%−10
0 2 4 6 8 10
0
0.2
0.4
0.6
30%−20
0 2 4 6 8 10
)c (GeV/
T
p
0
0.2
0.4
0.6
)
2
F(
40%−30
0 2 4 6 8 10
)c (GeV/
T
p
0
0.2
0.4
0.6
50%−40
0 2 4 6 8 10
)c (GeV/
T
p
0
0.2
0.4
0.6
60%−50
0 2 4 6 8 10
0
0.2
0.4
0.6
±
h
±
π
±
K
S
0
K
±
h
±
π
±
K
S
0
K
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
ALICE
= 5.02 TeV
NN
s
Pb −Pb
| < 0.8η|
Figu e 7. The ela i e ellip ic low luc ua ions (F( 2)) as a unc ion o pT o di e en pa icle
species and cen ali ies in Pb–Pb collisions a √sNN = 5.02 TeV. The e ical e o ba s and he
illed boxes ep esen s a is ical and sys ema ic unce ain ies, espec i ely.
o had ons and cen ali y in e als as in he p e ious igu es. Assuming ha he non-
low con ibu ion in 2
2{2,|∆η|>0.8}is negligible [21,36], his mean alue is calcula ed
acco ding o eq. 3.5 by eplacing 2
2{2}wi h 2
2{2,|∆η|>0.8}measu emen .
Figu e 6p esen s he ans e se momen um dependence o he second momen o he
2dis ibu ion, i.e. he s anda d de ia ion σ 2, measu ed o he i s ime o di e en
– 15 –
JHEP05(2023)243
pa icle species. As in he p e ious case, assuming negligible non- low con ibu ion in
2
2{2,|∆η|>0.8},σ 2is app oxima ed acco ding o eq. 3.6. The da a poin s o bo h
h 2iand σ 2show, as expec ed, he same quali a i e ea u es as in he p e ious cases o
igu es 2and 3: namely he mass o de ing de eloping a low alues o pTand he pa icle
ype g ouping ha is e iden a highe pT.
Combining h 2iand σ 2, one can quan i y he ela i e 2 luc ua ions (F( 2)) acco d-
ing o eq. 3.7. This quan i y is displayed in igu e 7as a unc ion o pTand cen ali y
in e als o he a ious pa icle species p esen ed in his a icle. I can be seen ha o
cen al e en s, he e is no signi ican pTo pa icle species dependence. Howe e , o mo e
pe iphe al collisions, and in pa icula s a ing om he in e al 30–40% and abo e, he
da a poin s exhibi a non-mono onic ans e se momen um dependence, wi h a minimum
in F( 2) ha lies a highe alues o pT o ba yons han o mesons. In addi ion, he F( 2)
o ba yons in 1< pT<3 GeV/c is sys ema ically lowe han o mesons. In e es ingly,
he momen um egion whe e his appa en pa icle ype g ouping de elops o F( 2)does
no coincide wi h he egion whe e a simila g ouping is epo ed o measu emen s o 2.
This could poin o a di e en o igin o hese wo obse a ions. Fo pT>3 GeV/c, all
da a poin s con e ge in o a uni e sal band wi hin he unce ain ies. The o igin o his
cha ac e is ic beha iou o F( 2)is s udied using hyd odynamical models in he ollowing
sec ion.
Finally, o u he s udy he na u e o low luc ua ions, igu e 8p esen s he pT-
dependence o he a io 2{4}/ 2{2,|∆η|>0.8}. This a io is expec ed o be sensi i e
o he luc ua ions wi hin he pic u e o ini ial s a e models. Wi hin hese models, he
spa ial eccen ici y 2 luc ua es om e en o e en . These luc ua ions a e ans e ed
h ough he low iscosi y QGP o he inal s a e and a e imp in ed in how 2 luc ua es.
Since 2∝2, he a io 2{4}/ 2{2,|∆η|>0.8}is expec ed o e lec he a io be ween
2{4}and 2{2}, which ha e posi i e and nega i e con ibu ions om he ini ial eccen ici y
luc ua ions, and hus can p o ide s ong cons ain s on ini ial s a e models. I can be seen
ha o cen al collisions, his a io does no exhibi any signi ican pTo pa icle species
dependence. S a ing om he 20–30% cen ali y in e al, howe e , a dec ease in he a io
can be seen be ween 1 and 5 GeV/c. I becomes p og essi ely mo e p onounced o mo e
pe iphe al e en s. In addi ion, s a ing om he 30–40% cen ali y in e al, and simila o
he pic u e ha de elops o F( 2), he da a poin s indica e a pa icle ype g ouping, wi h
he alues o ba yons being sys ema ically la ge han he ones o mesons. This appa en
dependence on pa icle species highligh s ha inal s a e e ec s play a signi ican ole in
hese obse ables.
