This is a sel -a chi ed e sion o an o iginal a icle. This e sion
may di e om he o iginal in pagina ion and ypog aphic de ails.
Au ho (s):
Ti le:
Yea :
Ve sion:
Copy igh :
Righ s:
Righ s u l:
Please ci e he o iginal e sion:
CC BY 4.0
h ps://c ea i ecommons.o g/licenses/by/4.0/
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
www.else ie .com/loca e/physle b
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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, pT5GeV), 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.
JID:PLB AID:135318 /SCO Doc opic: Phenomenology [m5G; 1.283; P n:24/02/2020; 16:03] P.2 (1-7)
2C. And es e al. / Physics Le e s B •••(••••)••••••
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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.
JID:PLB AID:135318 /SCO Doc opic: Phenomenology [m5G; 1.283; P n:24/02/2020; 16:03] P.3 (1-7)
C. And es e al. / Physics Le e s B •••(••••)•••••• 3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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 nψso
n−ψha d
n(pT)
 so
n2
,(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.
JID:PLB AID:135318 /SCO Doc opic: Phenomenology [m5G; 1.283; P n:24/02/2020; 16:03] P.4 (1-7)
4C. And es e al. / Physics Le e s B •••(••••)••••••
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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 -

JID:PLB AID:135318 /SCO Doc opic: Phenomenology [m5G; 1.283; P n:24/02/2020; 16:03] P.5 (1-7)
C. And es e al. / Physics Le e s B •••(••••)•••••• 5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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.
JID:PLB AID:135318 /SCO Doc opic: Phenomenology [m5G; 1.283; P n:24/02/2020; 16:03] P.6 (1-7)
6C. And es e al. / Physics Le e s B •••(••••)••••••
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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.
Re e ences
[1] H. Man ysaa i, B. Schenke, C. Shen, P. T ibedy, Phys. Le . B 772 (2017) 681–686.
[2] H. Man ysaa i, B. Schenke, Phys. Re . D 98 (2018) 034013.
[3] C. Loizides, Nucl. Phys. A 956 (2016) 200–207.
[4] V. Khacha yan, e al., J. High Ene gy Phys. 09 (2010) 091.
[5] B. Abele , e al., Phys. Le . B 719 (2013) 29–41.
[6] A. Ada e, e al., Phys. Re . Le . 111 (2013) 212301.
[7] S. Cha chyan, e al., Phys. Le . B 724 (2013) 213–240.
[8] B.B. Abele , e al., Phys. Re . C 90 (2014) 054901.
[9] M. Aaboud, e al., Eu . Phys. J. C 77 (2017) 428.
[10] V. Khacha yan, e al., Phys. Re . Le . 115 (2015) 012301.
[11] A.M. Si unyan, e al., Phys. Re . Le . 121 (2018) 082301.
[12] J. Adam, e al., Na . Phys. 13 (2017) 535–539.
7Using DSS07 [48] FFs and ending he ene gy loss a Tq=Tchem = 175 MeV.
[13] V. Khacha yan, e al., J. High Ene gy Phys. 04 (2017) 039.
[14] H.A. And ews, e al., 2018.
[15] L. Apoliná io, J.G. Milhano, G.P. Salam, C.A. Salgado, Phys. Re . Le . 120 (2018)
232301.
[16] X.-N. Wang, Phys. Re . C 63 (2001) 054902.
[17] M. Gyulassy, I. Vi e , X.N. Wang, Phys. Re . Le . 86 (2001) 2537–2540.
[18] S.S. Adle , e al., Phys. Re . Le . 96 (2006) 032302.
[19] T. Renk, H. Holopainen, J. Au inen, K.J. Eskola, Phys. Re . C 85 (2012) 044915.
[20] J. Xu, A. Buzza i, M. Gyulassy, J. High Ene gy Phys. 08 (2014) 063.
[21] J. Liao, E. Shu yak, Phys. Re . Le . 102 (2009) 202302.
[22] J. Jia, W.A. Ho owi z, J. Liao, Phys. Re . C 84 (2011) 034904.
[23] B. Be z, M. Gyulassy, G. To ie i, Phys. Re . C 84 (2011) 024913.
[24] N. A mes o, e al., Phys. Re . C 86 (2012) 064904.
[25] B. Be z, M. Gyulassy, Phys. Re . C 86 (2012) 024903.
[26] B. Be z, M. Gyulassy, J. High Ene gy Phys. 08 (2014) 090, J. High Ene gy Phys.
10 (2014) 043 (E a um).
[27] J. Xu, J. Liao, M. Gyulassy, Chin. Phys. Le . 32 (2015) 092501.
[28] W.A. Ho owi z, Phys. Re . D 91 (2015) 085019.
