Jet quenching as a probe of the initial stages in heavy-ion collisions
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Je quenching as a p obe o he ini ial s ages in hea y-ion collisions
© 2020 The Au ho (s)
Published e sion
And es, Ca lo a; A mes o, Nés o ; Niemi, Ha i; Paa elainen, Ris o; Salgado,
Ca los A.
And es, Ca lo a; A mes o, Nés o ; Niemi, Ha i; Paa elainen, Ris o; Salgado, Ca los A. (2020). Je
quenching as a p obe o he ini ial s ages in hea y-ion collisions. Physics Le e s B, Ea ly online.
DOI: 10.1016/j.physle b.2020.135318
2020
JID:PLB AID:135318 /SCO Doc opic: Phenomenology [m5G; 1.283; P n:24/02/2020; 16:03] P.1 (1-7)
Physics Le e s B ••• (••••)••••••
Con en s lis s a ailable a ScienceDi ec
Physics Le e s B
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Je quenching as a p obe o he ini ial s ages in hea y-ion collisions ✩
Ca lo a And es a, Nés o A mes o b, Ha i Niemi c,d, Ris o Paa elainen e,d, Ca los A. Salgadob
aJe e son Lab, 12000 Je e son A enue, Newpo News, VA 23606, USA
bIns i u o Galego de Física de Al as Ene xías IGFAE, Uni e sidade de San iago de Compos ela, E-15782 Galicia, Spain
cUni e si y o Jy äskylä, Depa men o Physics, P.O. Box 35, FI-40014 Uni e si y o Jy äskylä, Finland
dHelsinki Ins i u e o Physics, P.O. Box 64, FI-00014 Uni e si y o Helsinki, Finland
eTheo e ical Physics Depa men , CERN, CH-1211 Genè e 23, Swi ze land
a i c l e i n o a b s a c
A icle his o y:
Recei ed 17 Sep embe 2019
Recei ed in e ised o m 31 Janua y 2020
Accep ed 19 Feb ua y 2020
A ailable online xxxx
Edi o : J.-P. Blaizo
Keywo ds:
Hea y-ions
Je quenching
Ini ial s ages
Je quenching p o ides a e y flexible a ie y o obse ables which a e sensi i e o di e en ene gy- and
ime-scales o he s ongly in e ac ing ma e c ea ed in hea y-ion collisions. Exploi ing his e sa ili y
would make je quenching an excellen ch onome e o he yoc osecond s uc u e o he e olu ion
p ocess. He e we show, o he fi s ime, ha a combina ion o je quenching obse ables is sensi i e o
he ini ial s ages o hea y-ion collisions, when he app oach o local he mal equilib ium is expec ed o
happen. Specifically, we find ha in o de o ep oduce a he same ime he inclusi e pa icle p oduc ion
supp ession, RAA, and he high-pTazimu hal asymme ies, 2, ene gy loss mus be s ongly supp essed
o he fi s ∼0.6 m. This explo a o y analysis shows he po en ial o je obse ables, possibly mo e
sophis ica ed han he ones s udied he e, o cons ain he dynamics o he ini ial s ages o he e olu ion.
©2020 The Au ho (s). 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
Hea y-ion collisions a e he expe imen al ools designed o
s udy he p ope ies o he ho and dense Qua k Gluon Plasma
(QGP). A e wo decades o expe imen s a he Rela i is ic Hea y
Ion Collide (RHIC) and he La ge Had on Collide (LHC), je
quenching, he modifica ion o he Quan um Ch omodynamics
(QCD) je s uc u es due o hei in e ac ion wi h he su ound-
ing ma e , has become a undamen al ool o his p og am.
Al hough he QGP is ou inely p oduced and s udied in hese col-
lide s, he ac ual p ocess ha so efficien ly leads o he p oduc ion
o his locally he malized s a e s a ing om a comple ely ou -
o -equilib ium collision sys em is la gely unknown. This p ocess
mus happen in a e y sho ime, O(1 m)o a ew yoc osec-
onds. This is why his line o esea ch, ha has become one o
he mos ac i e and in e es ing opics in QCD, is some imes nick-
named Ini ial S ages. Up o now, all expe imen al in o ma ion on
he ini ial s ages o he e olu ion comes, essen ially, om az-
imu hal asymme ies in co ela ions be ween di e en pa icles
in he so egime (say, pT5GeV), and om deep inelas ic sca -
e ing [1,2].
