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Two-pion em oscopy in p-Pb collisions a √sNN = 5.02 TeV
ALICE Collabo a ion
ALICE Collabo a ion. (2015). Two-pion em oscopy in p-Pb collisions a √sNN = 5.02
TeV. Physical Re iew C, 91(3), A icle 034906.
h ps://doi.o g/10.1103/PhysRe C.91.034906
2015
PHYSICAL REVIEW C 91, 034906 (2015)
Two-pion em oscopy in p-Pb collisions a √sNN =5.02 TeV
J. Adam e al.∗
(ALICE Collabo a ion)
(Recei ed 3 Feb ua y 2015; published 24 Ma ch 2015)
We epo he esul s o he em oscopic analysis o pai s o iden ical pions measu ed in p-Pb collisions a
√sNN =5.02 TeV. Fem oscopic adii a e de e mined as a unc ion o e en mul iplici y and pai momen um in
h ee spa ial dimensions. As in he pp collision sys em, he analysis is complica ed by he p esence o sizable
backg ound co ela ion s uc u es in addi ion o he em oscopic signal. The adii inc ease wi h e en mul iplici y
and dec ease wi h pai ans e se momen um. When aken a compa able mul iplici y, he adii measu ed in p-Pb
collisions, a high mul iplici y and low pai ans e se momen um, a e 10%–20% highe han hose obse ed in
pp collisions bu below hose obse ed in A-Acollisions. The esul s a e compa ed o hyd odynamic p edic ions
a la ge e en mul iplici y as well as discussed in he con ex o calcula ions based on gluon sa u a ion.
DOI: 10.1103/PhysRe C.91.034906 PACS numbe (s): 25.75.Dw,24.10.Nz,25.75.Ag
I. INTRODUCTION
The La ge Had on Collide (LHC) [1] deli e ed Pb-Pb
collisions a √sNN =2.76 TeV in 2010 and in 2011. Se e al
signa u es o a qua k-gluon plasma we e obse ed, including
a s ong supp ession o high-pTpa icle p oduc ion (“je
quenching”) [2–4], as well as collec i e beha io a low
pT[5,6], which is well desc ibed by hyd odynamic models
wi h a low shea - iscosi y- o-en opy a io. A compa ison
o e e ence esul s om pp collisions a √s=0.9, 2.76,
and 7 TeV shows ha hese e ec s canno be desc ibed by
an incohe en supe posi ion o nucleon-nucleon collisions.
As such, hey can be in e p e ed as inal-s a e phenomena,
cha ac e is ic o he new s a e o ma e [7–10] c ea ed in
hea y-ion collisions. To e i y he c ea ion o such a s a e,
p-Pb collisions a √sNN =5.02 TeV, whe e a qua k-gluon
plasma is no expec ed o o m, we e p o ided by he
LHC. In pa icula , cold-nuclea -ma e e ec s, such as gluon
sa u a ion, which a e expec ed o in luence a numbe o
obse ables, a e being in es iga ed [11].
One o he obse ables cha ac e izing he bulk collec i e
sys em is he size o he pa icle-emi ing egion a eeze-
ou , which can be ex ac ed wi h em oscopic echniques
[12,13]. In pa icula , wo-pa icle co ela ions o iden ical
pions [ e e ed o as Bose-Eins ein, o Hanbu y-B own–Twiss
co ela ions] p o ide a de ailed pic u e o he sys em size and
i s dependence on he pai ans e se momen um and he e en
mul iplici y. Fem oscopy measu es he appa en wid h o he
dis ibu ion o ela i e sepa a ion o emission poin s, which
is con en ionally called he “ adius pa ame e .” The adius
can be de e mined independen ly o h ee di ec ions: long
along he beam axis, ou along he pai ans e se momen um,
and side, pe pendicula o he o he wo. Such measu emen s
we e pe o med a he LHC o cen al Pb-Pb collisions [14]
∗Full au ho lis gi en a he end o he a icle.
Published by he Ame ican Physical Socie y unde he e ms o he
C ea i e Commons A ibu ion 3.0 License. Fu he dis ibu ion o
his wo k mus main ain a ibu ion o he au ho (s) and he published
a icle’s i le, jou nal ci a ion, and DOI.
as well as o pp collisions a √s=0.9 and 7 TeV [15–18]
and compa ed o esul s om hea y-ion collisions a lowe
collision ene gies. Two clea ends we e ound. (i) In A-A
collisions all adii scale app oxima ely linea ly wi h he cube
oo o he inal-s a e cha ged-pa icle mul iplici y densi y
a mid apidi y dNch/dη1/3 o all h ee adii sepa a ely,
consis en wi h p e ious indings [13]. Fo pp collisions, he
adii scale linea ly wi h he cube oo o cha ged-pa icle
mul iplici y densi y as well; howe e , he slope and in e cep
o he scaling line a e clea ly di e en han o A-A. (ii) A
signi ican , uni e sal dec ease o he adii wi h pai momen um
has been obse ed in A-Acollisions, while he analogous end
in pp depends on he conside ed di ec ion (ou , side, o long)
and e en mul iplici y. A ans e se momen um dependence o
he adii simila o A-Awas obse ed o he asymme ic d-Au
collision sys em a he BNL Rela i is ic Hea y Ion Collide
(RHIC) [19,20]. The one-dimensional adii ex ac ed om he
ALICE h ee-pion cumulan analysis we e also in es iga ed
in pp,p-Pb, and Pb-Pb collisions a he LHC [21]. Fo he
p-Pb sys em, a a gi en mul iplici y, he adii we e ound o
be 5%–15% la ge han hose in pp, while he adii in Pb-Pb
we e 35%–55% la ge han hose in p-Pb.
The A-Apion em oscopy esul s a e in e p e ed wi hin
he hyd odynamic amewo k as a signa u e o collec i e
adial low. Models including his e ec a e able o ep oduce
he ALICE da a o cen al collisions [22,23]. A emp s
o desc ibe he pp da a in he same amewo k ha e no
been success ul so a and i is specula ed ha addi ional
e ec s ela ed o he unce ain y p inciple may play a ole
in such small sys ems [24]. In p-Acollisions, hyd odynamic
models ha assume he c ea ion o a ho and dense sys em
expanding hyd odynamically p edic sys em sizes la ge han
hose obse ed in pp, and compa able o hose obse ed in
lowe -ene gy A-Acollisions a he same mul iplici y [24,25].
Howe e , such models ha e an inhe en unce ain y o he
ini ial-s a e shape and size, which can also di e be ween pp
and pe iphe al A-Acollisions.
Al e na i ely, a model based on gluon sa u a ion sugges s
ha he ini ial sys em size in p-Acollisions should be simila
o ha obse ed in pp collisions, a leas in he ans e se
di ec ion [26,27]. A ha s age bo h sys ems a e ea ed in
0556-2813/2015/91(3)/034906(18) 034906-1 ©2015 CERN, o he ALICE Collabo a ion
J. ADAM e al. PHYSICAL REVIEW C 91, 034906 (2015)
he same manne in he colo glass condensa e (CGC) model,
so ha hei subsequen e olu ion should lead o compa able
adius pa ame e a eeze-ou . Re e ence [28] sugges s a
(small) Yang-Mills e olu ion in addi ion. The obse a ion o
a la ge size in he p-Asys em wi h espec o pp would
mean ha a compa able ini ial s a e e ol es di e en ly in
he wo cases, which is no easily explained wi hin he
CGC app oach alone. The d-Au da a measu ed a RHIC
sugges ha hyd odynamic e olu ion may be p esen in such a
sys em, while he ALICE h ee-pion analysis a he LHC [21]
lea es oom o di e en in e p e a ions. The pion em oscopic
adii as a unc ion o pai ans e se momen um om p-Pb
collisions a √sNN =5.02 TeV, which a e epo ed in his
pape , p o ide addi ional cons ain s on he alidi y o bo h
app oaches.
The pape is o ganized as ollows. In Sec. II he da a- aking
condi ions, oge he wi h e en and ack selec ions, a e
desc ibed. The em oscopic co ela ion unc ion analysis, as
well as he ex ac ion o he adii and associa ed sys ema ic
unce ain ies and he discussion o he i ing p ocedu e, a e
explained in Sec. III. In Sec. IV he esul s o he adii
a e shown and compa ed o model p edic ions. Sec ion V
concludes he pape .
II. DATA TAKING AND TRACK RECONSTRUCTION
The LHC deli e ed p-Pb collisions a he beginning o 2013
a √sNN =5.02 TeV (4 and 1.58 TeV pe nucleon o he pand
Pb beams, espec i ely). The nucleon-nucleon cen e -o -mass
sys em is shi ed wi h espec o he ALICE labo a o y sys em
by 0.465 uni o apidi y in he di ec ion o he p o on beam.
