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One-dimensional cha ged kaon em oscopy in p-Pb collisions a √sNN = 5.02 TeV
© 2019 CERN, o he ALICE Collabo a ion
Published e sion
ALICE Collabo a ion
ALICE Collabo a ion. (2019). One-dimensional cha ged kaon em oscopy in p-Pb collisions a
√sNN = 5.02 TeV. Physical Re iew C, 100(2), A icle 024002.
h ps://doi.o g/10.1103/PhysRe C.100.024002
2019
PHYSICAL REVIEW C 100, 024002 (2019)
One-dimensional cha ged kaon em oscopy in p-Pb collisions a √sNN =5.02 TeV
S. Acha ya e al.∗
(ALICE Collabo a ion)
(Recei ed 5 Ap il 2019; published 22 Augus 2019)
The co ela ions o iden ical cha ged kaons we e measu ed in p-Pb collisions a √sNN =5.02 TeV by he
ALICE expe imen a he LHC. The em oscopic in a ian adii and co ela ion s eng hs we e ex ac ed om
one-dimensional kaon co ela ion unc ions and we e compa ed wi h hose ob ained in pp and Pb-Pb collisions
a √s=7 TeV and √sNN =2.76 TeV, espec i ely. The p esen ed esul s also complemen he iden ical-pion
em oscopic da a published by he ALICE collabo a ion. The ex ac ed adii inc ease wi h inc easing cha ged-
pa icle mul iplici y and dec ease wi h inc easing pai ans e se momen um. A compa able mul iplici ies,
he adii measu ed in p-Pb collisions a e ound o be close o hose obse ed in pp collisions. The ob ained
em oscopic pa ame e s a e ep oduced by he EPOS 3 had onic in e ac ion model and dis a o models wi h
la ge ini ial size o s ong collec i e expansion a low mul iplici ies.
DOI: 10.1103/PhysRe C.100.024002
I. INTRODUCTION
The Bose-Eins ein enhancemen o he p oduc ion o wo
iden ical pions a low ela i e momen a (o , in o he wo ds,
quan um s a is ics co ela ions) was i s obse ed in he pp
annihila ion mo e han 50 yea s ago [1]. These co ela ions
encode in o ma ion abou he space- ime s uc u e o he
in e ac ion egion o pa icles c ea ed in collisions a kine ic
eeze-ou (pa icle-emi ing sou ce) [2–4]. Since ha ime he
co ela ion me hod has been de eloped [5,6] and i is now
known as co ela ion em oscopy. Fem oscopy measu es he
appa en wid h o he dis ibu ion o he ela i e sepa a ion
o emission poin s, which is con en ionally called he adius
pa ame e . The me hod was success ully applied o he mea-
su emen o he space- ime cha ac e is ics o pa icle p oduc-
ion p ocesses a high ene gies in pa icle [7,8] and hea y-ion
collisions (see, e.g., Re s. [4,9] and e e ences he ein).
Iden ical boson co ela ions, especially o iden ical
cha ged pions, ha e been used ex ensi ely o e he yea s
o expe imen ally s udy p ope ies o he emi ing sou ce
c ea ed in a ious collision sys ems [10]. Iden ical cha ged
kaon em oscopy s udies we e also ca ied ou , o example,
in Au-Au collisions a √sNN =200 GeV by he STAR [11]
and PHENIX [12] collabo a ions and in ppcollisions a √s=
7 TeV and Pb-Pb collisions a √sNN =2.76 TeV by he
ALICE collabo a ion [13,14].
The s udy o em oscopic co ela ions in asymme ic col-
lision sys ems is pa icula ly in e es ing because i p o ides a
b idge be ween small (pp) and la ge (A-A) collision sys ems,
and may lead o addi ional cons ain s on model scena ios,
∗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 4.0 In e na ional 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.
which we e success ully used o desc ibe pp and A-Acolli-
sions. The A-A 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 [10,15–17]. 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 [18]. The esul s ob ained in
asymme ic collisions a e di icul o in e p e unambiguously.
Fo ins ance, he em oscopic s udy o he da a ob ained a
RHIC o d-Au collisions [19,20] sugges ha a hyd ody-
namic e olu ion may be p esen in such a sys em, while a
he LHC he ALICE h ee-pion [21] and h ee-dimensional
wo-pion [22] analyses in p-Pb collisions a √sNN =5.02 TeV
demons a e he mo e impo an ole o he ini ial s a e shape
and size o he c ea ed sys em.
The excellen pa icle iden i ica ion capabili ies o he
ALICE de ec o [23] and he da a sample collec ed in p-Pb
collisions a √sNN =5.02 TeV in 2013 allow one o pe o m
he K±K± em oscopic analysis. Kaons a e a con enien
ool o s udy Bose-Eins ein co ela ions because hey a e
less in luenced by esonance decays han pions and he e o e
mo e e ec i ely p obe em oscopic co ela ions o di ec ly
p oduced pa icles. The compa ison o kaon and pion co ela-
ion adii [14,21,22] as a unc ion o pai ans e se momen-
um kT=|pT,1+pT,2|/2 o ans e se mass mT=√k2
T+m2,
whe e pT,1(pT,2) is he ans e se momen um o he i s
(second) pa icle and mis he kaon o pion mass, allows
one o unde s and he collec i e dynamics (collec i e low)
o he sou ce c ea ed in high-ene gy collisions. In pa icula ,
in he sys em c ea ed by colliding hea y ions, he dec ease o
he co ela ion adii wi h inc easing kT(mT) is usually con-
side ed as a mani es a ion o he s ong collec i e expansion
o he ma e c ea ed in such collisions. I he dependence
o he in e e ome y adii on pai momen um in p-Pb col-
lisions ollowed he ends seen in hea y-ion collisions, i
would be an indica ion o collec i i y o he c ea ion o a ho
and dense sys em expanding hyd odynamically [24–26]. In
2469-9985/2019/100(2)/024002(15) 024002-1 ©2019 CERN, o he ALICE Collabo a ion
S. ACHARYA e al. PHYSICAL REVIEW C 100, 024002 (2019)
addi ion, compa ing kaon em oscopic esul s in pp,p-A, and
A-Acollision sys ems can p o ide expe imen al cons ain s
on he alidi y o hyd odynamic [24,26] and/o colo glass
condensa e [27,28] app oaches p oposed o he in e p e a ion
o he p-Pb da a. In his wo k, he kaon em oscopic adii in
p-Pb collisions a √sNN =5.02 TeV a e shown as a unc ion
o kTand mul iplici y, and a e compa ed wi h hose in pp and
Pb-Pb collisions a √s=7TeV[13] and √sNN =2.76 TeV
[14], espec i ely. The p esen ed da a a e also compa ed
wi h he EPOS 3.111 model [26], an e en gene a o based
on a (3 +1)-dimensional [(3 +1)D] iscous hyd odynamical
e olu ion s a ing om lux ube ini ial condi ions, which a e
gene a ed in he G ibo -Regge mul iple sca e ing amewo k.