5.3 Compa ison wi h models
The compa ison o esul s om aniso opic low s udies wi h hyd odynamic calcula ions
has been ins umen al in cons aining some o he basic anspo coe icien s o he QGP.
Howe e , such compa isons we e limi ed un il now o he low pT egion, i.e. in anges whe e
he mass o de ing discussed in he p e ious sec ion is p ominen . One o he i s a emp s
o p o ide a uni ied physics pic u e h oughou he en i e ans e se momen um ange o
di e en pa icle species was p esen ed ecen ly in e . [60]. In his a icle, he au ho s
– 16 –
JHEP05(2023)243
0 2 4 6 8 10
0.6
0.8
1
1.2
| > 0.8}η∆{2,|
2
/
{4}
2
20%−10
0 2 4 6 8 10
0.6
0.8
1
1.2 30%−20
0 2 4 6 8 10
)c (GeV/
T
p
0.6
0.8
1
1.2
| > 0.8}η∆{2,|
2
/
{4}
2
40%−30
0 2 4 6 8 10
)c (GeV/
T
p
0.6
0.8
1
1.2 50%−40
0 2 4 6 8 10
)c (GeV/
T
p
0.6
0.8
1
1.2 60%−50
0 2 4 6 8 10
0.6
0.8
1
1.2
±
h
±
π
±
K
S
0
K
±
h
±
π
±
K
S
0
K
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
)p p(
)Λ(Λ
)Ξ(Ξ
)Ω(Ω
ALICE
= 5.02 TeV
NN
s
Pb −Pb
| < 0.8η|
Figu e 8. The a io 2{4}/ 2{2,|∆η|>0.8}as a unc ion o pT o di e en pa icle species and
cen ali ies in Pb–Pb collisions a √sNN = 5.02 TeV. The e ical e o ba s and he illed boxes
ep esen s a is ical and sys ema ic unce ain ies, espec i ely.
0 1 2 3 4 5 6 7 8 9 10
)c (GeV/
T
p
0
0.1
0.2
0.3
{4}
2
±
π
±
K
)p p(
±
π
±
K
)p p(
ALICE CoLBT
Hyd o+coal+ ag
= 5.02 TeV
NN
sPb −Pb
| < 0.8η|
20%−10
±
π
±
K
)pp(
0 1 2 3 4 5 6 7 8 9 10
)c (GeV/
T
p
0
0.1
0.2
0.3
{4}
2
±
π
±
K
)p p(
±
π
±
K
)p p(
ALICE CoLBT
Hyd o+coal+ ag
= 5.02 TeV
NN
sPb −Pb
| < 0.8η|
50%−40
±
π
±
K
)pp(
Figu e 9. The pT-di e en ial 2{4} o π±,K±, and p+pmeasu ed in Pb–Pb collisions a √sNN =
5.02 TeV compa ed wi h expec a ions o he same quan i y om he CoLBT hyd odynamic model
wi h qua k coalescence [60]. The le and igh panels p esen he compa ison o he 10–20% and
40–50% cen ali y in e als, espec i ely. The e ical e o ba s and he illed boxes ep esen
s a is ical and sys ema ic unce ain ies o he da a, espec i ely. The hickness o he model cu es
e lec he unce ain ies o he hyd odynamic calcula ions.
used he CoLBT hyd odynamic model [59] which allows o he simul aneous desc ip ion
o he e olu ion o pa on showe s and he bulk medium. The la e is p esc ibed by a
(3+1)-D iscous hyd odynamic model ha is ini ialized a τ0= 0.6 m/cand uses a alue
o speci ic shea iscosi y η/s = 0.10. The eeze-ou empe a u e is se o T o = 150 MeV,
beyond which a had onic a e -bu ne desc ibes he in e ac ions be ween had ons. The
emaining pa ame e s o he model we e adjus ed o ep oduce he measu ed yields, pT
– 17 –
JHEP05(2023)243
0 1 2 3 4 5 6 7 8 9 10
)c (GeV/
T
p
0
0.1
0.2
0.3
{4}
2
±
π
±
K
)p p(
±
π
±
K
)p p(
ALICE CoLBT
Hyd o+ ag
= 5.02 TeV
NN
sPb −Pb
| < 0.8η|
50%−40
±
π
±
K
)pp(
Figu e 10. The pT-di e en ial 2{4} o π±,K±, and p+pmeasu ed in Pb–Pb collisions a
√sNN = 5.02 TeV compa ed wi h expec a ions o he same quan i y om he CoLBT hyd odynamic
model wi hou qua k coalescence [60] in 40–50% cen ali y in e al. The e ical e o ba s and
he illed boxes ep esen s a is ical and sys ema ic unce ain ies o he da a, espec i ely. The
hickness o he model cu es e lec he unce ain ies o he hyd odynamic calcula ions.