✩JLAB-THY-19-2888, CERN-TH-2019-012.
E-mail add esses: ca lo[email p o ec ed] (C. And es), nes o .a mes [email protected]
(N. A mes o), ha i.m.niemi@jyu.fi (H. Niemi), is o.saka i.paa [email p o ec ed]
(R. Paa elainen), [email p o ec ed] (C.A. Salgado).
Fu he mo e, ecen expe imen al esul s om he LHC, and
la e om RHIC, in small sys em p-Pb, high-mul iplici y p-p and
d-Au collisions, show cha ac e is ics [3]usually a ibu ed o QGP
o ma ion. Indeed, usual key p obes o he QGP, such as long-
ange angula co ela ions and flow ha monics [4–11], and he
s angeness enhancemen [12]ha e been obse ed in small sys-
ems. In e es ingly, he only long-es ablished QGP signa u e miss-
ing in hese expe imen al da a is je quenching [13]. Since he -
maliza ion and je quenching a e mani es a ions o basically he
same dynamics, he p esence o he o me and he absence o he
la e in hese sys ems is su p ising. Fo his eason, he e is an
ample consensus ha je quenching is c i ical o unde s and small
sys ems and he maliza ion. We will a gue he e ha je quench-
ing can be used, in ac , as a complemen a y and e sa ile way o
p obe he dynamics a he ea ly imes o he e olu ion. Ac ually,
je s a e ex ended objec s in space and ime, and di e en modifi-
ca ions measu e di e en ime o ene gy scales [14,15].
Using azimu hal asymme ies o ha d pa icles as a je quench-
ing p obe was p oposed o he fi s ime in [16,17]. The fi s da a
on high-pTellip ic flow, 2, was published in 2006 by he PHENIX
Collabo a ion [18]. Howe e , e en hough he nuclea modifica ion
ac o , RAA, was ai ly-well desc ibed by all he ene gy loss o -
malisms (e.g. embedded in e en -by-e en (EbyE) hyd odynamics
[19]), he compu ed high-pTellip ic flow unde es ima ed he ex-
pe imen al da a [20], an issue add essed in many s udies [21–31]
along he las decade. I was a gued in [32,33] ha so -ha d co -
ela ions a e decisi e o p ope ly de e mine he ha monic coeffi-
h ps://doi.o g/10.1016/j.physle b.2020.135318
0370-2693/©2020 The Au ho (s). 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.
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2C. And es e al. / Physics Le e s B •••(••••)••••••
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cien s in he ha d sec o , whose co ec defini ion is gi en by he
scala p oduc , SP
n[33], o be defined below.
In his wo k, we compu e he azimu hally a e aged RAA o
he 20–30% cen ali y class in √sNN = 2.76 TeV Pb-Pb collisions
a he LHC [34]. We ha e also checked ha ou conclusions hold
o o he cen ali y classes, see Figs. A.1-A.2 in Appendix A. Ou
amewo k consis s o a adia i e ene gy loss implemen ed wi h
he Quenching Weigh s (QWs) om Re . [35], embedded in an
EKRT EbyE hyd odynamic simula ion o he medium [36]. Follow-
ing he app oach in [37,38], we define he je anspo coefficien
as ˆ
q≡K·2 ε3/4, d i en by he ideal es ima e ˆ
qideal ∼2 ε3/4[39].
The local ene gy densi y ε, is aken om EKRT hyd odynamic p o-
files, so ha he e is only one ee pa ame e , he K- ac o , which
is fi ed o he high-pTRAA expe imen al da a [34] and used o
he calcula ion o he high-pTha monic coefficien s.
We will show ha he ea men o ini ial s ages is c ucial o
he simul aneous desc ip ion o bo h ype o obse ables, since he
je ha monic coefficien s show up o be e y sensi i e o he s a -
ing poin o he quenching. In ac , he expe imen al da a on 2
a high-pTcan only be desc ibed by delaying he beginning o he
ene gy loss o ∼0.6 m. This gene al conclusion ha we d aw
he e o he fi s ime1is no limi ed o ou specific implemen-
a ion, since all s udies ha desc ibe he je ha monic coefficien s
s a he ene gy loss and hyd odynamical e olu ion a he same
ime [33,41–44], implici ly implemen ing his ime delay. We do
no a emp he e a comp ehensi e s udy o expe imen al da a on
RAA and nbu a he o show he impo ance o he ini ial s ages
o he e olu ion o hei co ec in e p e a ion. I would be emp -
ing, on he o he hand, o ela e ou findings o he absence o
je quenching in p-Pb collisions. We lea e hese s udies o u u e
wo ks.