The ALICE de ec o and i s pe o mance a e desc ibed
in Re s. [29,30]. The main igge ing de ec o is he V0,
consis ing o wo a ays o 32 scin illa o coun e s, which
a e ins alled on each side o he in e ac ion poin and co e
2.8<η
lab <5.1 (V0A, loca ed on he Pb- emnan side),
and −3.7<η
lab <−1.7 (V0C). The minimum-bias igge
equi es a signal in bo h V0 de ec o s wi hin a ime window
ha is consis en wi h he collision occu ing a he cen e o
he ALICE de ec o . Addi ionally, speci ic selec ion c i e ia
o emo e pileup collisions a e applied [30]. App oxima ely
8×107minimum-bias e en s we e analyzed.
The analysis was pe o med in mul iplici y classes, which
we e de e mined based on he signal om he V0A de-
ec o , loca ed along he Pb-going beam. This ensu es ha
he mul iplici y de e mina ion p ocedu e uses pa icles a
apidi ies signi ican ly di e en om he ones used o he pion
co ela ion analysis, a oiding po en ial au oco ela ion e ec s.
E en s a e g ouped in ou mul iplici y classes: 0%–20%,
20%–40%, 40%–60%, and 60%–90%, de ined as ac ions o
he analyzed e en sample so ed by dec easing V0A signal,
which is p opo ional o he mul iplici y wi hin he accep ance
o his de ec o . Table Ishows he mul iplici y class de ini ions
and he co esponding mean cha ged-pa icle mul iplici y
densi ies dNch/dηa e aged o e |ηlab|<0.5 as ob ained
using he me hod p esen ed in Re . [31]. The dNch/dη
alues a e no co ec ed o igge and e ex- econs uc ion
ine iciency, which is abou 4% o nonsingle di ac i e e en s
[31].
TABLE I. De ini ion o he V0A mul iplici y classes as ac-
ions o he analyzed e en sample and hei co esponding
dNch/dη(|ηlab|0.5,pT0). The gi en unce ain ies a e sys ema ic
only because he s a is ical unce ain ies a e negligible.
E en class (%) dNch/dη
|ηlab|0.5,pT0 (GeV/c)
60–90 8.2±0.3
40–60 16.1±0.4
20–40 23.2±0.5
0–20 35.5±0.8
Cha ged ack econs uc ion is pe o med using he Time
P ojec ion Chambe (TPC) and he Inne T acking Sys em
(ITS). The TPC is a la ge- olume cylind ical gaseous acking
chambe , p o iding in o ma ion o pa icle ajec o ies and
hei speci ic ene gy loss. The eadou chambe s moun ed on
he end caps a e a anged in 18 sec o s on each side (co e ing
he ull azimu hal angle) measu ing up o 159 samples pe
ack. The TPC co e s an accep ance o |ηlab|<0.8 o acks
which each he ou e adius o he TPC and |ηlab|<1.5
o sho e acks. The ITS is composed o posi ion-sensi i e
silicon de ec o s. I consis s o six cylind ical laye s: wo
laye s o silicon pixel de ec o (SPD) closes o he beam
pipe co e ing |ηlab|<2.0 and |ηlab|<1.4 o inne and ou e
laye s, espec i ely, wo laye s o silicon d i de ec o in he
middle co e ing |ηlab|<0.9, and wo laye s o silicon s ip
de ec o on he ou side co e ing |ηlab|<1.0. The in o ma ion
om he ITS is used o acking and p ima y pa icle selec ion.
The momen um o each ack is de e mined om i s cu a u e
in he uni o m magne ic ield o 0.5 T o ien ed along he beam
axis, p o ided by he ALICE solenoidal magne .
The p ima y- e ex posi ion is de e mined wi h acks
econs uc ed in he ITS and TPC, as desc ibed in Re . [32].
E en s a e selec ed i he e ex posi ion along he beam
di ec ion is wi hin ±10 cm o he cen e o he de ec o . This
ensu es a uni o m accep ance in ηlab.
Each ack is equi ed o exploi signals in bo h TPC and
ITS. The ack segmen s om bo h de ec o s ha e o ma ch.
Addi ionally, each ack is equi ed o ha e a leas one hi in
he SPD. A TPC ack segmen is econs uc ed om space
poin s (clus e s). Each ack is equi ed o be composed o
a leas 50 o he 159 such clus e s. The pa ame e s o he
ack a e de e mined by a Kalman i o he se o TPC +ITS
clus e s. The quali y o he i χ2was equi ed o be be e
han 4 pe clus e in he TPC and be e han 36 in ITS.
T acks ha show a kink opology in he TPC a e ejec ed. To
ensu e ha dominan ly p ima y-pa icle acks a e selec ed,
he dis ance o closes app oach o he p ima y e ex is
equi ed o be close han 2.0 cm in he longi udinal di ec ion
and (0.0105 +0.0350 ×p−1.1
T) cm, wi h pTin GeV/c,in he
ans e se di ec ion. The kinema ic ange o pa icles selec ed
o his analysis is 0.12 <p
T<4.0GeV/c and |ηlab|<0.8.
The ime-o - ligh (TOF) de ec o is used oge he wi h
he TPC o pion iden i ica ion. The TOF is a cylind ical
de ec o o modula s uc u e, consis ing o 18 azimu hal
sec o s di ided in o 5 modules along he beam axis a a
034906-2
TWO-PION FEMTOSCOPY IN p-Pb COLLISIONS AT . . . PHYSICAL REVIEW C 91, 034906 (2015)
adius ≃380 cm. The ac i e elemen s a e mul igap esis i e
chambe s (MRPCs). Fo bo h TPC and TOF, he signal
(speci ic ene gy loss dE/dx o he TPC and he ime o ligh
o TOF) o each econs uc ed pa icle is compa ed wi h he
one expec ed o a pion. The di e ence is con on ed wi h
he de ec o esolu ion. The allowed de ia ions a y be ween
2σand 5σ o he TPC and 2σand 3σ o TOF depending
on he momen um o he pa icle. The selec ion c i e ia a e
op imized o ob ain a high-pu i y sample while maximizing
e iciency, especially in he egions whe e he expec ed signal
o o he pa icles (elec ons, kaons, and p o ons o he TPC;
kaons o TOF) app oaches he pion alue. The pu i y o he
pion sample is abo e 98%.
The accep ed pa icles om each e en a e combined
o pai s. The wo-pa icle de ec o accep ance e ec s, ack
spli ing and ack me ging, a e p esen . T ack spli ing occu s
when a single ajec o y is mis akenly econs uc ed as wo
acks. The ALICE acking algo i hm has been speci ically
designed o supp ess such cases. In a a e e en when spli ing
happens, wo acks a e econs uc ed mos ly om he same
clus e s in he ALICE TPC. The e o e, pai s which sha e mo e
han 5% o clus e s a e emo ed om he sample. Toge he
wi h he an ime ging cu desc ibed below, his elimina es he
in luence o he spli pai s. T ack me ging can be unde s ood
as wo-pa icle co ela ed e iciency and sepa a ion powe . In
he ALICE TPC, wo acks canno be dis inguished i hei
ajec o ies s ay close o each o he h ough a signi ican pa
o he TPC olume. Al hough his happens a ely, such pai s
by de ini ion ha e low ela i e momen um and he e o e hei
absence dis o s he co ela ion unc ion in he signal egion.
T ack spli ing and ack me ging a e aken in o accoun and
co ec ed wi h he p ocedu e desc ibed in Re . [16]. The e ec
o he wo-pa icle de ec o accep ance on he inal esul s is
simila o wha was obse ed in pp and is limi ed o low
pai ela i e momen um, whe e i sligh ly a ec s he shape
o he co ela ion unc ion. Howe e , in p-Pb collisions he
em oscopic e ec is an o de o magni ude wide han any
egion a ec ed by his ine iciency and, as a consequence, he
ex ac ed adii a e no a ec ed by he wo- ack accep ance.
III. CORRELATION FUNCTION ANALYSIS
A. Cons uc ion o he co ela ion unc ion
The co ela ion unc ion C(p1,p2) o wo pa icles wi h
momen a p1and p2is de ined as
C(p1,p2)=A(p1,p2)
B(p1,p2).(1)
The signal dis ibu ion Ais cons uc ed om pai s o pa icles
om he same e en . The backg ound dis ibu ion Bshould
be cons uc ed om unco ela ed pa icles measu ed wi h
he same single-pa icle accep ance. I is buil using he
e en mixing me hod wi h he wo pa icles coming om
wo di e en e en s o which he e ex posi ions in beam
di ec ion ag ee wi hin 2 cm and he mul iplici ies di e by
no mo e han 1/4 o he wid h o he gi en e en class. The
denomina o is no malized o he numbe o en ies in he
nume a o , so ha he absence o co ela ion gi es a co ela ion
unc ion a uni y.