0 1 2 3 4 5 6 7
0.1
0.2
0.3
>
2
<
±
π
±
K
)p p(
±
π
±
K
)p p(
ALICE
= 5.02 TeV
NN
sPb −Pb
| < 0.8η|
50%−40
(a)
0 1 2 3 4 5 6 7
)c (GeV/
T
p
0.05
0.1
0.15
2
σ
±
π
±
K
)p p(
CoLBT (b)
0 1 2 3 4 5 6 7
0.6
0.8
1
{2}
2
/ {4}
2
(c)
Hyd o+coal+ ag
0 1 2 3 4 5 6 7
)c (GeV/
T
p
0.2
0.4
0.6
0.8
)
2
F(
(d)
Figu e 11. The pT-di e en ial (a) h 2i, (b) σ 2, (c) 2{4}/ 2{2}, and (d) F( 2) o π±,K±, and
p+pmeasu ed in one indica i e cen ali y in e al (40–50%) o Pb–Pb collisions a √sNN = 5.02 TeV
compa ed wi h expec a ions o he same quan i ies om he CoLBT hyd odynamic model [60].
The e ical e o ba s and he illed boxes ep esen s a is ical and sys ema ic unce ain ies o he
da a, espec i ely. The hickness o he model cu es e lec he unce ain ies o he hyd odynamic
calcula ions.
spec a, and in eg a ed no uniden i ied cha ged had ons in Pb–Pb collisions. One o he
impo an ing edien s which is in oduced in his model is he way had ons eme ge, wi h
he ypical hyd odynamic eeze-ou a low pTbeing complemen ed by a qua k coalescence
p esc ip ion a in e media e pTand agmen a ion a high pT[60].
– 18 –
JHEP05(2023)243
Figu e 9p esen s he e olu ion o 2{4}as a unc ion o pT o π±,K±, and p+p o
wo cha ac e is ic cen ali y in e als, 10–20% (cen al) and 40–50% (pe iphe al), in he
le and igh panels, espec i ely. The measu emen s a e compa ed wi h he expec a ions
o he same pa icle species om he CoLBT hyd odynamic model, ep esen ed by he
shaded bands. I can be seen ha he model desc ibes he pTdependence o 2{4}o e he
en i e pT ange. In pa icula , a low alues o pT(<2–3 GeV/c) whe e he hyd odynamic
expansion o he medium plays a dominan ole, he model desc ibes bo h he inc ease as
a unc ion o pTand he mass o de ing. The 2{4} eaches a peak alue a a ound pT
≈3GeV/c o pions and kaons and a pT≈4GeV/c o p o ons, be o e dec easing a
high pT. This can be na u ally explained by he in e play be ween he hyd odynamical
expansion, had on p oduc ion h ough qua k coalescence, and je agmen a ion [60].
Wi hin he CoLBT model, he hyd odynamic con ibu ion o 2is dominan o all
pa icle species up o pT= 4 GeV/c, whe eas he je agmen a ion plays an inc easingly
impo an ole o pT>6 GeV/c. In he in e media e pT egion (4–6 GeV/c), qua k
coalescence con ibu es in CoLBT o he de elopmen o he alue o 2, e en hough in he
model his mechanism accoun s o less han 25%o he o al pa icle yield. This is because
he alue o 2 om coalescence is signi ican ly la ge han he 2 om agmen a ion up
o 6 GeV/c. The addi ional mechanism o he coalescence p esc ip ion in he model is
impo an o ep oduce he expe imen al esul s quan i a i ely and o p o ide he p ope
connec ion be ween he low and high pT egions. In he o me , he mass o de ing de elops,
while in he la e he agmen a ion is he dominan pa icle p oduc ion mechanism and
no signi ican pa icle species dependence is obse ed.