2. The o malism
Ene gy loss: We ollow he same o malism as in [38], o which we
e e he eade o u he de ails. Fo a discussion on i s limi a-
ions see also [24]. He e we summa ize i s mos ele an ea u es.
The c oss sec ion o a had on ha apidi y yand ans e se mo-
men um pTis gi en by
dσAA→h
dydpT=dqTdzdσAA→k
dydqT
P()
×Dk→h(z,μF≡pT)δ(pT−z(1−)qT),(1)
whe e he c oss sec ion o p oducing a pa on k, dσAA→k/dydqT,
is compu ed a nex - o leading o de (NLO) by using he code in
[45]. Fo he pa on dis ibu ion unc ions, we use CTEQ6.6M [46]
oge he wi h EPS09 nuclea modifica ions [47]. Fo he agmen-
a ion unc ions (FFs) Dk→h(z, μF), we use ei he DSS07 [48]o
DSS14 [49]. The QWs P()a e employed in he mul iple so ap-
p oxima ion [35].2These p obabili y dis ibu ions depend on wo
a iables, ωcand R, which, o a dynamic expanding medium,
a e p opo ional, espec i ely, o he fi s and second momen o
he je quenching pa ame e ˆ
q(ξ), defined along he ajec o y o
he adia ing pa on pa ame ized by ξ[35,38]. The e o e, we only
need a defini ion o he je anspo coefficien in e ms o he lo-
1In [40] he au ho s commen ha ene gy loss models wi h delayed quenching
desc ibe be e in- and ou -o -plane RAA da a a RHIC, bu no claim is made on he
po en ial o cons aining p ope ies o he ea ly s ages.
2Ou esul s and conclusions emain o sca e ing on a single cen e ins ead o
mul iple so sca e ings (see Fig. A.3 in Appendix A).
cal p ope ies o he medium. We make use o he a o emen ioned
exp ession3:
ˆ
q(ξ) =K·2ε3/4(ξ). (2)
The p e ious equa ion is alid bo h o he pa onic and o
he had onic phase o he e olu ion [39]. Ne e heless, mos o
he phenomenological wo ks ha y o ex ac he alue o he
quenching pa ame e assume no ene gy loss du ing he had onic
phase [50]. We analyze he e wo di e en scena ios: ending he
ene gy loss a he chemical eeze-ou Tq=Tchem = 175 MeV, ha
is, no ene gy loss in he had onic phase, and using Eq. (2)all he
way down o he kine ic eeze-ou Tq=Tdec = 100 MeV, i.e., in-
cluding je quenching in bo h phases.4
EKRT hyd odynamics: The EbyE fluc ua ing ini ial ene gy densi y
p ofiles o he hyd odynamical e olu ion a e calcula ed wi hin he
EKRT amewo k [51]. This amewo k is based on he collinea ly
ac o ized NLO compu a ion in pe u ba i e QCD (pQCD) o minije
ans e se ene gy p oduc ion and he conjec u e o gluon sa u a-
ion. The sa u a ion momen um psa con ols he compu ed ans-
e se ene gy p oduc ion, and is a unc ion o he gi en collision
ene gy √sNN, he nuclea mass numbe A, and i s dependence
on he ans e se coo dina e x⊥comes h ough he p oduc o
he nuclea hickness unc ions TA(x⊥), compu ed e en -by-e en .
The essen ial ee pa ame e Ksa in he sa u a ion conjec u e is
fixed by he cha ged had on mul iplici y in 0–5% Pb-Pb collisions
a √sNN =2.76 TeV. Once Ksa is fixed, he ini ial ene gy den-
si y p ofiles can be compu ed o any √sNN and Aas long as he
sa u a ion momen um emains in he pe u ba i e egime, psa =
psa (√sNN, A, TATA(x⊥)) >pmin =1 GeV. The o ma ion ime o
he ini ial condi ion is hen ob ained as τ =1/pmin =0.197 m.