The em oscopic co ela ion is measu ed as a unc ion o
he momen um di e ence o he pai q=p2−p1as
C(q)=A(q)
B(q),(2)
whe e he dependence on he pai o al ans e se momen um
kT=|p1,T+p2,T|/2 is in es iga ed by pe o ming he analysis
in he ollowing anges in kT: 0.2–0.3, 0.3–0.4, 0.4–0.5, 0.5–
0.6, 0.6–0.7, 0.7–0.8, and 0.8–1.0 GeV/c.ThekT anges a e he
same o each mul iplici y class, esul ing in 28 independen
co ela ion unc ions o e all. Sys ema ic unce ain ies on he
co ela ion unc ions a e discussed in Sec. III D.
The momen um di e ence qis e alua ed in he lon-
gi udinally como ing sys em (LCMS) ame in which he
o al longi udinal pai momen um anishes: p1,L+p2,L=0,
simila ly o p e ious measu emen s in small sys ems [16].
In Fig. 1co ela ion unc ions a e shown, p ojec ed o e
128 MeV/c-wide slices along he qou ,qside, and qlong axes.
An enhancemen a low ela i e momen um is seen in all
p ojec ions. The wid h o his co ela ion peak g ows wi h
dec easing mul iplici y o wi h inc easing kT. The em oscopic
e ec is expec ed o disappea a la ge q=|q|, wi h he
co ela ion unc ion app oaching uni y. We obse e, especially
o la ge kTand small mul iplici ies, ha he co ela ion
unc ion is no la in his egion and has di e en alues
in di e en p ojec ions.1The cause may be non em oscopic
co ela ions, which a e p esumably also a ec ing he shape
o he co ela ion unc ion in he em oscopic (low-q) egion.
This issue is a majo sou ce o sys ema ic unce ain y on he
ex ac ed adii and is discussed in de ail in Secs. III B and III C.
The pai dis ibu ions and he co ela ion unc ion can be
ep esen ed in sphe ical ha monics (SH) [33,34] al e na i ely
o he adi ionally used Ca esian coo dina es. All odd-l
and odd-mcomponen s o such a ep esen a ion anish o
symme y easons. The impo an ea u es o he co ela ion
unc ion a e ully cap u ed by he ollowing ones: l=0,
m=0 is sensi i e o he o e all size o he pion sou ce,
l=2, m=0 is sensi i e o he di e ence be ween he
longi udinal and ans e se sizes, and l=2, m=2 e lec s
he di e ence be ween he sidewa ds and ou wa ds ans e se
adii. The e o e, h ee independen sizes o he sou ce can also
be ex ac ed om hese h ee SH componen s.
In Fig. 2we show he i s h ee non anishing componen s
o he SH ep esen a ion co esponding o he co ela ion unc-
ions shown in Fig. 1.In he(0,0) componen , he enhancemen
a low qis clea ly isible, dec easing (inc easing) in wid h wi h
mul iplici y (kT). The o he wo componen s, (2,0) and (2,2),
also show s uc u es in his egion, indica ing ha he sou ce
shape is no sphe ically symme ic in he LCMS ame.
B. Non em oscopic s uc u es
As men ioned in he discussion o Figs. 1and 2,a
signi ican non em oscopic co ela ion is obse ed in he ange
1We no e ha he o e all no maliza ion o he co ela ion unc ion
is a single alue o he ull h ee-dimensional objec and canno be
independen ly uned in all p ojec ions.
034906-3
J. ADAM e al. PHYSICAL REVIEW C 91, 034906 (2015)
)
ou
q(C
1
1.2
1.4
1.6 = 5.02 TeV
NN
sALICE p-Pb
pai s
+
π
+
π
c| < 64 MeV/
side
q|
c| < 64 MeV/
long
q|
)
side
q(C
1
1.2
1.4
1.6 V0A mul iplici y classes (Pb-side)
)c < 0.3 (GeV/
T
k0-20%, 0.2 <
)c < 0.7 (GeV/
T
k0-20%, 0.6 <
)c < 0.3 (GeV/
T
k60-90%, 0.2 <
c| < 64 MeV/
ou
q|
c| < 64 MeV/
long
q|
)c (GeV/
ou ,side,long
q
0 0.2 0.4
)
long
q(C
1
1.2
1.4
1.6 c| < 64 MeV/
ou
q|
c| < 64 MeV/
side
q|
FIG. 1. (Colo online) P ojec ions o he h ee-dimensional
π+π+co ela ion unc ions o h ee selec ed mul iplici y and kT
anges along he ou ( op), side (middle), and long (bo om) di ec ions.
The o he componen s a e in eg a ed o e he ou bins closes o ze o
in hei espec i e qdi ec ions.
in q ha is much la ge han he cha ac e is ic wid h o
he em oscopic e ec . As an example, in Fig. 3we show
he co ela ion in he SH ep esen a ion up o 2.0GeV/c
in q. Fo he lowes mul iplici y, and o a smalle deg ee a
highe mul iplici ies, a signi ican slope in he low-q egion
is seen in he (0,0) componen and a de ia ion om ze o in
he (2,0) componen up o app oxima ely 1 GeV/c. Simila
co ela ions ha e been obse ed by ALICE in pp collisions
[16]. They we e in e p e ed, based on Mon e Ca lo model
simula ions, o be a mani es a ion o minije s, he collima ed
agmen a ion o pa ons sca e ed wi h modes momen um
ans e . The lowes mul iplici ies obse ed in p-Pb collisions
a e compa able o hose in pp collisions a √s=7TeV.
The e o e, a simila in e p e a ion o he non em oscopic
co ela ions in his analysis is na u al. Simila s uc u es ha e
been obse ed in d-Au collisions by STAR [19]. This pic u e
)q(
0
0
C
1
1.2
1.4
1.6
= 5.02 TeV
NN
sALICE p-Pb
pai s
+
π
+
π
)q(
0
2
C
-0.1
-0.05
0
0.05
0.1 V0A mul iplici y classes (Pb-side)
)c < 0.3 (GeV/
T
k0-20%, 0.2 <
)c < 0.7 (GeV/
T
k0-20%, 0.6 <
)c < 0.3 (GeV/
T
k60-90%, 0.2 <
)c (GeV/q
0 0.2 0.4 0.6
)q(
2
2
C
-0.1
-0.05
0
0.05
0.1
FIG. 2. (Colo online) Fi s h ee non anishing componen s o
he SH ep esen a ion o he π+π+co ela ion unc ions o h ee
mul iplici y and kT anges, l=0, m=0 ( op), l=2, m=0 (middle),
and l=2, m=2 (bo om).
is co obo a ed by he analysis using he h ee-pion cumulan s,
whe e, expec edly, he minije con ibu ion is supp essed [21].
Two impo an ea u es o he non em oscopic co ela ion
a ec he in e p e a ion o ou esul s. Fi s , i is a b oad
s uc u e, ex ending up o 1 GeV/c and we ha e o assume
ha i also ex ends o 0 GeV/c in q. The e o e, i a ec s he
ex ac ed em oscopic adii and has o be aken in o accoun in
he i ing p ocedu e. I can be quan i ied in he high-q egion
and hen ex apola ed, wi h some assump ions, o he low-q
egion, unde he em oscopic peak. The p ocedu e leads o
a sys ema ic unce ain y. Second, i becomes isibly la ge
as mul iplici y dec eases and also as kTinc eases, which is
consis en wi h he minije -like co ela ion.
The backg ound was s udied in Mon e Ca lo models,
such as, o p-Pb collisions, AMPT [35], HIJING [36], DPMJET
[37], EPOS 3.076 [38,39], and PYTHIA 6.4 (Pe ugia-0 une)
[40,41] o pp collisions a simila mul iplici ies. In all
034906-4

TWO-PION FEMTOSCOPY IN p-Pb COLLISIONS AT . . . PHYSICAL REVIEW C 91, 034906 (2015)
)q(
0
0
C
1
1.2
1.4
= 5.02 TeV
NN
sALICE p-Pb
)c < 0.4 (GeV/
T
k pai s, 0.3 <
+
π
+
π
)q(
0
2
C
-0.05
0
0.05
V0A mul iplici y classes (Pb-side)
0-20%
20-40%
40-60%
60-90%
)c (GeV/q
0 0.5 1 1.5 2
)q(
2
2
C
-0.05
0
0.05
0.1
FIG. 3. (Colo online) Dependence o he SH componen s o
he co ela ion unc ion on e en mul iplici y in a b oad ela i e
momen um ange.
cases, he Mon e Ca lo co ela ion unc ions exhibi signi ican
s uc u es simila o he long- ange e ec s obse ed in da a,
which is ano he a gumen o hei non em oscopic o igin.