The app oach con ains a ull iscous hyd odynamical simula-
ion and a mo e sophis ica ed ea men o nonlinea e ec s in
he pa on e olu ion by conside ing indi idual (pe Pome on)
sa u a ion scales han in p e ious EPOS e sions [25,29].
The e a e also changes in he co e-co ona p ocedu e [30]
c ucial in p o on-nucleus collisions, so ha he ini ial ene gy
o he lux ubes is sepa a ed in o a pa , which cons i u es
he ini ial condi ions o hyd odynamic expansion (co e) and
he pa icles, which lea e he ma e (co ona). This model
easonably ep oduces mul iplici y dis ibu ions, ans e se
momen um spec a, and low esul s, and i gi es he bes
desc ip ion o kaon spec a [25,29,31–33].
The pape is o ganized as ollows: Sec. II sho ly desc ibes
he ALICE expe imen al se up and cha ged kaon selec ion
c i e ia used in he p esen ed wo k. In Sec. III, he em-
oscopic co ela ion unc ion analysis is desc ibed in de ail
and he sou ces o sys ema ic unce ain ies a e discussed.
The ex ac ed adii and co ela ion s eng hs a e shown and
compa ed wi h model p edic ions in Sec. IV. The ob ained
esul s a e summa ized in Sec. V.
II. DESCRIPTION OF THE EXPERIMENT
AND DATA SELECTION
A. Expe imen
The ALICE de ec o and i s pe o mance in he LHC Run
1 (2009–2013) a e desc ibed in Re s. [23,34], espec i ely.
Abou 55 ×106p-Pb collision e en s collec ed in 2013 a a
cen e -o -mass ene gy pe nucleon-nucleon pai o √sNN =
5.02 TeV we e analyzed in his wo k. Gi en he ene gies o
he colliding pand Pb beams, he 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 s o apidi y in he di ec ion o he p o on
beam. Th oughou his pape η ep esen s he pseudo apidi y
measu ed in he labo a o y ame.
The analyzed e en s we e classi ied acco ding o hei mul-
iplici y [35,36] using he measu ed ene gy deposi ion in he
V0 de ec o s [37], which consis o wo a ays o scin illa o s
loca ed along he beam line ins alled on each side o he in e -
ac ion poin and co e ing 2.8<η<5.1 (V0A, loca ed on he
Pb- emnan side) and −3.7<η<−1.7(V0C)[38]. Cha ged
kaons we e econs uc ed wi h he cen al ba el de ec o s
placed inside a solenoidal magne p o iding a 0.5 T ield pa -
allel o he beam di ec ion, namely he Time P ojec ion Cham-
be (TPC) [39] and he Inne T acking Sys em (ITS) [23]. The
p ima y e ex was ob ained om he ITS. I s posi ion along
he beam di ec ion ( he zposi ion) was equi ed o be wi hin
±10 cm o he cen e o he ALICE de ec o o ensu e uni o m
acking pe o mance. The TPC was used o econs uc acks
and hei momen a. The TPC is di ided by he cen al elec-
ode in o wo hal es, each o which is composed o 18 sec o s
(co e ing he ull azimu hal angle) wi h 159 pad ows placed
adially in each sec o . A ack signal in he TPC consis s o
space poin s (clus e s), each o which is econs uc ed in one
o he pad ows. The TPC co e s an accep ance o |η|<0.8
o acks, which each he ou e adius o he de ec o and
|η|<1.5 o sho e acks. The pa ame e s o he ack we e
de e mined by pe o ming a Kalman i o a se o clus e s
wi h an addi ional cons ain ha he ack passes h ough
he p ima y e ex. The quali y o he i is equi ed o ha e
χ2/NDF less han 2. The ans e se momen um o each ack
was de e mined om i s cu a u e in he uni o m magne ic
ield. The ack selec ion c i e ia based on he quali y o he
ack econs uc ion i and he numbe o de ec ed acking
poin s in he TPC [34,40] we e used o ensu e ha only
well- econs uc ed acks we e conside ed in he analysis.
Pa icle iden i ica ion (PID) o econs uc ed acks was
ca ied ou using he TPC oge he wi h he ime-o - ligh
(TOF) [40] de ec o . The TOF is a cylind ical de ec o con-
sis ing o 18 azimu hal sec o s di ided in o i e modules
along he beam axis a a adius ≃380 cm. The ac i e
elemen s a e mul igap esis i e pla e chambe s. Fo TPC PID,
a pa ame ized Be he-Bloch o mula was used o calcula e
he speci ic ene gy loss dE/dx in he de ec o expec ed o
a pa icle wi h a gi en mass, cha ge, and momen um. Fo
PID based on TOF in o ma ion, he pa icle mass was used
o calcula e he expec ed ime-o - ligh as a unc ion o ack
leng h and momen um. Fo each PID me hod, he signal o
each econs uc ed pa icle is compa ed wi h he one expec ed
o a kaon aking in o accoun he de ec o esolu ion. The
allowed de ia ions (nσ) depend on he momen um o he
pa icle [14,34,40].