A e o ma ion, he subsequen space ime e olu ion is com-
pu ed using a boos -in a ian ansien Is ael-S ewa ype o sec-
ond o de ela i is ic dissipa i e hyd odynamics, whe e he essen-
ial physical inpu s a e he QCD ma e equa ion o s a e and he
empe a u e dependence o shea iscosi y η/s(T), o de ails see
Re . [36]. In pa icula , we ob ain he space ime e olu ion o he
ene gy densi y p ofile ε(τ, x⊥) o each e en , which a e hen used
in he compu a ion o he je quenching pa ame e in Eq. (2).
As an equa ion o s a e (EoS) we use he s95p pa ame iza ion
o he la ice QCD esul s [52]wi h chemical eeze-ou imple-
men ed as in Re . [53], and he shea iscosi y pa ame iza ion
is η/s(T) =pa am1 om Re . [36]. The co esponding esul s o
so had onic obse ables like mul iplici y, a e age ans e se mo-
men um, flow coefficien and flow co ela ions a e in an excellen
ag eemen wi h he measu emen s o 200 GeV Au-Au collisions a
RHIC, and 2.76 TeV Pb-Pb, 5.023 TeV Pb-Pb and 5.44 TeV Xe-Xe
collisions a he LHC [36,54–56].
Ea ly- imes ea men : The dynamics p io o he applicabili y o
hyd odynamics and, he e o e, he associa e ene gy loss phenom-
ena, a e no es ablished ye . Thus, he e is eedom in he defini-
ion o ˆ
q(ξ) om he p oduc ion ime o he had on o he ini ial-
iza ion p ope ime τ o EKRT EbyE hyd odynamics, see Eq. (2).
Ene gy loss in he BDMPS-Z o malism does no equi e, in p inci-
ple, nei he he maliza ion no iso opiza ion, so o imes smalle
han τ i can be employed and ˆ
q(ξ) has o be ob ained ia ex ap-
ola ions. Up o now, any phenomenological s udy o his kind – ex-
cep explici ly indica ed – assumes no quenching du ing he ea ly
s ages o he collision.5Indeed, all he p oposed solu ions o he
3O he ene gy loss models ha include flow e ec s [33] equi e he same de-
layed quenching o desc ibe he high-pT n.
4Tqdeno es he empe a u e a which we s op he ene gy loss.
5See Re s. [37]and[38] o some ea ly ime ex apola ions.
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C. And es e al. / Physics Le e s B •••(••••)•••••• 3
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Fig. 1. (a) Supp ession o inclusi e cha ged pa icles, (b) high-pTellip ic flow, (c) high-pT iangula flow o he 20–30% cen ali y class o √sNN = 2.76 TeV Pb-Pb collisions
a he LHC, compu ed as a unc ion o pT. Expe imen al da a a e om [34,57–59]. The blue solid and g een do ed lines co espond, espec i ely, o he use o DSS07 [48]
and DSS14 [49] FFs. Fo he ini ial and final imes o he ene gy loss, Case ii) τq=0.197 and Tq=Tchem = 175 MeV a e aken.
long-s anding p oblem o desc ibing he high-pT 2delay he in-
e ac ion o he ha d pa on wi h he medium up o he ini ial
ime o he hyd odynamic simula ion [33,41,42], usually use τ =
0.6 m, o equi e a e y subs an ial g ow h o ˆ
q o empe a u es
close o he deconfinemen empe a u e [43,44]. Since he s a -
ing ime o EKRT EbyE hyd odynamics is se o τ = 0.197 m, we
can s udy how he RAA and high-pTje ha monic coefficien s a y
when we delay he je quenching up o a ime compa able wi h
ha in [33,41,42]. Deno ing by τq he ime whe e he je quench-
ing begins, we conside he ollowing h ee cases:
i) τq=0. He e, ˆ
q(ξ) =ˆ
q(τ ) o ξ<τ =0.197 m.
ii) τq=0.197 m. He e, ˆ
q(ξ) =0 o ξ<τ =0.197 m. In his
case, he quenching begins a 0.197 m.
iii) τq=0.572 m. He e, ˆ
q(ξ) =0 o ξ<τq=0.572 m. Hence,
he ene gy loss s a s a 0.572 m.