I is known ha nei he he hyd odynamic expansion no he agmen a ion alone
leads o he p ecise NCQ scaling de elopmen . Such con ibu ions in he inal 2could
consequen ly gi e a na u al explana ion o he signi ican de ia ion om a uni e sal NCQ
scaling obse ed in igu e 4. On he o he hand, he model calcula ion wi h only con-
ibu ions om hyd odynamic expansion and agmen a ion bu wi hou he con ibu ion
om qua k coalescence signi ican ly unde es ima es 2{4} o pTabo e 3 GeV/c o π±,
K±, shown in igu e 10. Ne e heless, he c ossing o 2o pions, kaons, and p o ons can
de elop acco ding o CoLBT wi h a combina ion o he hyd odynamic expansion coupled
only o je agmen a ion ( o de ails e e o igu e 4 in e . [60]). This migh challenge
he p e ailing idea discussed in he li e a u e (see, e.g., e . [61]) ha he c ossing can be
a ibu ed o qua k coalescence. I is impo an o no e ha he de elopmen o he c oss-
ing poin in he absence o coalescence in CoLBT a ises om a pa icle species-dependen
pT alue whe e agmen a ion becomes dominan o e hyd odynamics.
To u he in es iga e he coalescence con ibu ions on low luc ua ions, igu es 11
and 12 p esen he compa ison o he pT-di e en ial h 2i(panel a), σ 2(panel b),
2{4}/ 2{2}(panel c), and F( 2)(panel d) o π±,K±, and p+pwi h he calcula ion
om CoLBT model wi h he combina ions o hyd odynamics, qua k coalescence, and je
agmen a ion as well as wi h CoLBT model wi h only he combina ions o hyd odynamics
and je agmen a ion, espec i ely [60]. The 40–50% cen ali y in e al was chosen as
ep esen a i e o hese compa isons. The model wi hou qua k coalescence con ibu ion
desc ibes quali a i ely he ea u es and he pTdependence o he measu emen s, bu signi -
– 19 –

JHEP05(2023)243
0 1 2 3 4 5 6 7
0.1
0.2
0.3
>
2
<
±
π
±
K
)p p(
±
π
±
K
)p p(
ALICE
= 5.02 TeV
NN
sPb −Pb
| < 0.8η|
50%−40
(a)
0 1 2 3 4 5 6 7
)c (GeV/
T
p
0.05
0.1
0.15
2
σ
±
π
±
K
)p p(
CoLBT (b)
0 1 2 3 4 5 6 7
0.6
0.8
1
{2}
2
/ {4}
2
(c)
Hyd o+ ag
0 1 2 3 4 5 6 7
)c (GeV/
T
p
0.2
0.4
0.6
0.8
)
2
F(
(d)
Figu e 12. The pT-di e en ial (a) h 2i, (b) σ 2, (c) 2{4}/ 2{2}, and (d) F( 2) o π±,K±,
and p+pmeasu ed in one indica i e cen ali y in e al (40–50%) o Pb–Pb collisions a √sNN =
5.02 TeV compa ed wi h expec a ions o he same quan i ies om he CoLBT hyd odynamic model
wi hou qua k coalescence [60]. The e ical e o ba s and he illed boxes ep esen s a is ical
and sys ema ic unce ain ies o he da a, espec i ely. The hickness o he model cu es e lec he
unce ain ies o he hyd odynamic calcula ions.
ican ly unde es ima es h 2io pion and kaon o pTabo e 3 GeV/c. This is e y di e en
om wha has been obse ed in igu es 9and 11. Despi e he sizable unce ain ies o
CoLBT calcula ions, he con ibu ion om qua k coalescence seems non-negligible o σ 2,
2{4}/ 2{2}, and F( 2), when compa ing he calcula ions o hyd o+coal+ ag (shown in
igu e 11) and hyd o+ ag (shown in igu e 12).
6 Summa y
In summa y, he i s measu emen o pT-di e en ial ellip ic low using wo- and ou -
pa icle cumulan s o π±,K±, p+p,K0
S,Λ+Λ,φ,Ξ−+Ξ+, and Ω−+Ω+in Pb–Pb collisions
a √sNN = 5.02 TeV is p esen ed. The mean ellip ic low, ellip ic low luc ua ions, and
ela i e ellip ic low luc ua ions a e ob ained o a ious pa icle species. Di e ences in
he alue o ela i e low luc ua ions o di e en pa icle species a e obse ed, sugges ing
ha inal s a e had onic in e ac ions u he modi y he low luc ua ions. A dis inc mass
o de ing is ound in he 10–60% cen ali y in e al o pT<3 GeV/c, which a ises om he
in e play be ween he ellip ic and adial low. In he in e media e pT ange, he magni ude
o 2{4},h 2i, and σ 2 o ba yons is la ge han ha o mesons by abou 50%. In addi ion,
pa icles show an app oxima e cons i uen qua k scaling. This scaling is es ed o 2{4},
which is expec ed o measu e low wi h li le (o no) non- low con amina ion. NCQ scaling
desc ibes he da a no be e han ±20%, an accu acy simila o wha was epo ed o he
– 20 –
JHEP05(2023)243
2using wo-pa icle co ela ions. Fu he mo e, he ela i e low luc ua ion F( 2) o he
iden i ied had ons shows an appa en spli ing be ween ba yons and mesons o cen ali y
abo e 30%, which sugges s a signi ican ole o inal-s a e in e ac ions in de eloping his
obse able. Las bu no leas , CoLBT hyd odynamic calcula ions wi h he implemen a ion
o qua k coalescence desc ibe he measu emen s o e a la ge pT ange, which con i ms he
ele ance o he qua k coalescence had oniza ion mechanism in he pa icle p oduc ion in
Pb–Pb collisions a he LHC.