Howe e , quan i a i e di e ences in he magni ude and shape
o hese s uc u es when compa ed o hose obse ed in
da a a e seen o AMPT,HIJING, and DPMJET. These models
a e he e o e unsui able o a p ecise cha ac e iza ion o he
backg ound, which is needed o he i ing p ocedu e. The
only models ha quali a i ely desc ibe he ea u es o he
backg ound (enhancemen a low q, g owing wi h kT, and
alling wi h mul iplici y) a e EPOS 3.076 and PYTHIA 6.4
(Pe ugia-0 une), which was also used in he pp analysis
[16]. We no e ha PYTHIA simula ion included ull de ec o
esponse modeling, while he EPOS 3.076 one did no . The
compa ison wi h da a is shown in Fig. 4. The beha io o he
co ela ion is well ep oduced abo e 0.5 GeV/c in q, whe e
non em oscopic co ela ions a e expec ed o domina e. A low
q, below 0.3 GeV/c, he da a and models di e ge, which is
expec ed, as he em oscopic co ela ions a e no included in
he model calcula ion. Abo e 0.3 GeV/c,EPOS ep oduces
he (0,0) componen well, PYTHIA sligh ly o e es ima es he
da a. Fo he (2,0) and (2,2) componen s, which desc ibe he
)q(
0
0
C
1
1.2
1.4
1.6 = 5.02 TeV
NN
sALICE p-Pb
)c < 0.7 (GeV/
T
k pai s, 0.6 <
+
π
+
π
V0A mul iplici y classes (Pb-side)
= 35.5〉
η
/d
ch
N d〈0-20%,
= 35.5〉
η
/d
ch
N d〈EPOS 3.076,
= 27.6〉
η
/d
ch
N d〈 = 7 TeV, sPYTHIA 6.4 Pe ugia-0, pp
)q(
0
2
C
-0.1
-0.05
0
0.05
)c (GeV/q
0 0.5 1 1.5 2
)q(
2
2
C
-0.1
0
FIG. 4. (Colo online) Fi s h ee non anishing componen s o
he SH ep esen a ion o he π+π+co ela ion unc ions o a selec ed
mul iplici y and kT ange, compa ed o a calcula ion om EPOS3.076
[38,39] (gene a o le el only) and PYTHIA6.4 Pe ugia-0 une [40,41]
o pp a √s=7 TeV ( ull simula ion wi h de ec o esponse).
h ee-dimensional shape o he non em oscopic co ela ions,
PYTHIA is close o he expe imen al da a. O e all, o like-sign
pai s, bo h models a e easonable app oxima ions o he
non em oscopic backg ound. We use hese models o ix he
backg ound pa ame e s in he i ing p ocedu e.
Simila ly o he pp analysis [16], he unlike-sign pai s
ha e also been s udied. We ound ha co ela ions in he
(0,0) componen o PYTHIA a e sligh ly la ge han in da a
in he em oscopic egion o all kT anges and simila o
da a in he (2,0) and (2,2) componen s. EPOS was ound o
easonably desc ibe he unlike-sign pai s o low kT anges
and has smalle co ela ion han da a in he (0,0) componen
in highe kT anges.
C. Fi ing he co ela ion unc ions
The space- ime cha ac e is ics o he sou ce a e e lec ed in
he co ela ion unc ion
C(q)=S( ,q)|(q, )|2d4 , (3)
034906-5
J. ADAM e al. PHYSICAL REVIEW C 91, 034906 (2015)
whe e is he pai space- ime sepa a ion ou - ec o . Sis he
sou ce emission unc ion, in e p e ed as a p obabili y densi y
desc ibing he emission o a pai o pa icles wi h a gi en
ela i e momen um and space- ime sepa a ion. is he wo-
pa icle in e ac ion ke nel.
P e ious em oscopy s udies in hea y-ion collisions a
CERN Supe P o on Synch o on [42], RHIC [43–49], and
a he LHC [14] used a Gaussian s a ic sou ce S,
S( )≈exp − 2
ou
4RG
ou
2− 2
side
4RG
side
2− 2
long
4RG
long
2.(4)
The RG
ou ,RG
side, and RG
long pa ame e s desc ibe he single-
pa icle sou ce size in he LCMS in he ou , side, and long
di ec ions, espec i ely.
The Gaussian sou ce p o ides a commonly used app oxi-
ma ion o he sou ce size and was used o compa e o o he
expe imen al esul s, especially he ones coming om A-A
collisions, whe e he sou ce shape is mo e Gaussian han in
small sys ems. While pu suing he s anda d p ocedu e wi h
he Gaussian assump ion, we also ca e ully look o any
de ia ions be ween he i unc ion and da a ha migh sugges
a signi ican ly non-Gaussian shape o he sou ce, which would
be an impo an simila i y o he pp case.
In he analysis o pp collisions by ALICE [16], a Gaussian
is used oge he wi h o he sou ce shapes, exponen ial and
Lo en zian [16]. A Lo en zian pa ame iza ion in he ou and
long di ec ions and a Gaussian pa ame iza ion in he side
di ec ion we e ound o i he da a bes acco ding o χ2/nd .
The e o e, we use his sou ce pa ame iza ion also in he
analysis o p-Pb collisions,
S( )≈1
2
ou +RE
ou
2exp − 2
side
4RG
side
21
2
long +RE
long
2.(5)
The co esponding sou ce sizes in ou and long a e RE
ou and
RE
long, while o he side di ec ion he size pa ame e RG
side is
he same as in he Gaussian case.
Fo iden ical pions, which a e bosons, mus be sym-
me ized. Because cha ged pions also in e ac ia he Coulomb
and s ong inal-s a e in e ac ions (FSIs), ||2co esponds o
he Be he-Salpe e ampli ude [50]. Fo like-sign pion pai s he
con ibu ion o he s ong in e ac ion is small o he expec ed
sou ce sizes [50] and is neglec ed he e. The used  he e o e
is a symme ized Coulomb wa e unc ion. I is app oxima ed
by sepa a ing he Coulomb pa and in eg a ing i sepa a ely,
ollowing he p ocedu e known as Bowle -Sinyuko i ing
[51,52], which was used p e iously o la ge sizes obse ed
in Pb-Pb [14], as well as smalle sizes obse ed in pp collisions
[16]. In his app oxima ion, he in eg a ion o Eq. (3) wi h S
gi en by Eq. (4) esul s in he ollowing unc ional o m o
he co ela ion unc ion which is used o i he da a
C (q)=(1 −λ)+λKC(q)1+exp −RG
ou
2q2
ou
−RG
side
2q2
side −RG
long
2q2
long.(6)
The unc ion KC(q) is he Coulomb pa o he wo-pion wa e
unc ion in eg a ed o e he sphe ical Gaussian sou ce wi h a
ixed adius. The alue o his adius is chosen o be 2 m.
I s unce ain y has sys ema ic e ec s on he inal esul s (see
Sec. III D). This o m o he co ela ion unc ion om Eq. (6)
is deno ed in he ollowing as GGG. Simila ly o he sou ce
shape gi en by Eq. (5), he co ela ion unc ion is
C (q)=(1 −λ)+λKC1+exp −RE
ou
2q2
ou
−RG
side
2q2
side −RE
long
2q2
long.(7)
I has an exponen ial shape in ou and long and a Gaussian
shape in he side di ec ion. The e o e, i is e e ed o as EGE
o m o he co ela ion unc ion. Pa ame e λin Eqs. (6) and
(7) ep esen s he co ela ion s eng h.
Addi ionally, a componen desc ibing non em oscopic
co ela ions needs o be in oduced. The e is no ap io i
unc ional o m which can be used o his componen .
Se e al o i s ea u es can be deduced om he co ela ions
shown in Figs. 1,2, and 3: I has o allow o di e en
shapes in he ou , side, and long di ec ions; in he (0,0)
componen i has o ex apola e smoo hly o low qand ha e
a anishing slope a q=0. Because his s uc u e is no
known, maximum in o ma ion abou i s shape and magni ude
should be gained om an obse a ion o he aw co ela ion
unc ions and he co esponding e ec s in Mon e Ca lo in
as many ep esen a ions as possible. I is he e o e c ucial o
simul aneously use he Ca esian and SH ep esen a ions as
hey p o ide complemen a y ways o s udy he co ela ion
shape.
An ad hoc, Mon e Ca lo-d i en pa ame iza ion o he
non em o backg ound ha easonably desc ibes he co ela ion
unc ion is , composed o h ee independen one-dimensional
unc ions 0
0(Gaussian plus ixed cons an ), 0
2(Gaussian plus
a iable cons an ), and 2
2(Gaussian plus an addi ional linea
componen ),
0
0(q)=N0
01+α0
0exp −q2
2(σ0
0)2,(8)
0
2(q)=α0
2exp −q2
2(σ0
2)2+β0
2,(9)
2
2(q)=α2
2exp −q2
2(σ2
2)2+β2
2+γ2
2q, (10)
whe e N0
0,α0
0,σ0
0,α0
2,σ0
2,α2
2,σ2
2, and γ2
2a e ixed o he alues
ob ained om i s o Mon e Ca lo e en s sepa a ely o each
mul iplici y and kT ange. In he i p ocedu e he β0
2and β2
2
pa ame e s a e kep ee. This esul s in he i o mula
C(q)=N·C (q)·0
0(q)·Y0
0(θ,ϕ)
+0
2(q)·Y0
2(θ,ϕ)+2
2(q)·Y2
2(θ,ϕ),(11)
whe e Nis he o e all no maliza ion ac o and Y0
0(θ,ϕ),
Y0
2(θ,ϕ), and Y2
2(θ,ϕ) a e he eal pa s o he ele an sphe ical
ha monic unc ions.