On he o he hand, he o igin o he delay could be he empe a-
u e/ene gy densi y dependence o ˆ
q. Thus, we ha e also s udied
he case whe e ˆ
q=0 o T>Tcu =350 o 380 MeV (see Fig. A.4
in Appendix A), which supp esses quenching a ea ly imes when
he ene gy densi y is la ge.
High-pTha monics: Up o his poin , we ha e calcula ed he
medium-modified pa icle spec a, Eq. (1), using he me hod de-
sc ibed in Re . [38]bu o a hyd odynamic p ofile p oduced o
a single e en . Then we a e age hese single e en spec a o e
all e en s in a gi en cen ali y class o p oduce he co espond-
ing spec um o ha cen ali y class. A his s age, he K- ac o in
Eq. (2)can be fi ed o he expe imen al RAA da a o a gi en cen-
ali y class. Once he K- ac o is fixed, he ha monic coefficien s
associa ed o he RAA(pT, φ) Fou ie se ies ha d
na e calcula ed in
he co esponding cen ali y class, e en by e en . Then, each ha d
n
is co ela ed wi h he so flow ha monic in he e en and, finally,
an a e age o e all he e en s in he cen ali y class is pe o med:
SP
n(pT)= so
n ha d
n(pT)cos nψso
n−ψha d
n(pT)
so
n2
,(3)
whe e ψso
nis he e en plane angle and ...deno es he a e age
o e he e en s. This is he scala p oduc defini ion o he high-pT
azimu hal ha monics [32,33].
3. Resul s
We es ic ou s udy o he nuclea modifica ion ac o and he
high-pTha monics o one cen e o mass ene gy and one cen-
ali y class: LHC Pb-Pb 20–30% semi-cen al collisions a √sNN =
2.76 TeV. We ha e al eady analyzed he ene gy and cen ali y de-
pendence o he nuclea modifica ion ac o o se e al smoo h-
a e aged hyd odynamics in Re . [38], showing ha , su p isingly,
he K- ac o o a gi en cen e o mass ene gy seems o be al-
mos independen o he cen ali y o he collision. Mo e ecen ly,
simila esul s ha e been ound by all he phenomenological wo ks
ha se he dependence o he medium pa ame e on he medium
p ope ies o be local and mono onous [60,61]. Finally, in Re . [62],
we ha e also checked ha using an EbyE o malism, he EKRT
hyd odynamic simula ion employed also he e, he conclusions ob-
ained in Re . [38] emain.
We compu e he nuclea modifica ion ac o o a se o alues
o ou ee pa ame e , he K- ac o , as explained in he p e ious
sec ions. Nex , we pe o m a χ2-fi o de e mine he K- alue ha
be e desc ibes ALICE RAA da a [34] o pT>5GeV – o s ay
in he pQCD egion.6Then, he fi ed Kis used o ob ain he
high-pTasymme ies by means o he scala p oduc gi en by
Eq. (3). In Fig. 1we show he dependence o hese obse ables
on he FFs employed, i.e., DSS07 o DSS14. In his figu e, he e is
nei he ene gy loss be o e he ini ial p ope ime o he hyd o-
dynamic p ofile, τ =0.197 m, no a e he chemical eeze-ou ,
Tchem = 175 MeV. I can be seen ha , independen ly o he FFs
used, ou model ai ly-well desc ibes he RAA bu unde es ima es
he azimu hal asymme ies in he ha d sec o . Mo eo e , ou cal-
cula ions o bo h he nuclea modifica ion ac o and he high-pT
ha monics a e ha dly sensi i e o he FFs. Consequen ly, any o
hem can be implemen ed in ou compu a ions, wi hou al e -
ing ou conclusions. He ea e , esul s we e ob ained using DSS07
FFs.