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 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 ac-
knowledges 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, 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 í ico 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; Bulga ian
Minis y o Educa ion and Science, wi hin he Na ional Roadmap o Resea ch In as uc-
u es 2020¿2027 (objec CERN), Bulga ia; Minis y o Educa ion o China (MOEC) , Min-
is y o Science & Technology o China (MSTC) and Na ional Na u al Science Founda ion
o China (NSFC), China; Minis y o Science and Educa ion and C oa ian Science Foun-
da 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 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 omique (CEA) and 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 i ique (CNRS), F ance; Bundesminis 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 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; Na ional Re-
sea ch and Inno a ion Agency — BRIN, Indonesia; Is i u o Nazionale di Fisica Nuclea e
(INFN), I aly; Japanese Minis y o Educa ion, Cul u e, Spo s, Science and Technol-
– 21 –
JHEP05(2023)243
ogy (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 nacional 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 (COMSATS), Pak-
is an; Pon i icia Uni e sidad Ca ólica del Pe ú, Pe u; Minis y o Educa ion and Science,
Na ional Science Cen e and WUT ID-UB, Poland; Ko ea Ins i u e o Science and Technol-
ogy 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, Minis y o
Resea ch and Inno a ion and Ins i u e o A omic Physics and Uni e si y Poli ehnica o
Bucha es , Romania; 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 o-
pean 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 (NSTDA), Thailand Sci-
ence Resea ch and Inno a ion (TSRI) and Na ional Science, Resea ch and Inno a ion Fund
(NSRF), Thailand; Tu kish Ene gy, Nuclea and Mine al Resea ch Agency (TENMAK),
Tu key; Na ional Academy o Sciences o Uk aine, Uk aine; Science and Technology Facil-
i 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. In addi ion, indi idual g oups o membe s ha e e-
cei ed suppo om: Ma ie Skłodowska Cu ie, Eu opean Resea ch Council, S ong 2020 —
Ho izon 2020 (g an nos. 950692, 824093, 896850), Eu opean Union; Academy o Finland
(Cen e o Excellence in Qua k Ma e ) (g an nos. 346327, 346328), Finland; P og ama
de Apoyos pa a la Supe ación del Pe sonal Académico, UNAM, Mexico.
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. SCOAP3suppo s
he goals o he In e na ional Yea o Basic Sciences o Sus ainable De elopmen .