The i is pe o med wi h he log-likelihood me hod in h ee
dimensions o he Ca esian ep esen a ion. The Gaussian i
ep oduces he o e all wid h o he em oscopic co ela ion in
all cases. The backg ound componen desc ibes he beha io o
034906-6
TWO-PION FEMTOSCOPY IN p-Pb COLLISIONS AT . . . PHYSICAL REVIEW C 91, 034906 (2015)
)q(
0
0
C
1
1.2
1.4
1.6 = 5.02 TeV
NN
sALICE p-Pb
)c < 0.7 (GeV/
T
k pai s, 0.6 <
+
π
+
π
V0A mul iplici y classes (Pb-side)
0-20%
Full i
Fem oscopic e ec (Gaussian)
Non- em oscopic backg ound
)q(
0
2
C
-0.1
-0.05
0
0.05
0.1
)c (GeV/q
0 0.5 1
)q(
2
2
C
-0.1
-0.05
0
FIG. 5. (Colo online) Fi s h ee non anishing componen s o
he SH ep esen a ion o he π+π+co ela ion unc ions o h ee
mul iplici y and kTcombina ions, l=0, m=0 ( op), l=2, m=0
(middle), and l=2, m=2 (bo om). The lines show he co espond-
ing componen s o he Gaussian (GGG) i .
he co ela ion a la ge q, bu can also ha e nonze o co ela ion
a 0 in q.
A co esponding i is also pe o med o he SH ep-
esen a ion o he co ela ion, which is shown in Fig. 5.
The o mula om Eq. (6)o Eq.(7) ( o he GGG i o
he EGE i , espec i ely) is nume ically in eg a ed on a
ϕ−θsphe e o each qbin, wi h p ope Ym
lweigh s, o
p oduce he h ee componen s o he SH decomposi ion.
S a is ical unce ain ies on each componen as well as he
co a iance ma ix be ween hem a e aken in o accoun in his
simul aneous i o he h ee his og ams. The esul s a e shown
in Fig. 5. The i desc ibes he gene al di ec ion-a e aged
wid h o he co ela ion unc ion, shown in he op panel. The
backg ound componen desc ibes he beha io a la ge q
bu also con ibu es o he co ela ion a low q. The shape
in h ee-dimensional space, cap u ed by he (2,0) and (2,2)
componen s, is also a combina ion o he em oscopic and
non em oscopic co ela ions.
O e all, he GGG i desc ibes he wid h o he co ela ion
bu he da a a low qa e no pe ec ly ep oduced, which can be
)q(
0
0
C
1
1.2
1.4
1.6 = 5.02 TeV
NN
sALICE p-Pb
)c < 0.7 (GeV/
T
k pai s, 0.6 <
+
π
+
π
V0A mul iplici y classes (Pb-side)
0-20%
Full i
Fem oscopic e ec (Exp-Gauss-Exp)
Non- em oscopic backg ound
)q(
0
2
C
-0.1
-0.05
0
0.05
0.1
)c (GeV/q
0 0.5 1
)q(
2
2
C
-0.1
-0.05
0
FIG. 6. (Colo online) Fi s h ee non anishing componen s o
heSH ep esen a iono heπ+π+co ela ion unc ions o h ee
mul iplici y and kTcombina ions, l=0, m=0 ( op), l=2, m=0
(middle), and l=2, m=2 (bo om). The lines show he co espond-
ing componen s o he EGE i .
a ibu ed o he limi a ions o he Bowle -Sinyuko o mula
as well as o he non-Gaussian, long- ange ails which a e
possibly p esen in he sou ce. Some de ia ions om he pu e
Gaussian shape can also be seen o he long di ec ion o he
highe mul iplici ies. The EGE i [Eq. (7)] be e ep oduces
he co ela ion peak in he (0,0) componen , as shown in Fig. 6.
The (2,0) and (2,2) componen s show simila quali y o he i .
The χ2 alues o bo h i s a e compa able.
D. Sys ema ic unce ain ies on he adii
The analysis was pe o med sepa a ely o posi i ely and
nega i ely cha ged pions. Fo he p ac ically ze o-ne -ba yon-
densi y sys em p oduced a he LHC hey a e expec ed o gi e
consis en esul s. Bo h da a se s a e s a is ically consis en a
he co ela ion unc ion le el.
The main con ibu ions o he sys ema ic unce ain y a e
gi en in Table II o GGG adii and in Table III o EGE adii.
We used wo al e na i e ep esen a ions (Ca esian and
SH) o he co ela ion unc ion. The same unc ional o m
o bo h o hem was used o he i ing p ocedu e.
034906-7
J. ADAM e al. PHYSICAL REVIEW C 91, 034906 (2015)
TABLE II. Lis o con ibu ions o he sys ema ic unce ain y o
he em oscopic adii ex ac ed ia GGG i s. Values a e a e aged
o e kTand mul iplici y excep o he i s ow whe e a minimum-
maximum ange is shown.
Unce ain y sou ce RG
ou (%) RG
side (%) RG
long (%)
CF ep esen a ion and 5–32 4–22 4–35
backg ound pa ame iza ion
Fi - ange dependence 10 8 10
π+π+ s π−π−33 3
Momen um esolu ion co ec ion 3 3 3
Two- ack cu a ia ion <1<1<1
Coulomb co ec ion <1<1<1
To al co ela ed 12–34 9–24 11–36
To al 12–34 11–24 12–36
Howe e , he implemen a ion o he i ing p ocedu e is
qui e di e en : log-likelihood o Ca esian s egula χ2
i o SH, h ee-dimensional Ca esian his og am s h ee
one-dimensional his og ams, cubic o sphe ical i ing ange
in he (qou ,qside,qlong) space. The e o e, he i s o he wo
ep esen a ions may eac in a sys ema ically di e en way
o he a ia ion o he i ing p ocedu e ( i anges, Bowle -
Sinyuko app oxima ion, e c.).
The i ing p ocedu e equi es he knowledge o he non-
em oscopic backg ound shape and magni ude. Two models
we e used o es ima e i , EPOS 3.076 [39] and PYTHIA 6.4
(Pe ugia-0 une) [40,41], as desc ibed in Sec. III B.
In addi ion, he co ela ion unc ion shape is no ideally
desc ibed by a Gaussian o m. The EGE o m is be e (lowe
χ2 alues o he i ), bu s ill no exac ly accu a e. As a esul ,
he i alues depend on he i ing ange used in he p ocedu e
o adius ex ac ion. We ha e pe o med i s wi h an uppe
limi o he i ange a ied be ween 0.3 and 1.1 GeV/c.
The h ee e ec s men ioned abo e a e he main sou ces o
sys ema ic unce ain y on he adii. Thei in luence, a e aged
o e he e en mul iplici y and pai kT, is gi en in Tables II and
III. The backg ound pa ame iza ion and he CF ep esen a ion
e ec s lead o sys ema ic unce ain ies o less han 10% a
low kTand up o 35% o la ge kTand low mul iplici ies.
TABLE III. Lis o con ibu ions o he sys ema ic unce ain y
o he em oscopic adii ex ac ed ia EGE i s. Values a e a e aged
o e kTand mul iplici y excep o he i s ow, whe e a minimum-
maximum ange is shown.
Unce ain y sou ce RE
ou (%) RG
side (%) RE
long (%)
CF ep esen a ion and 4–18 3–14 8–20
backg ound pa ame iza ion
Fi - ange dependence 10 6 10
π+π+ s π−π−33 3
Momen um esolu ion co ec ion 3 3 3
Two- ack cu a ia ion <1<1<1
Coulomb co ec ion <1<1<1
To al co ela ed 11–21 7–16 13–23
To al 12–21 8–16 14–23
In pa icula , he adius could no be eliably ex ac ed o
he wo highes kT anges in he lowes mul iplici y ange;
he e o e, hese wo se s o adii a e no shown. Mo eo e ,
adii ob ained wi h he backg ound pa ame iza ion om
PYTHIA a e always la ge han he ones ob ained wi h he EPOS
pa ame iza ion. These unce ain ies a e co ela ed be ween kT
anges. Simila ly, he adii om he na ow i ange a e always,
on a e age, 10% highe han he ones om he wide i ange.