In Fig. 2we analyze how he RAA and he je ha monic co-
efficien s a y wi h he end-poin o he ene gy loss. As in he
p e ious figu e, we assume he e no ene gy loss be o e he s a ing
ime o EKRT hyd odynamic p ofile, ha is, Case ii) τq=0.197, ac-
co ding o he no a ion in he p eceding sec ion. While he nuclea
modifica ion ac o can be well desc ibed bo h wi h and wi hou
ene gy loss in he had onic phase, he high-pTasymme ies a e
sensi i e, especially he SP
2(pT), o he end-poin o he quench-
ing, poin ing ou o a be e desc ip ion o he da a when he e
is only ene gy loss in he pa onic phase. Ne e heless, no ma -
e when we s op ou simula ion, ye he je ha monic coefficien s
emain unde es ima ed.
The dependence o he RAA(pT), SP
2(pT), and SP
3(pT)on he
s a ing ime on he ene gy loss is p esen ed in Fig. 3. This is done
o he case whe e he e is no quenching in he had onic phase,
Tq=Tchem. As i can be seen on he le panel o his figu e, he
dependence o he nuclea modifica ion ac o on τqis mild, how-
6Conside ing only da a wi h pT>10 GeV does no modi y ou main esul s and
conclusions.
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Fig. 2. (a) RAA(pT), (b) SP
2(pT), (c) SP
3(pT) o he 20–30% cen ali y class o √sNN = 2.76 TeV Pb-Pb collisions a he LHC compa ed o hei espec i e expe imen al da a
[34,57–59]. The blue solid line co esponds o s opping he ene gy loss a he kine ic eeze-ou , Tq=Tdec = 100 MeV. Fo he g een do ed line he quenching finishes a
Tq=Tchem = 175 MeV. DSS07 [48] FFs and Case ii) τq=0.197 m a e employed.
Fig. 3. (a) RAA(pT), (b) SP
2(pT), (c) SP
3(pT) o he 20–30% cen ali y class o √sNN = 2.76 TeV Pb-Pb collisions a he LHC compa ed o hei espec i e expe imen al da a
[34,57–59]. The blue solid, τq=0 m, do ed g een, τq=0.197 m, and dashed-do ed pu ple, τq=0.572 m, lines co espond, espec i ely, o Cases i), ii) and iii) o he
ea ly imes ea men . DSS07 [48] FFs and Tq=Tchem = 175 MeV a e used.
Table 1
K- ac o ob ained om fi s o he ALICE RAA da a [34] o he
h ee di e en ea ly ime ex apola ions and he co esponding
χ2/d.o. . o he 2CMS da a wi h pT>10 GeV. DSS07 FFs and
Tq=Tchem =175 MeV a e employed.
Ea ly ime ex apola ion K- ac o χ2/d.o. . o 2
Case i) τq=0 m 2.120+0.091
−0.074 26.2
Case ii) τq=0.197 m 2.90+0.13
−0.11 12.9
Case iii) τq=0.572 m 4.56 ±0.20 3.5
e e , he co esponding K-fi ed alues o he h ee cu es o his
panel, shown in Table 1, a e qui e di e en . Rega ding he asym-
me ies in he ha d sec o , Fig. 3shows ha hey a e e y sensi i e
o he s a ing poin o he quenching. Ac ually, he high-pT 2ex-
pe imen al da a can be desc ibed subs an ially be e wi hin ou
o malism i and only i he s a ing poin o he ene gy loss is de-
layed up o ∼0.6 m – he co esponding χ2/d.o. .a e shown in
Table 1. This co esponds o he se -up employed in any app oach
ha aims o desc ibe he je ha monics coefficien s using a smoo h
dependence o he medium pa ame e on he medium p ope ies
[33,41,42].
4. Conclusions
In his Le e we ha e compu ed he nuclea modifica ion ac o
and he high-pTha monics 2, 3 o cha ged pa icle p oduc-
ion in 20–30% cen ali y class √sNN = 2.76 TeV Pb-Pb collisions
a he LHC. The calcula ions a e done by using he o malism o
QWs embedded in he s a e-o - he a EbyE EKRT hyd odynamic
model o he medium. We ha e analyzed he dependence o hese
obse ables on he FFs, on he lack -o no -o ene gy loss in he
had onic phase o he e olu ion, and on he s a ing ime o he
quenching. Any wo k ha co ec ly de e mines he inclusi e pa i-
cle supp ession and ha monic coefficien s in he ha d sec o s a s
he ene gy loss a he ini ial ime o he hyd odynamic simula ion
employed, which usually is τ = 0.6 m (o la e ). The e o e, hey
implici ly assume no quenching du ing he fi s 0.6 m a e he
collision. Since he s a ing ime o he EKRT hyd odynamic e olu-
ion is τ = 0.197 m, i p o ides he fi s amewo k ha enables
he a ia ion o he quenching in he ea ly s ages o he e olu ion,
and hus he de e mina ion o i s beginning in a con olled way.