B. Cha ged kaon selec ion
T ack econs uc ion o he cha ged kaon analysis was
pe o med using he signals in he TPC. To ensu e a good
momen um esolu ion, each ack was equi ed o be com-
posed o a leas 70 ou o he 159 TPC clus e s. T acks we e
selec ed based on hei dis ance o closes app oach (DCA) o
he p ima y e ex, which was equi ed o be less han 2.4 cm
in he ans e se plane and less han 3.0 cm in he longi udinal
di ec ion. The kinema ic ange o kaons selec ed in his
analysis is 0.14 <pT<1.5GeV/cand |η|<0.8. Cha ged
acks wi h momen um p<0.5GeV/cwe e iden i ied as
kaons i hey sa is ied he equi emen nσ,TPC <2 in he TPC.
T acks wi h p>0.5GeV/cwe e equi ed o ma ch o a signal
in he TOF, and sa is y nσ,TPC <3aswellas he ollow-
ing momen um-dependen nσselec ion: nσ,TOF <2 o 0.5<
p<0.8GeV/c,nσ,TOF <1.5 o 0.8<p<1.0GeV/cand
nσ,TOF <1 o 1.0<p<1.5GeV/c. All selec ion c i e ia a e
lis ed in Table I.
The es ima ion o pu i y o p<0.5GeV/cwas pe -
o med by pa ame izing he TPC dE/dx dis ibu ion o he
024002-2
ONE-DIMENSIONAL CHARGED KAON FEMTOSCOPY … PHYSICAL REVIEW C 100, 024002 (2019)
TABLE I. Cha ged kaon selec ion c i e ia.
pT0.14 <pT<1.5 GeV/c
|η|<0.8
DCA ans e se o p ima y e ex <2.4cm
DCAlongi udinal o p ima y e ex <3.0cm
nσ,TPC ( o p<0.5 GeV/c)<2
nσ,TPC ( o p>0.5 GeV/c)<3
nσ,TOF ( o 0.5<p<0.8 GeV/c)<2
nσ,TOF ( o 0.8<p<1.0 GeV/c)<1.5
nσ,TOF ( o 1.0<p<1.5 GeV/c)<1.0
Numbe o ack poin s in TPC ⩾70
expe imen al da a in momen um slices and compu ing he
ac ion o pa icle species ha could mis akenly con ibu e
o he kaon signal [34]. The use o momen um-dependen
alues o nσ,TPC and nσ,TOF was he esul o s udies o
ob ain he bes kaon pu i y, de ined as he ac ion o accep ed
kaon acks ha co espond o ue kaons, while e aining
a decen e iciency o he PID. The dominan con amina-
ion o cha ged kaons comes om e±in he momen um
ange 0.4<p<0.5GeV/c. The pa ame e s o he unc ion,
which i s he TPC dis ibu ion in momen um slices depend
on he i in e al and can be a sou ce o he sys ema ic
unce ain y associa ed wi h he single pu i y. The pu i y o
p>0.5GeV/c, whe e he TOF in o ma ion was employed,
was s udied wi h DPMJET [41] simula ions using GEANT [42]
o model pa icle anspo h ough he de ec o . Based on
he esul s o his s udy, he nσ,TOF alues we e chosen o
p o ide a cha ged kaon pu i y g ea e han 99%. The mo-
men um dependence o he single-kaon pu i y in he egion o
maximal con amina ion is shown in Fig. 1(a). The pai pu i y
is calcula ed as he p oduc o wo single-pa icle pu i ies
o pai s wi h qin <0.25 GeV/c, whe e he momen a a e
aken om he expe imen ally de e mined dis ibu ion. The
ob ained K±pai pu i y is shown in Fig. 1(b) as a unc ion
o kT. I can be seen om he igu e ha , despi e he lowe
pu i y o single kaons in he ange 0.45 <p<0.5GeV/c,
he pai pu i y emains high in he wide kTbins used in
he analysis due o he e ec s o a e aging o e low-pu i y
0.45 <p<0.5GeV/cand high-pu i y p<0.45 GeV/co
p>0.5GeV/cbins in he ull single-kaon momen um ange.
The sys ema ic unce ain ies o he single pu i y alues lead,
in u n, o sys ema ic unce ain ies o he ob ained pai
pu i y.
The analysis was pe o med in h ee e en mul iplici y
classes [35,36,43]: 0–20%, 20–40%, and 40–90% and wo
pai ans e se momen um kTbins: (0.2–0.5) and (0.5–1.0)
GeV/c. The mul iplici y was de e mined based on he sum o
he signal ampli udes o V0A and V0C de ec o s, commonly
e e ed o as V0M. Table II shows he co esponding mean
cha ged-pa icle mul iplici y densi ies dNch/dηa e aged
o e |η|<0.5 using he me hod p esen ed in Re . [35]. The
dNch/dη alues we 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 [44]. A leas one pa icle in he e en
had o be econs uc ed and iden i ied as a cha ged kaon.
The co ela ion signal was cons uc ed om e en s ha ing a
leas wo iden ical cha ged kaons. E en s wi h a single kaon
we e included in he e en mixing p ocedu e o de e mine he
e e ence dis ibu ion.