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– 30 –

JHEP05(2023)243
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1A.I. Alikhanyan Na ional Science Labo a o y (Ye e an Physics Ins i u e) Founda ion, Ye e an,
A menia
2AGH Uni e si y o Science and Technology, C acow, Poland
3Bogolyubo Ins i u e o Theo e ical Physics, Na ional Academy o Sciences o Uk aine, Kie , Uk aine
4Bose Ins i u e, Depa men o Physics and Cen e o As opa icle Physics and Space Science
(CAPSS), Kolka a, India
5Cali o nia Poly echnic S a e Uni e si y, San Luis Obispo, Cali o nia, Uni ed S a es
6Cen al China No mal Uni e si y, Wuhan, China
7Cen o de Aplicaciones Tecnológicas y Desa ollo Nuclea (CEADEN), Ha ana, Cuba
8Cen o de In es igación y de Es udios A anzados (CINVESTAV), Mexico Ci y and Mé ida, Mexico
9Chicago S a e Uni e si y, Chicago, Illinois, Uni ed S a es
10 China Ins i u e o A omic Ene gy, Beijing, China
11 Chungbuk Na ional Uni e si y, Cheongju, Republic o Ko ea
12 Comenius Uni e si y B a isla a, Facul y o Ma hema ics, Physics and In o ma ics, B a isla a, Slo ak
Republic
13 COMSATS Uni e si y Islamabad, Islamabad, Pakis an
14 C eigh on Uni e si y, Omaha, Neb aska, Uni ed S a es
15 Depa men o Physics, Aliga h Muslim Uni e si y, Aliga h, India
16 Depa men o Physics, Pusan Na ional Uni e si y, Pusan, Republic o Ko ea
17 Depa men o Physics, Sejong Uni e si y, Seoul, Republic o Ko ea
– 31 –
JHEP05(2023)243
18 Depa men o Physics, Uni e si y o Cali o nia, Be keley, Cali o nia, Uni ed S a es
19 Depa men o Physics, Uni e si y o Oslo, Oslo, No way
20 Depa men o Physics and Technology, Uni e si y o Be gen, Be gen, No way
21 Dipa imen o di Fisica, Uni e si à di Pa ia, Pa ia, I aly
22 Dipa imen o di Fisica dell’Uni e si à and Sezione INFN, Caglia i, I aly
23 Dipa imen o di Fisica dell’Uni e si à and Sezione INFN, T ies e, I aly
24 Dipa imen o di Fisica dell’Uni e si à and Sezione INFN, Tu in, I aly
25 Dipa imen o di Fisica e As onomia dell’Uni e si à and Sezione INFN, Bologna, I aly
26 Dipa imen o di Fisica e As onomia dell’Uni e si à and Sezione INFN, Ca ania, I aly
27 Dipa imen o di Fisica e As onomia dell’Uni e si à and Sezione INFN, Pado a, I aly
28 Dipa imen o di Fisica ‘E.R. Caianiello’ dell’Uni e si à and G uppo Collega o INFN, Sale no, I aly
29 Dipa imen o DISAT del Poli ecnico and Sezione INFN, Tu in, I aly
30 Dipa imen o di Scienze MIFT, Uni e si à di Messina, Messina, I aly
31 Dipa imen o In e a eneo di Fisica ‘M. Me lin’ and Sezione INFN, Ba i, I aly
32 Eu opean O ganiza ion o Nuclea Resea ch (CERN), Gene a, Swi ze land
33 Facul y o Elec ical Enginee ing, Mechanical Enginee ing and Na al A chi ec u e, Uni e si y o Spli ,
Spli , C oa ia
34 Facul y o Enginee ing and Science, Wes e n No way Uni e si y o Applied Sciences, Be gen, No way
35 Facul y o Nuclea Sciences and Physical Enginee ing, Czech Technical Uni e si y in P ague, P ague,
Czech Republic
36 Facul y o Physics, So ia Uni e si y, So ia, Bulga ia
37 Facul y o Science, P.J. Ša á ik Uni e si y, Košice, Slo ak Republic
38 F ank u Ins i u e o Ad anced S udies, Johann Wol gang Goe he-Uni e si ä F ank u , F ank u ,
Ge many
39 Fudan Uni e si y, Shanghai, China
40 Gangneung-Wonju Na ional Uni e si y, Gangneung, Republic o Ko ea
41 Gauha i Uni e si y, Depa men o Physics, Guwaha i, India
42 Helmhol z-Ins i u ü S ahlen- und Ke nphysik, Rheinische F ied ich-Wilhelms-Uni e si ä Bonn,
Bonn, Ge many
43 Helsinki Ins i u e o Physics (HIP), Helsinki, Finland
44 High Ene gy Physics G oup, Uni e sidad Au ónoma de Puebla, Puebla, Mexico
45 Ho ia Hulubei Na ional Ins i u e o Physics and Nuclea Enginee ing, Bucha es , Romania