We find ha he simul aneous and p ope desc ip ion o hese
h ee obse ables equi es no ene gy loss o he fi s ∼0.6 m
a e he collision (o a la ge T>350 MeV), in acco d wi h he
implici se -up in o he s udies.
Clea ly, ou esul comes om a smalle ˆ
qa ea ly imes, bu
we lack a conclusi e physical explana ion o his finding. I would
be emp ing o link ˆ
qwi h he Knudsen numbe which is la ge a
hese ea ly imes. Fo ins ance, in weakly coupled heo ies ˆ
q/T3∝
(η/s)−1[63]. The e o e, a la ge Knudsen numbe due o a la ge
η/s(and no due o la ge g adien s) would imply a small ˆ
qand
he supp ession o je quenching. We also no e ha , al hough he
EoS a ec s he empe a u e dependence o ˆ
q h ough Eq. (2) o
some ex en , he high empe a u e pa o he EoS is e y well
es ablished om la ice QCD calcula ions [64]. On he o he hand,
he low- empe a u e pa o he EoS [65]can be s ongly a ec ed
by he chemical eeze-ou . Howe e , we ha e es ed, by changing
he quenching endpoin , ha he had onic e olu ion does no al e
ou conclusions.
We conclude ha his is no a pa icula ea u e o ou ap-
p oach bu a gene al ou come. Hence, high-pTasymme ies a e
in oduced he e, o he fi s ime, as a di ec signa u e o he less
known ini ial s ages o he collision, showing he impossibili y o
he simul aneous desc ip ion o he expe imen al measu emen s
on he cha ged had on supp ession and he azimu hal asymme-
ies wi hou s ongly supp essing he ene gy loss o he fi s
∼0.6 m a e he collision. This wo k clea ly shows ha exploi -
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ing he e sa ili y o je quenching o access di e en ime-scales
o e s unique possibili ies o imp o e ou unde s anding o he ini-
ial s ages in hea y-ion collisions, and is ex endable om la ge o
small sys ems.
Acknowledgemen s
We acknowledge help ul discussions wi h J. No onha-Hos le ,
compu a ional esou ces om he CSC-IT Cen e o Science in
Espoo, Finland, and financial suppo by he US DOE (CA, con-
ac DEAC05-06OR23177 unde which Je e son Science Asso-
cia es, LLC ope a es Je e son Lab), he Academy o Finland (HN,
p ojec 297058), he ERC (RP, g an no. 725369), MICINN o Spain
(NA, CAS, p ojec FPA2017-83814-P and Unidad de Excelencia
Ma ía de Mae zu MDM-2016-069), Xun a de Galicia (NA, CAS, Con-
selle ía de Educación) and FEDER (NA, CAS). This wo k has been
pe o med wi hin COST Ac ion CA15213 THOR.
Appendix A. Addi ional checks
Di e en cen ali ies: We ha e in es iga ed he e ec o he cu in
ime o di e en cen ali y classes. The esul s o RAA(pT)and
SP
2(pT) o he 0–10% and 40–50% cen ali y classes o √sNN =
2.76 TeV Pb-Pb collisions a he LHC a e shown, espec i ely, in
Fig. A.1 and Fig. A.2. Fo bo h cen ali y classes, we conside again
he h ee ea ly imes ex apola ions: τq=0 m, τq=0.197 m and
τq=0.572 m, aking DSS07 [48] FFs and Tq=Tchem = 175 MeV.
The co esponding cen al alues o he K- ac o a e, espec i ely,
2.12, 2.79 and 4.12 o he 0–10% cen ali y class and 2.14, 3.10
and 5.27 o he 40–50% cen ali y class, in line wi h he findings
in [38]. The imp o emen in he desc ip ion o 2wi h inc easing
τqis mani es .