The em oscopic co ela ion unc ions (CFs) o iden ical
pa icles a e sensi i e o wo- ack econs uc ion e ec s be-
cause he conside ed pa icles a e close in momen um and
ha e close ajec o ies. Two kinds o wo- ack e ec s we e
in es iga ed. T ack spli ing occu s when one ack is mis ak-
enly econs uc ed as wo. T ack me ging is he e ec when
wo di e en acks a e econs uc ed as one. To emo e hese
e ec s, pai s wi h ela i e pseudo apidi y |η|<0.02 and
ela i e azimu hal angle |ϕ∗|<0.045 we e ejec ed. The
modi ied azimu hal angle ϕ∗ akes in o accoun he bending
o he acks inside he magne ic ield and was calcula ed a a
adial dis ance o 1.2 m [45].
)c (GeV/p
0.3 0.35 0.4 0.45 0.5 0.55
pu i y
±
single K
0.5
0.6
0.7
0.8
0.9
1
pai s
±
K
±
K
(a)
= 5.02 TeV
NN
s
Pb -ALICE p
20%-0
40%-20
90%-40
)c (GeV/
T
k
0.2 0.4 0.6 0.8
pai pu i y
±
K
0.8
0.85
0.9
0.95
1 = 5.02 TeV
NN
sPb -ALICE p
pai s
±
K
±
K
(b)
20%-0
40%-20
90%-40
FIG. 1. (a) Single and (b) pai K±pu i ies o di e en e en mul iplici y classes. The sys ema ic unce ain ies associa ed wi h he pu i y
co ec ion a e shown as boxes. S a is ical unce ain ies a e negligible. The momen um p(kT) alues o lowe mul iplici y classes (blue and
g een symbols) a e sligh ly o se o cla i y.
024002-3
S. ACHARYA e al. PHYSICAL REVIEW C 100, 024002 (2019)
TABLE II. V0M e en classes and hei co e-
sponding dNch/dη[35]. The gi en unce ain ies
a e sys ema ic only since he s a is ical unce ain-
ies a e negligible.
E en class dNch/dη,|η|<0.5
0–20% 47.3 ±0.7
20–40% 24.3 ±0.7
40–90% 17.3 ±1.5
III. ANALYSIS TECHNIQUE
The co ela ion unc ion o wo pa icles wi h momen a p1
and p2is de ined as a a io
C(p1,p2)=A(p1,p2)
B(p1,p2)(1)
o he wo-pa icle dis ibu ion in he gi en e en A(p1,p2)
o he e e ence dis ibu ion B(p1,p2)[46]. The e e ence
dis ibu ion is o med by mixing e en s con aining a leas
one cha ged kaon, whe e each e en is mixed wi h i e o he
e en s, which ha e simila zposi ion o he p ima y e ex
and simila mul iplici y [10]. The mixed pa icles come om
e en s o which he e ex posi ions in he beam di ec ion
ag ee wi hin 2 cm and he mul iplici ies do no di e by
mo e han 1/4 o he wid h o he gi en mul iplici y class.
The co ela ion unc ion is measu ed as a unc ion o he
in a ian pai ela i e momen um qin =√|q|2−q2
0, whe e
q0=E1−E2and q=p1−p2a e de e mined by he ene gy
componen s E1,E2and momen a p1,p2o he pa icles,
espec i ely. The co ela ion unc ion is no malized o uni y
such ha C→1 in he absence o a co ela ion signal.
The ob ained co ela ion unc ion C aw was also co ec ed
o pu i y be o e he i [14,47] acco ding o
Cco ec ed =(C aw −1+P)/P,(2)
whe e he pai pu i y Pis aken om Fig. 1(b).
A. Co ela ion unc ion pa ame iza ion
The CFs can be pa ame ized by a ious o mulas de-
pending on he o igin o co ela ions be ween he consid-
e ed pa icles. The pai wise in e ac ions be ween K±K± ha
o m he basis o em oscopy a e quan um s a is ics and he
Coulomb in e ac ion. S ong inal-s a e in e ac ions be ween
kaons a e negligible [48]. Assuming a Gaussian dis ibu ion
o a pa icle sou ce in he pai es ame, he i o he kaon
CF is pe o med using he Bowle -Sinyuko o mula [49,50]
C(qin )=N1−λ+λK( ,qin )
×1+exp −R2
in q2
in  D(qin ).(3)
The ac o K( ,qin ) desc ibes he Coulomb in e ac ion wi h
a adius ,D(qin ) pa ame izes he baseline including all
non em oscopic e ec s, o ins ance esonance decays, and
Nis a no maliza ion coe icien . The Coulomb in e ac ion is
de e mined as
K( ,qin )=CQS+Coulomb
CQS
,(4)
0.5
1
1.5
= 5.02 TeVsPb -ALICE p
pai s
KK
c<0.5 GeV/
T
k0.2<
20%– 0
0.5
1
1.5 c<0.5 GeV/
T
k0.2<
40%– 20
) i
in
q(C
) i
in
q(D
0 0.5 1
0.5
1
1.5 c<0.5 GeV/
T
k0.2<
90%
– 40
expe imen
EPOS
c<1.0 GeV/
T
k0.5<
20%
– 0
c<1.0 GeV/
T
k0.5<
40%
– 20
0 0.5 1
c<1.0 GeV/
T
k0.5<
90%
– 40
)c (GeV/
in
q
)
in
qC(
FIG. 2. K±K±expe imen al co ela ion unc ions co ec ed o
pu i y acco ding o Eq. (2) ( ed poin s) and EPOS 3 model baselines
[26] (black poin s) e sus pai ela i e in a ian momen um qin .