This also gi es a co ela ed con ibu ion o he sys ema ic
unce ain y. The inal adii a e calcula ed as an a e age o ou
se s o adii: he wo ep esen a ions wi h bo h EPOS and PYTHIA
backg ound pa ame iza ion. The sys ema ic unce ain ies a e
symme ic and equal o he la ges di e ence be ween he
adius and one o he ou se s o adii.
The e ec o he momen um esolu ion on he co ela ion
unc ion was s udied using a Mon e Ca lo simula ion. Fo
acks wi h a low pT, below 1 GeV/c, he momen um
esolu ion in he TPC is be e han 1%. Smea ing o he
single-pa icle momen a educes he heigh and inc eases he
wid h o he co ela ion unc ion. I was es ima ed ha his
e ec changes he econs uc ed adius by 2% o a sys em
size o 2 m and 3% o a size o 3 m. The e o e, he 3%
co ela ed con ibu ion om momen um esolu ion is always
added o he inal sys ema ic unce ain y es ima ion.
Smalle sou ces o sys ema ic unce ain ies include hose
o igina ing om he di e ence be ween posi i ely and nega-
i ely cha ged pion pai s (a ound 3%), ack selec ion a ia ion
(less han 1%), and he Coulomb ac o (less han 1%). All he
unce ain ies a e added in quad a u e.
IV. RESULTS
A. Th ee-dimensional adii
We ha e ex ac ed Rou ,Rside, and Rlong in in e als o
mul iplici y and kT, which esul s in 26 adii in each di ec ion.
The i p ocedu e did no make i possible o eliably ex ac
alues o he adii o he wo highes kT anges in he
60%–90% mul iplici y class. Fo he GGG i , hey a e shown
in Fig. 7. The adii a e in he ange o 0.6 o 2.4 m in all
di ec ions and uni e sally dec ease wi h kT. The magni ude o
his dec ease is simila o all mul iplici ies in he ou and long
di ec ions and is isibly inc easing wi h mul iplici y in he
side di ec ion. The adii ise wi h e en mul iplici y. The plo
also shows da a om pp collisions a √s=7TeV[16]a he
highes mul iplici ies measu ed by ALICE, which is sligh ly
highe han he mul iplici y measu ed o he 20%–40% V0A
signal ange in he p-Pb analysis. A small kT, hepp adii
a e lowe by 10% ( o side) o 20% ( o ou ) han he p-Pb
adii a he same dNch/dη1/3.A highkT he di e ence in
adius g ows o Rou , while o Rlong he adii o bo h sys ems
become compa able. The dis inc dec ease o adii wi h kTis
obse ed bo h in bo h pp and p-Pb.
The co ela ion s eng h λinc eases wi h kT om 0.44 o
0.58 o he collisions wi h he highes mul iplici ies. I is
also highe o low-mul iplici y collisions, wi h a di e ence o
0.1 be ween collisions wi h highes mul iplici ies and lowes
mul iplici ies. A noncons an λpa ame e as a unc ion o kT
is an indica ion o a non-Gaussian shape o he co ela ion
034906-8
TWO-PION FEMTOSCOPY IN p-Pb COLLISIONS AT . . . PHYSICAL REVIEW C 91, 034906 (2015)
J. Nys and,18 H. Oeschle ,92 S. Oh,134 S. K. Oh,66,§A. Ohlson,36 A. Oka an,68 T. Okubo,46 L. Olah,133 J. Oleniacz,131
A. C. Oli ei a Da Sil a,118 M. H. Oli e ,134 J. Onde waa e ,96 C. Oppedisano,110 A. O iz Velasquez,62 A. Oska sson,34
J. O winowski,96,115 K. Oyama,92 M. Ozdemi ,52 Y. Pachmaye ,92 P. Pagano,31 G. Pai´
c,62 C. Paja es,17 S. K. Pal,130 J. Pan,132
D. Pan ,47 V. Papikyan,1G. S. Pappala do,106 P. Pa eek,48 W. J. Pa k,96 S. Pa ma ,86 A. Pass eld,53 V. Pa icchio,103 B. Paul,100
T. Pawlak,131 T. Pei zmann,56 H. Pe ei a Da Cos a,15 E. Pe ei a De Oli ei a Filho,118 D. Pe esunko,75,99 C. E. P´
e ez La a,80
V. Pesko ,52 Y. Pes o ,5V. Pe ´
aˇ
cek,39 V. Pe o ,111 M. Pe o ici,77 C. Pe a,29 S. Piano,109 M. Pikna,38 P. Pillo ,112
O. Pinazza,104,36 L. Pinsky,120 D. B. Piya a hna,120 M. Płosko´
n,73 M. Planinic,127 J. Plu a,131 S. Pochybo a,133
P. L. M. Podes a-Le ma,117 M. G. Poghosyan,85 B. Polich chouk,111 N. Poljak,127 W. Poonsawa ,113 A. Pop,77
S. Po eboeu -Houssais,69 J. Po e ,73 J. Pospisil,82 S. K. P asad,4R. P eghenella,104,36 F. P ino,110 C. A. P uneau,132
I. Pshenichno ,55 M. Puccio,110 G. Puddu,25 P. Pujaha i,132 V. Punin,98 J. Pu schke,132 H. Q igs ad,22 A. Rache ski,109 S. Raha,4
S. Rajpu ,89 J. Rak,121 A. Rako oza ind abe,15 L. Ramello,32 R. Raniwala,90 S. Raniwala,90 S. S. R¨
as¨
anen,45 B. T. Rascanu,52
D. Ra hee,86 V. Razazi,25 K. F. Read,123 J. S. Real,70 K. Redlich,76,R. J. Reed,132 A. Rehman,18 P. Reichel ,52 M. Reiche ,56
F. Reid ,36,92 X. Ren,7R. Ren o d ,52 A. R. Reolon,71 A. Reshe in,55 F. Re ig,42 J.-P. Re ol,12 K. Reyge s,92 V. Riabo ,84
R. A. Ricci,72 T. Riche ,34 M. Rich e ,22 P. Riedle ,36 W. Riegle ,36 F. Riggi,29 C. Ris ea,61 A. Ri e i,110 E. Rocco,56
M. Rod ´
ıguez Cahuan zi,11,2A. Rod iguez Manso,80 K. Røed,22 E. Rogochaya,65 D. Roh ,42 D. R¨
oh ich,18 R. Romi a,122
F. Ronche i,71 L. Ron le e,112 P. Rosne ,69 A. Rossi,36 F. Roukou akis,87 A. Roy,48 C. Roy,54 P. Roy,100 A. J. Rubio Mon e o,10
R. Rui,26 R. Russo,27 E. Ryabinkin,99 Y. Ryabo ,84 A. Rybicki,115 S. Sado sky,111 K. ˇ
Sa aˇ
´
ık,36 B. Sahlmulle ,52 P. Sahoo,48
R. Sahoo,48 S. Sahoo,60 P. K. Sahu,60 J. Saini,130 S. Sakai,71 M. A. Saleh,132 C. A. Salgado,17 J. Salzwedel,20 S. Sambyal,89
V. Samsono ,84 X. Sanchez Cas o,54 L. ˇ
S´
ando ,58 A. Sando al,63 M. Sano,126 G. San aga i,29 D. Sa ka ,130 E. Scappa one,104
F. Sca lassa a,30 R. P. Scha enbe g,94 C. Schiaua,77 R. Schicke ,92 C. Schmid ,96 H. R. Schmid ,35 S. Schuchmann,52
J. Schuk a ,36 M. Schulc,39 T. Schus e ,134 Y. Schu z,112,36 K. Schwa z,96 K. Schweda,96 G. Scioli,28 E. Scompa in,110
R. Sco ,123 K. S. Seede ,118 J. E. Sege ,85 Y. Sekiguchi,125 I. Selyuzhenko ,96 K. Senosi,64 J. Seo,66,95 E. Se adilla,63,10
A. Se cenco,61 A. Shabano ,55 A. Shabe ai,112 O. Shadu a,3R. Shahoyan,36 A. Shanga ae ,111 A. Sha ma,89 N. Sha ma,60,123
K. Shigaki,46 K. Sh eje ,27,9Y. Sibi iak,99 S. Siddhan a,105 K. M. Sielewicz,36 T. Siemia czuk,76 D. Sil e my ,83,34
C. Sil es e,70 G. Sima o ic,127 G. Simone i,36 R. Singa aju,130 R. Singh,89,78 S. Singha,78,130 V. Singhal,130 B. C. Sinha,130
T. Sinha,100 B. Si a ,38 M. Si a,32 T. B. Skaali,22 K. Skje dal,18 M. Slupecki,121 N. Smi no ,134 R. J. M. Snellings,56
T. W. Snellman,121 C. Søgaa d,34 R. Sol z,74 J. Song,95 M. Song,135 Z. Song,7F. So amel,30 S. So ensen,123 M. Spacek,39
E. Spi i i,71 I. Spu owska,115 M. Spy opoulou-S assinaki,87 B. K. S i as a a,94 J. S achel,92 I. S an,61 G. S e anek,76