[29] J. Xu, J. Liao, M. Gyulassy, J. High Ene gy Phys. 02 (2016) 169.
[30] J. Adam, e al., Phys. Le . B 753 (2016) 511–525.
[31] A. Ramamu i, E. Shu yak, Phys. Re . D 97 (2018) 016010.
[32] M. Luzum, J.-Y. Olli aul , Phys. Re . C 87 (2013) 044907.
[33] J. No onha-Hos le , B. Be z, J. No onha, M. Gyulassy, Phys. Re . Le . 116 (2016)
252301.
[34] B. Abele , e al., Phys. Le . B 720 (2013) 52–62.
[35] C.A. Salgado, U.A. Wiedemann, Phys. Re . D 68 (2003) 014008.
[36] H. Niemi, K.J. Eskola, R. Paa elainen, Phys. Re . C 93 (2016) 024907.
[37] N. A mes o, M. Caccia i, T. Hi ano, J.L. Nagle, C.A. Salgado, J. Phys. G 37 (2010)
025104.
[38] C. And és, N. A mes o, M. Luzum, C.A. Salgado, P. Zu i a, Eu . Phys. J. C 76
(2016) 475.
JID:PLB AID:135318 /SCO Doc opic: Phenomenology [m5G; 1.283; P n:24/02/2020; 16:03] P.7 (1-7)
C. And es e al. / Physics Le e s B •••(••••)•••••• 7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
[39] R. Baie , Nucl. Phys. A 715 (2003) 209–218.
[40] T. Renk, H. Holopainen, U. Heinz, C. Shen, Phys. Re . C 83 (2011) 014910.
[41] B. Be z, M. Gyulassy, M. Luzum, J. No onha, J. No onha-Hos le , I. Po illo, C.
Ra i, Phys. Re . C 95 (2017) 044901.
[42] D. Zigic, I. Salom, M. Djo dje ic, M. Djo dje ic, 2018.
[43] S. Shi, J. Liao, M. Gyulassy, Chin. Phys. C 42 (2018) 104104.
[44] S. Shi, J. Liao, M. Gyulassy, 2018.
[45] M. S a mann, W. Vogelsang, Phys. Re . D 64 (2001) 114007.
[46] P.M. Nadolsky, H.-L. Lai, Q.-H. Cao, J. Hus on, J. Pumplin, D. S ump, W.-K. Tung,
C.P. Yuan, Phys. Re . D 78 (2008) 013004.
[47] K.J. Eskola, H. Paukkunen, C.A. Salgado, J. High Ene gy Phys. 04 (2009) 065.
[48] D. de Flo ian, R. Sasso , M. S a mann, Phys. Re . D 75 (2007) 114010.
[49] D. de Flo ian, R. Sasso , M. Epele, R.J. He nández-Pin o, M. S a mann, Phys. Re .
D 91 (2015) 014035.
[50] K.M. Bu ke, e al., Phys. Re . C 90 (2014) 014909.
[51] K.J. Eskola, K. Kajan ie, P.V. Ruuskanen, K. Tuominen, Nucl. Phys. B 570 (2000)
379–389.
[52] P. Huo inen, P. Pe eczky, Nucl. Phys. A 837 (2010) 26–53.
[53] P. Huo inen, Eu . Phys. J. A 37 (2008) 121–128.
[54] H. Niemi, K.J. Eskola, R. Paa elainen, K. Tuominen, Phys. Re . C 93 (2016)
014912.
[55] K.J. Eskola, H. Niemi, R. Paa elainen, K. Tuominen, Phys. Re . C 97 (2018)
034911.
[56] H. Niemi, K.J. Eskola, R. Paa elainen, K. Tuominen, Nucl. Phys. A 982 (2019)
443–446.
[57] S. Cha chyan, e al., Phys. Re . Le . 109 (2012) 022301.
[58] G. Aad, e al., Phys. Le . B 707 (2012) 330–348.
[59] B. Abele , e al., Phys. Le . B 719 (2013) 18–28.
[60] E. Bianchi, J. Elledge, A. Kuma , A. Majumde , G.-Y. Qin, C. Shen, 2017.
[61] J. Casalde ey-Solana, Z. Hulche , G. Milhano, D. Pablos, K. Rajagopal, 2018.
[62] C. And es, N. A mes o, H. Niemi, R. Paa elainen, C.A. Salgado, P. Zu i a, Nucl.
Phys. A 967 (2017) 492–495.
[63] A. Majumde , B. Mulle , X.-N. Wang, Phys. Re . Le . 99 (2007) 192301.
[64] C. Ra i, Rep. P og. Phys. 81 (2018) 084301.
[65] T. Hi ano, K. Tsuda, Phys. Re . C 66 (2002) 054905.