The CFs a e p esen ed in h ee e en mul iplici y classes: 0–20%,
20–40%, and 40–90% and wo pai ans e se momen um kTbins:
(0.2–0.5) and (0.5–1.0) GeV/c. The black line shows he i o EPOS
3 by a i s -o de polynomial o 0 <qin <1.0 GeV/c.The ed
line shows he subsequen i o he CF up o qin <0.5 GeV/cby
Eq. (3). The CFs a e no malized o uni y in he ange 0.5<qin <
1.0 GeV/c. S a is ical (lines) and sys ema ic unce ain ies (boxes)
a e shown.
whe e CQS is a heo e ical CF calcula ed wi h pu e quan-
um s a is ical (QS) weigh s (wa e unc ion squa ed) and
CQS+Coulomb co esponds o quan um s a is ical plus Coulomb
weigh s [49,51]. The pa ame e s Rin and λdesc ibe he size
o he sou ce and he co ela ion s eng h, espec i ely.
B. Fi ing p ocedu e
The pa ame e s Rin and λcan be ex ac ed using Eq. (3)
wi h a ious assump ions o handle he non em oscopic base-
line D om backg ound e ec s ou side he em oscopic peak
egion. The e a e a ious me hods o deal wi h he baseline.
The simples way is o assume ha i is la , D(qin )=1,
which can be easonable in cases whe e non em oscopic
e ec s a e negligible. As can be seen in Fig. 2, he baseline
o he ob ained expe imen al unc ions is no la . The e-
o e, i would be mo e easonable o desc ibe i , o in-
s ance, by a i s -o de polynomial unc ion D(qin )=N(1 +
aqin ), which ep oduces his baseline slope. I in e pola es
he baseline beha io a high qin aking in o accoun all
non em oscopic e ec s, which make i non la . Then being
ex apola ed o low qin , i is supposed o imi a e he exis ing
non em oscopic e ec s. The mos na u al way o desc ibe he
024002-4

ONE-DIMENSIONAL CHARGED KAON FEMTOSCOPY … PHYSICAL REVIEW C 100, 024002 (2019)
baseline is o use Mon e Ca lo (MC) models whe e e en s
a e gene a ed om physical conside a ions and con ain all
bu QS and Coulomb e ec s. A sui able MC model has o
easonably desc ibe he baseline a high qin , whe e non em o-
scopic e ec s a e signi ican , and also con ain non em oscopic
e ec s a low qin .TheEPOS3[26] model wi hou QS and
Coulomb in e ac ion e ec s included was used o desc ibe he
baseline D(qin ). As seen om Fig. 2, EPOS 3 desc ibes he
expe imen al CF ou side he co ela ion peak. The ex ac ed
pa ame e alues depend on he i ange, which should be
chosen aking in o accoun he cha ac e is ic wid h o he em-
oscopic e ec obse ed. In his analysis, he EPOS 3 baseline
was i wi h a i s -o de polynomial in 0 <qin <1.0GeV/c
( o la en s a is ical unce ain ies) and hen he expe imen al
CF was i wi h Eq. (3) in he ange 0 <qin <0.5GeV/c.
The Coulomb in e ac ion adius was se o =1.5 m, which
is on a e age close o he ex ac ed adii alues.
C. Sys ema ic unce ain ies
The e ec s o a ious sou ces o sys ema ic unce ain y on
he ex ac ed pa ame e s we e s udied as unc ions o mul i-
plici y and kT. The sys ema ic unce ain ies we e es ima ed
by a ying he selec ion c i e ia used o he e en s, pa icles,
and pai s (wi h a ia ion limi s up o ±20%). The in luence
o he i ange was es ima ed by a ia ion o he qin uppe
limi by ±40%. Ano he sou ce o sys ema ic unce ain y is
he misiden i ica ion o pa icles and he associa ed pu i y
co ec ion. A ±10% a ia ion o he pa ame e s (Sec. II B)
used o he pu i y co ec ion es ima ion was pe o med. To
educe he elec on con amina ion, he PID c i e ia we e igh -
ened, in pa icula by ex ending he momen um ange whe e
he TOF signal was used and he ene gy-loss measu emen
was equi ed o be consis en wi h he kaon hypo hesis wi hin
nσ,TPC <1.
The e is also an unce ain y associa ed wi h he choice o
he adius o he Coulomb in e ac ion. I was se o 1.5 m
as a esul o a e aging o he h ee adii alues ha we e
ex ac ed om he espec i e mul iplici y bins and a ied by
±0.5 m. The ela i e di e ence was aken as a sys ema ic
TABLE III. Minimum and maximum unce ain y alues o a -
ious sou ces o sys ema ic unce ain y (in pe cen ), he punc ua ion
“–” means ha he con ibu ion om he gi en sou ce is negligible.
No e ha each alue is he minimum-maximum unce ain y om a
speci ic sou ce, bu can pe ain o di e en mul iplici y o kTbins.
Thus, he maximum o al unce ain ies a e smalle han (o equal o)
he sum o he maximum indi idual unce ain ies shown in his able.
Sys ema ic unce ain ies whose s a is ical signi icance le el exceeds
50% we e included in he o al sys ema ic unce ain y alue.
Rin (%) λ(%)
Single pa icle selec ion 0–1.5 0–3.2
PID and pu i y – 0–0.6
Pai selec ion 0–3 0–6
Baseline 1–4.8 0.2–4.1
Fi ange 0.6–7 0.5–5.7
Coulomb unc ion 0–2.3 1.8–3.8
Momen um esolu ion 0–1 0–1
unce ain y. Unce ain ies associa ed wi h momen um esolu-
ion we e es ima ed using a MC simula ion wi h he DPMJET
3.05 [41] model. The e ec is limi ed o low pai ela i e
momen um, whe e i smea s he co ela ion unc ion and is
especially p onounced o na ow em oscopic peaks. In p-Pb
collisions he qin egion o he em oscopic e ec is one
o de o magni ude wide han he egion a ec ed by his
ine iciency and, consequen ly, he co esponding unce ain y
is mino .