M. S einp eis,20 E. S enlund,34 G. S eyn,64 J. H. S ille ,92 D. S occo,112 P. S men,38 A. A. P. Suaide,118 T. Sugi a e,46 C. Sui e,50
M. Suleymano ,16 R. Sul ano ,57 M. ˇ
Sumbe a,82 T. J. M. Symons,73 A. Szabo,38 A. Szan o de Toledo,118 I. Sza ka,38
A. Szczepankiewicz,36 M. Szymanski,131 J. Takahashi,119 N. Tanaka,126 M. A. Tanga o,33 J. D. Tapia Takaki,50,¶
A. Ta an ola Peloni,52 M. Ta iq,19 M. G. Ta zila,77 A. Tau o,36 G. Tejeda Mu˜
noz,2A. Telesca,36 K. Te asaki,125 C. Te e oli,30,25
B. Teyssie ,128 J. Th¨
ade ,96,73 D. Thomas,56,116 R. Tieulen ,128 A. R. Timmins,120 A. Toia,52 S. T ogolo,110 V. T ubniko ,3
W. H. T zaska,121 T. Tsuji,125 A. Tumkin,98 R. Tu isi,107 T. S. T e e ,22 K. Ullaland,18 A. U as,128 G. L. Usai,25 A. U obicic,127
M. Vajze ,82 M. Vala,58 L. Valencia Palomo,69 S. Valle o,27 J. Van De Maa el,56 J. W. Van Hoo ne,36 M. an Leeuwen,56
T. Vana ,82 P. Vande Vy e,36 D. Va ga,133 A. Va gas,2M. Va gyas,121 R. Va ma,47 M. Vasileiou,87 A. Vasilie ,99 A. Vau hie ,70
V. Veche nin,129 A. M. Veen,56 M. Veldhoen,56 A. Velu e,18 M. Vena uzzo,72 E. Ve cellin,27 S. Ve ga a Lim´
on,2R. Ve ne ,8
M. Ve weij,132 L. Vicko ic,114 G. Vies i,30 J. Viinikainen,121 Z. Vilakazi,124 O. Villalobos Baillie,101 A. Vinog ado ,99
L. Vinog ado ,129 Y. Vinog ado ,98 T. Vi gili,31 V. Visla icius,34 Y. P. Viyogi,130 A. Vodopyano ,65 M.A. V¨
olkl,92
K. Voloshin,57 S. A. Voloshin,132 G. Volpe,36,133 B. on Halle ,36 I. Vo obye ,91 D. V anic,96,36 J. V l´
ako ´
a,40 B. Vulpescu,69
A. Vyushin,98 B. Wagne ,18 J. Wagne ,96 H. Wang,56 M. Wang,7,112 Y. Wang,92 D. Wa anabe,126 M. Webe ,36,120 S. G. Webe ,96
J. P. Wessels,53 U. Wes e ho ,53 J. Wiechula,35 J. Wikne,22 M. Wilde,53 G. Wilk,76 J. Wilkinson,92 M. C. S. Williams,104
B. Windelband,92 M. Winn,92 C. G. Yaldo,132 Y. Yamaguchi,125 H. Yang,56 P. Yang,7S. Yano,46 S. Yasnopolskiy,99 Z. Yin,7
H. Yokoyama,126 I.-K. Yoo,95 V. Yu chenko,3I. Yushmano ,99 A. Zabo owska,131 V. Zaccolo,79 A. Zaman,16 C. Zampolli,104
H. J. C. Zanoli,118 S. Zapo ozhe s,65 A. Za ochen se ,129 P. Z ´
a ada,59 N. Za iyalo ,98 H. Zb oszczyk,131 I. S. Zgu a,61
M. Zhalo ,84 H. Zhang,7X. Zhang,73 Y. Zhang,7C. Zhao,22 N. Zhiga e a,57 D. Zhou,7Y. Zhou,56 Z. Zhou,18 H. Zhu,7
J. Zhu,7,112 X. Zhu,7A. Zichichi,12,28 A. Zimme mann,92 M. B. Zimme mann,53,36 G. Zino je ,3and M. Zyzak42
(ALICE Collabo a ion)
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
2Benem´
e i a Uni e sidad Au ´
onoma de Puebla, Puebla, Mexico
3Bogolyubo Ins i u e o Theo e ical Physics, 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
5Budke Ins i u e o Nuclea Physics, No osibi sk, Russia
6Cali o nia Poly echnic S a e Uni e si y, San Luis Obispo, Cali o nia, USA
7Cen al China No mal Uni e si y, Wuhan, China
8Cen e de Calcul de l’IN2P3, Villeu banne, F ance
034906-15

J. ADAM e al. PHYSICAL REVIEW C 91, 034906 (2015)
9Cen o de Aplicaciones Tecnol´
ogicas y Desa ollo Nuclea (CEADEN), Ha ana, Cuba
10Cen o de In es igaciones Ene g´
e icas Medioambien ales y Tecnol´
ogicas (CIEMAT), Mad id, Spain
11Cen o de In es igaci´
on y de Es udios A anzados (CINVESTAV), Mexico Ci y and M´
e ida, Mexico
12Cen o Fe mi-Museo S o ico della Fisica e Cen o S udi e Rice che “En ico Fe mi,” Rome, I aly
13Chicago S a e Uni e si y, Chicago, Illinois, USA
14China Ins i u e o A omic Ene gy, Beijing, China
15Commissa ia `
a l’Ene gie A omique, IRFU, Saclay, F ance
16COMSATS Ins i u e o In o ma ion Technology (CIIT), Islamabad, Pakis an
17Depa amen o de F´
ısica de Pa ´
ıculas and IGFAE, Uni e sidad de San iago de Compos ela, San iago de Compos ela, Spain
18Depa men o Physics and Technology, Uni e si y o Be gen, Be gen, No way
19Depa men o Physics, Aliga h Muslim Uni e si y, Aliga h, India
20Depa men o Physics, Ohio S a e Uni e si y, Columbus, Ohio, USA
21Depa men o Physics, Sejong Uni e si y, Seoul, Sou h Ko ea
22Depa men o Physics, Uni e si y o Oslo, Oslo, No way
23Dipa imen o di Ele o ecnica ed Ele onica del Poli ecnico, Ba i, I aly
24Dipa imen o di Fisica dell’Uni e si `
a “La Sapienza” and Sezione INFN Rome, I aly
25Dipa imen o di Fisica dell’Uni e si `
a and Sezione INFN, Caglia i, I aly
26Dipa imen o di Fisica dell’Uni e si `
a and Sezione INFN, T ies e, I aly
27Dipa imen o di Fisica dell’Uni e si `
a and Sezione INFN, Tu in, I aly
28Dipa imen o di Fisica e As onomia dell’Uni e si `
a and Sezione INFN, Bologna, I aly
29Dipa imen o di Fisica e As onomia dell’Uni e si `
a and Sezione INFN, Ca ania, I aly
30Dipa imen o di Fisica e As onomia dell’Uni e si `
a and Sezione INFN, Pado a, I aly
31Dipa imen o di Fisica “E.R. Caianiello” dell’Uni e si `
a and G uppo Collega o INFN, Sale no, I aly
32Dipa imen o di Scienze e Inno azione Tecnologica dell’Uni e si `
a del Piemon e O ien ale and G uppo Collega o INFN, Alessand ia, I aly
33Dipa imen o In e a eneo di Fisica “M. Me lin” and Sezione INFN, Ba i, I aly
34Di ision o Expe imen al High Ene gy Physics, Uni e si y o Lund, Lund, Sweden
35Ebe ha d Ka ls Uni e si ¨
a T¨
ubingen, T¨
ubingen, Ge many
36Eu opean O ganiza ion o Nuclea Resea ch (CERN), Gene a, Swi ze land
37Facul y o Enginee ing, Be gen Uni e si y College, Be gen, No way
38Facul y o Ma hema ics, Physics and In o ma ics, Comenius Uni e si y, B a isla a, Slo akia
39Facul y o Nuclea Sciences and Physical Enginee ing, Czech Technical Uni e si y in P ague, P ague, Czech Republic
40Facul y o Science, P. J. ˇ
Sa ´
a ik Uni e si y, Koˇ
sice, Slo akia
41Facul y o Technology, Buske ud and Ves old Uni e si y College, Ves old, No way
42F ank u Ins i u e o Ad anced S udies, Johann Wol gang Goe he-Uni e si ¨
a F ank u , F ank u , Ge many
43Gangneung-Wonju Na ional Uni e si y, Gangneung, Sou h Ko ea
44Gauha i Uni e si y, Depa men o Physics, Guwaha i, India
45Helsinki Ins i u e o Physics (HIP), Helsinki, Finland
46Hi oshima Uni e si y, Hi oshima, Japan
47Indian Ins i u e o Technology Bombay (IIT), Mumbai, India
48Indian Ins i u e o Technology Indo e, Indo e (IITI), India
49Inha Uni e si y, Incheon, Sou h Ko ea
50Ins i u de Physique Nucl´
eai e d’O say (IPNO), Uni e si ´
e Pa is-Sud, CNRS-IN2P3, O say, F ance
51Ins i u ¨