46 Indian Ins i u e o Technology Bombay (IIT), Mumbai, India
47 Indian Ins i u e o Technology Indo e, Indo e, India
48 INFN, Labo a o i Nazionali di F asca i, F asca i, I aly
49 INFN, Sezione di Ba i, Ba i, I aly
50 INFN, Sezione di Bologna, Bologna, I aly
51 INFN, Sezione di Caglia i, Caglia i, I aly
52 INFN, Sezione di Ca ania, Ca ania, I aly
53 INFN, Sezione di Pado a, Pado a, I aly
54 INFN, Sezione di Pa ia, Pa ia, I aly
55 INFN, Sezione di To ino, Tu in, I aly
56 INFN, Sezione di T ies e, T ies e, I aly
57 Inha Uni e si y, Incheon, Republic o Ko ea
58 Ins i u e o G a i a ional and Suba omic Physics (GRASP), U ech Uni e si y/Nikhe , U ech ,
Ne he lands
59 Ins i u e o Expe imen al Physics, Slo ak Academy o Sciences, Košice, Slo ak Republic
60 Ins i u e o Physics, Homi Bhabha Na ional Ins i u e, Bhubaneswa , India
61 Ins i u e o Physics o he Czech Academy o Sciences, P ague, Czech Republic
62 Ins i u e o Space Science (ISS), Bucha es , Romania
63 Ins i u ü Ke nphysik, Johann Wol gang Goe he-Uni e si ä F ank u , F ank u , Ge many
64 Ins i u o de Ciencias Nuclea es, Uni e sidad Nacional Au ónoma de México, Mexico Ci y, Mexico
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JHEP05(2023)243
65 Ins i u o de Física, Uni e sidade Fede al do Rio G ande do Sul (UFRGS), Po o Aleg e, B azil
66 Ins i u o de Física, Uni e sidad Nacional Au ónoma de México, Mexico Ci y, Mexico
67 iThemba LABS, Na ional Resea ch Founda ion, Some se Wes , Sou h A ica
68 Jeonbuk Na ional Uni e si y, Jeonju, Republic o Ko ea
69 Johann-Wol gang-Goe he Uni e si ä F ank u Ins i u ü In o ma ik, Fachbe eich In o ma ik und
Ma hema ik, F ank u , Ge many
70 Ko ea Ins i u e o Science and Technology In o ma ion, Daejeon, Republic o Ko ea
71 KTO Ka a ay Uni e si y, Konya, Tu key
72 Labo a oi e de Physique des 2 In inis, I ène Jolio -Cu ie, O say, F ance
73 Labo a oi e de Physique Suba omique e de Cosmologie, Uni e si é G enoble-Alpes, CNRS-IN2P3,
G enoble, F ance
74 Law ence Be keley Na ional Labo a o y, Be keley, Cali o nia, Uni ed S a es
75 Lund Uni e si y Depa men o Physics, Di ision o Pa icle Physics, Lund, Sweden
76 Nagasaki Ins i u e o Applied Science, Nagasaki, Japan
77 Na a Women’s Uni e si y (NWU), Na a, Japan
78 Na ional and Kapodis ian Uni e si y o A hens, School o Science, Depa men o Physics , A hens,
G eece
79 Na ional Cen e o Nuclea Resea ch, Wa saw, Poland
80 Na ional Ins i u e o Science Educa ion and Resea ch, Homi Bhabha Na ional Ins i u e, Ja ni, India
81 Na ional Nuclea Resea ch Cen e , Baku, Aze baijan
82 Na ional Resea ch and Inno a ion Agency — BRIN, Jaka a, Indonesia
83 Niels Boh Ins i u e, Uni e si y o Copenhagen, Copenhagen, Denma k
84 Nikhe , Na ional ins i u e o suba omic physics, Ams e dam, Ne he lands
85 Nuclea Physics G oup, STFC Da esbu y Labo a o y, Da esbu y, Uni ed Kingdom
86 Nuclea Physics Ins i u e o he Czech Academy o Sciences, Husinec-Řež, Czech Republic
87 Oak Ridge Na ional Labo a o y, Oak Ridge, Tennessee, Uni ed S a es
88 Ohio S a e Uni e si y, Columbus, Ohio, Uni ed S a es
89 Physics depa men , Facul y o science, Uni e si y o Zag eb, Zag eb, C oa ia
90 Physics Depa men , Panjab Uni e si y, Chandiga h, India
91 Physics Depa men , Uni e si y o Jammu, Jammu, India
92 Physics Depa men , Uni e si y o Rajas han, Jaipu , India
93 Physics P og am and In e na ional Ins i u e o Sus ainabili y wi h Kno ed Chi al Me a Ma e
(SKCM2), Hi oshima Uni e si y, Hi oshima, Japan
94 Physikalisches Ins i u , Ebe ha d-Ka ls-Uni e si ä Tübingen, Tübingen, Ge many
95 Physikalisches Ins i u , Rup ech -Ka ls-Uni e si ä Heidelbe g, Heidelbe g, Ge many