As was explained in Sec. III B, he i ing p ocedu e e-
qui es knowledge o he non em oscopic backg ound shape
and magni ude. In his analysis, he EPOS 3 model was used
o his pu pose. The sys ema ic unce ain y associa ed wi h
he baseline was es ima ed using an al e na i e MC model,
DPMJET, as well as he wo me hods based on he use o
polynomials desc ibed in Sec. III B.
Table III p esen s he unce ain y ange o all consid-
e ed sou ces o sys ema ic unce ain y, whe e he minimum
(maximum) was chosen om all a ailable alues in all mul i-
plici y and kTbins. Fo each sou ce and each mul iplici y and
)c (GeV/
T
k
0.4 0.6 0.8
( m)
in
R
1
1.5
2ALICE EPOS
w/ casc
EPOS
w/o casc
20%- 0
40%-20
90%-40
= 5.02 TeV
NN
sPb -p
pai s
±
K
±
K
(a)
)c (GeV/
T
k
0.4 0.6 0.8
λ
0.5
1
ALICE EPOS
w/ casc
EPOS
w/o casc
20%- 0
40%-20
90%-40
= 5.02 TeV
NN
sPb -p
pai s
±
K
±
K
(b)
FIG. 3. (a) Expe imen al K±K±in a ian adii Rin and (b) co ela ion s eng hs λshown e sus pai ans e se momen um kT o h ee
mul iplici y classes and compa ed wi h he EPOS 3 model p edic ions wi h and wi hou he had onic cascade phase. S a is ical (lines) and
sys ema ic unce ain ies (boxes) a e shown. The poin s o lowe mul iplici y classes (blue and g een symbols) a e sligh ly o se in he x
di ec ion o cla i y.
024002-5
S. ACHARYA e al. PHYSICAL REVIEW C 100, 024002 (2019)
)c (GeV/
T
k
0.2 0.4 0.6 0.8 1
( m)
in
R
1
1.2
1.4
1.6
1.8
ALICE
pai s
±
K
±
K
= 17.2〉
ch
N〈 = 7 TeV, s
pp
= 17.3〉
ch
N〈 = 5.02 TeV,
NN
s
Pb -p
FIG. 4. Compa ison o em oscopic adii, as a unc ion o pai
ans e se momen um kT, ob ained in pp [13]andp-Pb collisions.
S a is ical (lines) and sys ema ic unce ain ies (boxes) a e shown.
kTbin, he maximum de ia ion om he pa ame e s ob ained
wi h he op imal da a selec ion c i e ia and i ing me hods
was aken and applied symme ically as he unce ain y. The
limi ed da a sample o p-Pb collisions leads o qui e high
s a is ical unce ain y alues and mos o he sys ema ic un-
ce ain y con ibu ions we e ound o be much smalle han he
quad a ic di e ence o he s a is ical unce ain ies. The e o e,
he sys ema ic unce ain y alues we e added in quad a u e,
conside ing only hose whose s a is ical signi icance le el
exceeded 50% [52]. As can be seen om Table III, hemain
sou ces o sys ema ic unce ain y on he ex ac ed pa ame e s
a e he pai selec ion c i e ia, he in luence o he i ange,
he adius o he Coulomb in e ac ion, and he baseline de-
sc ip ion. All o hem con ibu e o he unce ain y associa ed
wi h he adii. The ex ac ed co ela ion s eng hs ha e highe
s a is ical unce ain ies han he adii and, consequen ly, o
hem he pai selec ion c i e ia is he only sou ce o sys ema ic
unce ain y, which exceeds he s a is ical signi icance le el
chosen in his analysis.
IV. RESULTS AND DISCUSSION
The ex ac ed Rin and λpa ame e s a e depic ed in
Figs. 3(a) and 3(b), espec i ely. S a is ical and sys ema ic
unce ain ies as desc ibed in Sec. III C a e shown o all
esul s. Figu e 3also shows compa isons wi h he EPOS 3
model (wi h em oscopic e ec s included [29,53,54]) o he
same collision sys em and ene gy in he same mul iplici y
and kTbins as he expe imen al da a. Two cases a e consid-
e ed, one wi h and ano he one wi hou he had onic cascade
(U QMD) phase [55]. The EPOS 3 calcula ions o he adii
wi hou he cascade exhibi p ac ically no kTdependence and
do no desc ibe he da a, while he da a a e well ep oduced
by he ull EPOS 3 model calcula ions he eby showing he
impo ance o he had onic cascade phase a LHC ene gies.
This obse a ion ag ees wi h he conclusion om he h ee-
dimensional K± em oscopic analysis in Pb-Pb collisions
a √sNN =2.76 TeV [47] whe e he hyd okine ic model
HKM [56] wi h he had onic esca e ing phase desc ibed he
cha ged kaon em oscopic adii well. The ex ac ed expe i-
men al λ alues a e abou 0.45, whe eas he EPOS 3 ones
a e abou 0.65, i.e., appa en ly la ge han he expe imen al
λ alues. The alue o he λpa ame e may be in luenced
by non-Gaussian ea u es o he co ela ion unc ion [57],
by a ini e cohe en componen o kaon emission [51,58]
and also he con ibu ion o kaons om K∗decays (≈
50 MeV, whe e is he decay wid h) and om o he long-
li ed esonances [59]. The eason o he di e ence be ween
he expe imen al co ela ion s eng hs and hose ob ained wi h
EPOS 3 could be ha he model does no accu a ely accoun
o all con ibu ions o kaons om a ious esonance decays
[60]. Ano he explana ion could be a pa ial cohe ence o he
eal emi ing sou ce [50,58,61,62], which is no aken in o
accoun in he EPOS 3 model.