u In o ma ik, Johann Wol gang Goe he-Uni e si ¨
a F ank u , F ank u , Ge many
52Ins i u ¨
u Ke nphysik, Johann Wol gang Goe he-Uni e si ¨
a F ank u , F ank u , Ge many
53Ins i u ¨
u Ke nphysik, Wes ¨
alische Wilhelms-Uni e si ¨
a M¨
uns e , M¨
uns e , Ge many
54Ins i u Plu idisciplinai e Hube Cu ien (IPHC), Uni e si ´
e de S asbou g, CNRS-IN2P3, S asbou g, F ance
55Ins i u e o Nuclea Resea ch, Academy o Sciences, Moscow, Russia
56Ins i u e o Suba omic Physics o U ech Uni e si y, U ech , Ne he lands
57Ins i u e o Theo e ical and Expe imen al Physics, Moscow, Russia
58Ins i u e o Expe imen al Physics, Slo ak Academy o Sciences, Koˇ
sice, Slo akia
59Ins i u e o Physics, Academy o Sciences o he Czech Republic, P ague, Czech Republic
60Ins i u e o Physics, Bhubaneswa , India
61Ins i u e o Space Science (ISS), Bucha es , Romania
62Ins i u o de Ciencias Nuclea es, Uni e sidad Nacional Au ´
onoma de M´
exico, Mexico Ci y, Mexico
63Ins i u o de F´
ısica, Uni e sidad Nacional Au ´
onoma de M´
exico, Mexico Ci y, Mexico
64iThemba LABS, Na ional Resea ch Founda ion, Some se Wes , Sou h A ica
65Join Ins i u e o Nuclea Resea ch (JINR), Dubna, Russia
66Konkuk Uni e si y, Seoul, Sou h Ko ea
67Ko ea Ins i u e o Science and Technology In o ma ion, Daejeon, Sou h Ko ea
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68KTO Ka a ay Uni e si y, Konya, Tu key
69Labo a oi e de Physique Co pusculai e (LPC), Cle mon Uni e si ´
e, Uni e si ´
e Blaise Pascal, CNRS-IN2P3, Cle mon -Fe and, F ance
70Labo a oi e de Physique Suba omique e de Cosmologie, Uni e si ´
e G enoble-Alpes, CNRS-IN2P3, G enoble, F ance
71Labo a o i Nazionali di F asca i, INFN, F asca i, I aly
72Labo a o i Nazionali di Legna o, INFN, Legna o, I aly
73Law ence Be keley Na ional Labo a o y, Be keley, Cali o nia, USA
74Law ence Li e mo e Na ional Labo a o y, Li e mo e, Cali o nia, USA
75Moscow Enginee ing Physics Ins i u e, Moscow, Russia
76Na ional Cen e o Nuclea S udies, Wa saw, Poland
77Na ional Ins i u e o Physics and Nuclea Enginee ing, Bucha es , Romania
78Na ional Ins i u e o Science Educa ion and Resea ch, Bhubaneswa , India
79Niels Boh Ins i u e, Uni e si y o Copenhagen, Copenhagen, Denma k
80Nikhe , Na ional Ins i u e o Suba omic Physics, Ams e dam, Ne he lands
81Nuclea Physics G oup, STFC Da esbu y Labo a o y, Da esbu y, Uni ed Kingdom
82Nuclea Physics Ins i u e, Academy o Sciences o he Czech Republic, ˇ
Reˇ
z u P ahy, Czech Republic
83Oak Ridge Na ional Labo a o y, Oak Ridge, Tennessee, USA
84Pe e sbu g Nuclea Physics Ins i u e, Ga china, Russia
85Physics Depa men , C eigh on Uni e si y, Omaha, Neb aska, USA
86Physics Depa men , Panjab Uni e si y, Chandiga h, India
87Physics Depa men , Uni e si y o A hens, A hens, G eece
88Physics Depa men , Uni e si y o Cape Town, Cape Town, Sou h A ica
89Physics Depa men , Uni e si y o Jammu, Jammu, India
90Physics Depa men , Uni e si y o Rajas han, Jaipu , India
91Physik Depa men , Technische Uni e si ¨
a M¨
unchen, Munich, Ge many
92Physikalisches Ins i u , Rup ech -Ka ls-Uni e si ¨
a Heidelbe g, Heidelbe g, Ge many
93Poli ecnico di To ino, Tu in, I aly
94Pu due Uni e si y, Wes La aye e, Indiana, USA
95Pusan Na ional Uni e si y, Pusan, Sou h Ko ea
96Resea ch Di ision and Ex eMe Ma e Ins i u e EMMI, GSI Helmhol zzen um ¨
u Schwe ionen o schung, Da ms ad , Ge many
97Rudje Boˇ
sko i´
c Ins i u e, Zag eb, C oa ia
98Russian Fede al Nuclea Cen e (VNIIEF), Sa o , Russia
99Russian Resea ch Cen e Ku cha o Ins i u e, Moscow, Russia
100Saha Ins i u e o Nuclea Physics, Kolka a, India
101School o Physics and As onomy, Uni e si y o Bi mingham, Bi mingham, Uni ed Kingdom
102Secci´
on F´
ısica, Depa amen o de Ciencias, Pon i icia Uni e sidad Ca ´
olica del Pe ´
u, Lima, Pe u
103Sezione INFN, Ba i, I aly
104Sezione INFN, Bologna, I aly
105Sezione INFN, Caglia i, I aly
106Sezione INFN, Ca ania, I aly
107Sezione INFN, Pado a, I aly
108Sezione INFN, Rome, I aly
109Sezione INFN, T ies e, I aly
110Sezione INFN, Tu in, I aly
111SSC IHEP o NRC Ku cha o ins i u e, P o ino, Russia
112SUBATECH, Ecole des Mines de Nan es, Uni e si ´
e de Nan es, CNRS-IN2P3, Nan es, F ance
113Su ana ee Uni e si y o Technology, Nakhon Ra chasima, Thailand
114Technical Uni e si y o Spli FESB, Spli , C oa ia
115The Hen yk Niewodniczanski Ins i u e o Nuclea Physics, Polish Academy o Sciences, C acow, Poland
116The Uni e si y o Texas a Aus in, Physics Depa men , Aus in, Texas, USA
117Uni e sidad Au ´
onoma de Sinaloa, Culiac´
an, Mexico
118Uni e sidade de S˜
ao Paulo (USP), S˜
ao Paulo, B azil
119Uni e sidade Es adual de Campinas (UNICAMP), Campinas, B azil
120Uni e si y o Hous on, Hous on, Texas, USA
121Uni e si y o Jy ¨
askyl¨
a, Jy ¨
askyl¨
a, Finland
122Uni e si y o Li e pool, Li e pool, Uni ed Kingdom
123Uni e si y o Tennessee, Knox ille, Tennessee, USA
124Uni e si y o he Wi wa e s and, Johannesbu g, Sou h A ica
125Uni e si y o Tokyo, Tokyo, Japan
126Uni e si y o Tsukuba, Tsukuba, Japan
034906-17
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127Uni e si y o Zag eb, Zag eb, C oa ia
128Uni e si ´
e de Lyon, Uni e si ´
e Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeu banne, F ance
129V. Fock Ins i u e o Physics, S . Pe e sbu g S a e Uni e si y, S . Pe e sbu g, Russia
130Va iable Ene gy Cyclo on Cen e, Kolka a, India
131Wa saw Uni e si y o Technology, Wa saw, Poland
132Wayne S a e Uni e si y, De oi , Michigan, USA
133Wigne Resea ch Cen e o Physics, Hunga ian Academy o Sciences, Budapes , Hunga y
134Yale Uni e si y, New Ha en, Connec icu , USA
135Yonsei Uni e si y, Seoul, Sou h Ko ea
136Zen um ¨
u Technologie ans e und Telekommunika ion (ZTT), Fachhochschule Wo ms, Wo ms, Ge many
*Deceased.
†Also a M. V. Lomonoso Moscow S a e Uni e si y, D.V. Skobel syn Ins i u e o Nuclea Physics, Moscow, Russia.
‡Also a Uni e si y o Belg ade, Facul y o Physics and “Vinˇ
ca” Ins i u e o Nuclea Sciences, Belg ade, Se bia.
§Pe manen add ess: Konkuk Uni e si y, Seoul, Ko ea.
Also a Ins i u e o Theo e ical Physics, Uni e si y o W oclaw, W oclaw, Poland.
¶Also a Uni e si y o Kansas, Law ence, Kansas, USA.
034906-18