96 Physik Depa men , Technische Uni e si ä München, Munich, Ge many
97 Poli ecnico di Ba i and Sezione INFN, Ba i, I aly
98 Resea ch Di ision and Ex eMe Ma e Ins i u e EMMI, GSI Helmhol zzen um ü
Schwe ionen o schung GmbH, Da ms ad , Ge many
99 Saga Uni e si y, Saga, Japan
100 Saha Ins i u e o Nuclea Physics, Homi Bhabha Na ional Ins i u e, Kolka a, India
101 School o Physics and As onomy, Uni e si y o Bi mingham, Bi mingham, Uni ed Kingdom
102 Sección Física, Depa amen o de Ciencias, Pon i icia Uni e sidad Ca ólica del Pe ú, Lima, Pe u
103 S e an Meye Ins i u ü Suba oma e Physik (SMI), Vienna, Aus ia
104 SUBATECH, IMT A lan ique, Nan es Uni e si é, CNRS-IN2P3, Nan es, F ance
105 Su ana ee Uni e si y o Technology, Nakhon Ra chasima, Thailand
106 Technical Uni e si y o Košice, Košice, Slo ak Republic
107 The Hen yk Niewodniczanski Ins i u e o Nuclea Physics, Polish Academy o Sciences, C acow,
Poland
108 The Uni e si y o Texas a Aus in, Aus in, Texas, Uni ed S a es
109 Uni e sidad Au ónoma de Sinaloa, Culiacán, Mexico
110 Uni e sidade de São Paulo (USP), São Paulo, B azil
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JHEP05(2023)243
111 Uni e sidade Es adual de Campinas (UNICAMP), Campinas, B azil
112 Uni e sidade Fede al do ABC, San o And e, B azil
113 Uni e si y o Cape Town, Cape Town, Sou h A ica
114 Uni e si y o Hous on, Hous on, Texas, Uni ed S a es
115 Uni e si y o Jy äskylä, Jy äskylä, Finland
116 Uni e si y o Kansas, Law ence, Kansas, Uni ed S a es
117 Uni e si y o Li e pool, Li e pool, Uni ed Kingdom
118 Uni e si y o Science and Technology o China, He ei, China
119 Uni e si y o Sou h-Eas e n No way, Kongsbe g, No way
120 Uni e si y o Tennessee, Knox ille, Tennessee, Uni ed S a es
121 Uni e si y o he Wi wa e s and, Johannesbu g, Sou h A ica
122 Uni e si y o Tokyo, Tokyo, Japan
123 Uni e si y o Tsukuba, Tsukuba, Japan
124 Uni e si y Poli ehnica o Bucha es , Bucha es , Romania
125 Uni e si é Cle mon Au e gne, CNRS/IN2P3, LPC, Cle mon -Fe and, F ance
126 Uni e si é de Lyon, CNRS/IN2P3, Ins i u de Physique des 2 In inis de Lyon, Lyon, F ance
127 Uni e si é de S asbou g, CNRS, IPHC UMR 7178, F-67000 S asbou g, F ance, S asbou g, F ance
128 Uni e si é Pa is-Saclay Cen e d’E udes de Saclay (CEA), IRFU, Dépa men de Physique Nucléai e
(DPhN), Saclay, F ance
129 Uni e si à degli S udi di Foggia, Foggia, I aly
130 Uni e si à del Piemon e O ien ale, Ve celli, I aly
131 Uni e si à di B escia, B escia, I aly
132 Va iable Ene gy Cyclo on Cen e, Homi Bhabha Na ional Ins i u e, Kolka a, India
133 Wa saw Uni e si y o Technology, Wa saw, Poland
134 Wayne S a e Uni e si y, De oi , Michigan, Uni ed S a es
135 Wes älische Wilhelms-Uni e si ä Müns e , Ins i u ü Ke nphysik, Müns e , Ge many
136 Wigne Resea ch Cen e o Physics, Budapes , Hunga y
137 Yale Uni e si y, New Ha en, Connec icu , Uni ed S a es
138 Yonsei Uni e si y, Seoul, Republic o Ko ea
139 Zen um ü Technologie und T ans e (ZTT), Wo ms, Ge many
140 A ilia ed wi h an ins i u e co e ed by a coope a ion ag eemen wi h CERN
141 A ilia ed wi h an in e na ional labo a o y co e ed by a coope a ion ag eemen wi h CERN
IDeceased
II Also a : Max-Planck-Ins i u ü Physik, Munich, Ge many
III Also a : I alian Na ional Agency o New Technologies, Ene gy and Sus ainable Economic
De elopmen (ENEA), Bologna, I aly
IV Also a : Dipa imen o DET del Poli ecnico di To ino, Tu in, I aly
VAlso a : Depa men o Applied Physics, Aliga h Muslim Uni e si y, Aliga h, India
V I Also a : Ins i u e o Theo e ical Physics, Uni e si y o W oclaw, Poland
V II Also a : An ins i u ion co e ed by a coope a ion ag eemen wi h CERN
– 34 –