In Fig. 4, he adii om pp collisions a √s=7TeV[13]
and p-Pb collisions a √sNN =5.02 TeV a simila mul iplic-
i y a e compa ed as a unc ion o pai ans e se momen um
kT. The co esponding adii in Pb-Pb collisions a √sNN =
2.76 TeV [14] a e no shown because hey we e ob ained
o mul iplici ies, which a e no a ailable in his s udy. The
igu e shows ha a he same mul iplici y, he adii in p-Pb
collisions a e consis en wi h hose in pp collisions wi hin
unce ain ies. The s a is ical signi icance o his obse a ion
(4–15%) does no allow his esul o be p ecisely compa ed
wi h he esul s o he one-dimensional h ee-pion cumulan s
[21] and h ee-dimensional wo-pion [22] analyses whe e he
1/3
〉
ch
N〈
0 5 10 15
( m)
in
R
0
2
4
6
8
c = 0.42 GeV/〉
T
k〈 = 7 TeV, spp
c = 0.36 GeV/〉
T
k〈 = 5.02 TeV,
NN
sPb -p
c = 0.35 GeV/〉
T
k〈 = 2.76 TeV,
NN
sPb -Pb
ALICE
pai s
±
K
±
K
(a)
1/3
〉
ch
N〈
0 5 10 15
( m)
in
R
0
2
4
6
8
c = 0.8 GeV/〉
T
k〈 = 7 TeV, spp
c = 0.7 GeV/〉
T
k〈 = 5.02 TeV,
NN
sPb -p
c = 0.75 GeV/〉
T
k〈 = 2.76 TeV,
NN
sPb -Pb
ALICE
pai s
±
K
±
K
(b)
FIG. 5. Compa ison o em oscopic adii, as a unc ion o he measu ed cha ged-pa icle mul iplici y densi y Nch1/3,a (a)lowand
(b) high kTob ained in pp [13], p-Pb, and Pb-Pb [14] collisions. S a is ical (lines) and sys ema ic unce ain ies (boxes) a e shown.
024002-6
ONE-DIMENSIONAL CHARGED KAON FEMTOSCOPY … PHYSICAL REVIEW C 100, 024002 (2019)
1/3
〉
ch
N〈
0 5 10 15
λ
0
0.5
1
ALICE
pai s
±
K
±
K
(a)
c = 0.42 GeV/〉
T
k〈 = 7 TeV, spp
c = 0.36 GeV/〉
T
k〈 = 5.02 TeV,
NN
sPb -p
c = 0.35 GeV/〉
T
k〈 = 2.76 TeV,
NN
sPb -Pb
1/3
〉
ch
N〈
051015
λ
0
0.5
1
ALICE
pai s
±
K
±
K
(b)
c = 0.8 GeV/〉
T
k〈 = 7 TeV, spp
c = 0.7 GeV/〉
T
k〈 = 5.02 TeV,
NN
sPb -p
c = 0.75 GeV/〉
T
k〈 = 2.76 TeV,
NN
sPb -Pb
FIG. 6. Compa ison o co ela ion s eng hs λ, as a unc ion o he measu ed cha ged-pa icle mul iplici y densi y Nch1/3,a (a)lowand
(b) high kTob ained in pp [13], p-Pb, and Pb-Pb [14] collisions. S a is ical (lines) and sys ema ic unce ain ies (boxes) a e shown.
adii in pp collisions we e ob ained o be 5–15% and 10–20%
smalle han hose in p-Pb collisions, espec i ely.
Figu e 5compa es em oscopic adii as a unc ion o he
measu ed cha ged-pa icle mul iplici y densi y Nch1/3,a
low [Fig. 5(a)] and high [Fig. 5(b)]kTin pp [13], p-Pb, and
Pb-Pb [14] collisions. The ob ained adii inc ease wi h Nch
and ollow he mul iplici y end obse ed in pp collisions.
The adii a e equal in p-Pb and pp collisions a simila
mul iplici y wi hin unce ain ies. This esul could indica e
ha he dynamics o he sou ce in p-Pb collisions a low
mul iplici ies is simila o ha in ppcollisions. In pa icula , i
he e is a collec i e expansion o he sou ces c ea ed in ppand
p-Pb collisions, hese esul s indica e ha he expansion is no
signi ican ly s onge in p-Pb han in pp collisions [24]. As
seen om he igu e, he adii in p-Pb and Pb-Pb collisions
we e ob ained in e y di e en anges o mul iplici y and
canno be compa ed a he same Nch. In o de o make a
s onge conclusion be ween di e en collision sys ems, as
)c (GeV/
T
k
0 0.5 1
λ
0
0.5
1
1.5
ALICE
pai s
±
K
±
K
pp
= 7 TeVs
Pb–p
= 5.02 TeV
NN
s
Pb–Pb
= 2.76 TeV
NN
s
>22
ch
N20%–010%–0
22– 12
ch
N40%–20 30%–10
11– 1
ch
N90%–40 50%–30
FIG. 7. The K±K±co ela ion s eng hs λin pp [13], p-Pb, and
Pb-Pb [14] collisions e sus pai ans e se momen um kTin all mul-
iplici y and kTbins. S a is ical (lines) and sys ema ic unce ain ies
(boxes) a e shown. The da a poin s o lowe mul iplici y classes
(blue and g een symbols) a e sligh ly o se in kTwi h espec o he
highes mul iplici y classes ( ed symbols) o be e isibili y.
was done in he pion co ela ion analyses [21,22], a la ge
expe imen al da a se should be conside ed.