Ene gy loss modeling: We ha e examined he e ec o using a di -
e en ene gy loss model. Wi hin he same o malism o he QWs,
we ha e changed he app oxima ion used o compu e he adia ion
spec um om mul iple so sca e ings o a single ha d sca e ing,
ha is, he N=1opaci y limi ( aking ¯
R=R/3 and ¯
ωc=ωc/3,
see [35] and also [24]). No e ha he pe u ba i e ails la gely di -
e be ween hese wo app oxima ions. We show in Fig. A.3 he
esul s o RAA(pT)and SP
2(pT) o he 20–30% cen ali y class o
√sNN = 2.76 TeV Pb-Pb collisions a he LHC in he single opaci y
app oxima ion, oge he wi h he ones in he mul iple so sca e -
ing app oxima ion o τq=0 m, τq=0.197 m and τq=0.572 m
(using DSS07 [48] FFs and Tq=Tchem = 175 MeV). The co espond-
ing cen al alues o he K- ac o o he N=1opaci y cu es a e
2.80, 3.80 and 6.03, espec i ely. While he ans e se momen um
dependence o he esul s is somewha di e en , he imp o emen
in he desc ip ion o 2wi h inc easing τqis e iden .
Fig. A.1. (Le ) RAA(pT), ( igh ) SP
2(pT) o he 0–10% cen ali y class o √sNN = 2.76 TeV Pb-Pb collisions a he LHC compa ed o hei espec i e expe imen al da a [34,57].
The blue solid, τq=0 m, do ed g een, τq=0.197 m, and dashed-do ed pu ple, τq=0.572 m, lines co espond, espec i ely, o Cases i), ii) and iii) o he ea ly imes
ea men . DSS07 [48] FFs and Tq=Tchem = 175 MeV a e used.
Fig. A.2. (Le ) RAA(pT), ( igh ) SP
2(pT) o he 40–50% cen ali y class o √sNN = 2.76 TeV Pb-Pb collisions a he LHC compa ed o hei espec i e expe imen al da a
[34,57]. The blue solid, τq=0 m, do ed g een, τq=0.197 m, and dashed-do ed pu ple, τq=0.572 m, lines co espond, espec i ely, o Cases i), ii) and iii) o he ea ly
imes ea men . DSS07 [48] FFs and Tq=Tchem = 175 MeV a e used.
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Fig. A.3. (Le ) RAA(pT), ( igh ) SP
2(pT) o he 20–30% cen ali y class o √sNN = 2.76 TeV Pb-Pb collisions a he LHC compa ed o hei espec i e expe imen al da a
[34,57,58]. The colo s o he lines co espond o he ea ly imes ea men employed, ha is, blue o Case i) τq=0 m, g een o Case ii) τq=0.197 m and pu ple o Case
iii) τq=0.572 m. Solid lines e e o he esul s in he single opaci y app oxima ion, while do ed lines co espond o he mul iple so sca e ing app oxima ion used in he
main pa o he wo k, ha is, Figs. 1, 2and 3, and in all o he he Figs. in his Appendix. DSS07 [48] FFs and Tq=Tchem = 175 MeV a e used.
Fig. A.4. (Le ) RAA(pT), ( igh ) SP
2(pT) o he 20–30% cen ali y class o √sNN = 2.76 TeV Pb-Pb collisions a he LHC compa ed o hei espec i e expe imen al da a
[34,57,58]. The solid blue line co esponds o a cu in ime wi h τq=0.572 m. The do ed g een and dashed-do ed pu ple lines co espond o cu s in empe a u e
Tcu =380 and 350 MeV, espec i ely. DSS07 [48] FFs and Tq=Tchem = 175 MeV a e used.
Cu s in empe a u e: We ha e e alua ed he possibili y o a di -
e en way o cu ing he quenching a he ini ial s ages o he
collision. Specifically, we ha e aken ˆ
q=0 o T>Tcu =350 o
380 MeV.7The co esponding cen al alues o he K- ac o a e
7.00 and 5.77 o Tcu =350 and 380 MeV espec i ely. The e-
sul s o RAA(pT)and SP
2(pT) o he 20–30% cen ali y class o
√sNN = 2.76 TeV Pb-Pb collisions a he LHC a e shown in Fig. A.4,
oge he wi h he esul s wi h τq=0.572 m and no cu in em-
pe a u e. I u ns ou ha he e ec o dec easing Tcu is simila o
ha o inc easing τq, as expec ed.
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