Figu es 6(a) and 6(b) show he co ela ion s eng hs λin
pp [13], p-Pb, and Pb-Pb [14] collisions a low and high kT,
espec i ely. All λ alues a e less han uni y p obably due
o he in luence o long-li ed esonances and a non-Gaussian
shape o he kaon CF peak. I can be no iced om he igu e
ha he co ela ion s eng h pa ame e s in Pb-Pb collisions
end o be highe han hose in pp and p-Pb collisions. Tha
could poin o a mo e Gaussian sou ce c ea ed in Pb-Pb
collisions.
Figu e 7compa es co ela ion s eng hs λin pp[13], p-Pb,
and Pb-Pb collisions as a unc ion o kT o all a ailable mul i-
plici y bins. As seen om he igu e, he co ela ion s eng hs
in all mul iplici y and all kTbins do no show any no iceable
kTo mul iplici y dependence. The sys ema ic unce ain y
alues ob ained o he compa ed collision sys ems a e isibly
di e en since e en he same sou ce o unce ain y gi es a
a he di e en con ibu ion o he o al unce ain y alue in
e e y collision sys em.
V. SUMMARY
In his wo k, one-dimensional iden ical cha ged kaon co -
ela ions we e ob ained and analyzed o he i s ime in
p o on-nucleus collisions, ha is in p-Pb a √sNN =5.02 TeV.
The sou ce size Rin and co ela ion s eng h λwe e ex ac ed
om a co ela ion unc ion pa ame ized in e ms o he
in a ian pai ela i e momen um qin . The ob ained adii
Rin dec ease wi h inc easing pai ans e se momen um kT
and wi h dec easing e en mul iplici y. This is simila o he
beha io o pion adii in he h ee-dimensional wo-pion co -
ela ion analysis in p-Pb collisions a √sNN =5.02 TeV and
one-dimensional h ee-pion cumulan esul s in pp collisions
a √s=7TeV,p-Pb collisions a √sNN =5.02 TeV and
Pb-Pb collisions a √sNN =2.76 TeV.
The ob ained adii Rin a e ep oduced well by he EPOS
3 model (including em oscopic e ec s) calcula ions wi h
he had onic esca e ing phase, whose impo ance was also
demons a ed in he h ee-dimensional em oscopic analysis
o K±pai co ela ions in Pb-Pb collisions. The alues o he
024002-7
S. ACHARYA e al. PHYSICAL REVIEW C 100, 024002 (2019)
co ela ion s eng h pa ame e s λin EPOS 3 a e appa en ly
la ge han he expe imen al λ alues, which could be due o
cohe en sou ces no inco po a ed in EPOS 3 and long-li ed
esonances no aken in o accoun accu a ely enough in his
model.
The kaon Rin alues in p-Pb and pp collisions show he
same end wi h mul iplici y. Howe e , i is di icul o say
whe he he same is ue o he Pb-Pb poin s because o
a la ge gap in mul iplici ies a ailable in p-Pb and Pb-Pb
collisions. The esul s dis a o models, which inco po a e
subs an ially s onge collec i e expansion in p-Pb collisions
compa ed o pp collisions a simila mul iplici y. The co ela-
ion s eng h λdoes no show any ends wi h mul iplici y o
kT. The ac ha he co ela ion s eng h in Pb-Pb collisions
ends o be highe han in pp and p-Pb collisions could be
an indica ion o a mo e Gaussian sou ce c ea ed in Pb-Pb
collisions. Howe e , a s onge conclusion is p e en ed due
o la ge s a is ical and sys ema ic unce ain ies, especially o
he Pb-Pb da a.
ACKNOWLEDGMENTS
The ALICE Collabo a ion would like o hank all i s
enginee s and echnicians o hei in aluable con ibu ions
o he cons uc ion o he expe imen and he CERN accel-
e a o eams o he ou s anding pe o mance o he LHC
complex. The ALICE Collabo a ion g a e ully acknowledges
he esou ces and suppo p o ided by all G id cen es and
he Wo ldwide LHC Compu ing G id (WLCG) collabo a ion.
The ALICE Collabo a ion acknowledges he ollowing und-
ing agencies o hei suppo in building and unning he
ALICE de ec o : A. I. Alikhanyan Na ional Science Labo-
a o y (Ye e an Physics Ins i u e) Founda ion (ANSL), S a e
Commi ee o Science and Wo ld Fede a ion o Scien is s
(WFS), A menia; Aus ian Academy o Sciences, Aus ian
Science Fund (FWF): [M 2467-N36] and Na ionals i ung
ü Fo schung, Technologie und En wicklung, Aus ia; Min-
is y o Communica ions and High Technologies, Na ional
Nuclea Resea ch Cen e , Aze baijan; Conselho Nacional de
Desen ol imen o Cien í ico e Tecnológico (CNPq), Uni e si-
dade Fede al do Rio G ande do Sul (UFRGS), Financiado a
de Es udos e P oje os (Finep) and Fundação de Ampa o à
Pesquisa do Es ado de São Paulo (FAPESP), B azil; Min-
is y o Science & Technology o China (MSTC), Na ional
Na u al Science Founda ion o China (NSFC) and Minis y
o Educa ion o China (MOEC), China; C oa ian Science
Founda ion and Minis y o Science and Educa ion, C oa-
ia; Cen o de Aplicaciones Tecnológicas y Desa ollo Nu-
clea (CEADEN), Cubaene gía, Cuba; Minis y o Educa ion,
You h and Spo s o he Czech Republic, Czech Repub-
lic; The Danish Council o Independen Resea ch - Na u-
al Sciences, he Ca lsbe g Founda ion and Danish Na ional
Resea ch Founda ion (DNRF), Denma k; Helsinki Ins i u e
o Physics (HIP), Finland; Commissa ia à l’Ene gie A om-
ique (CEA), Ins i u Na ional de Physique Nucléai e e de
Physique des Pa icules (IN2P3) and Cen e Na ional de la
Reche che Scien i ique (CNRS) and Rlégion des Pays de la
Loi e, F ance; Bundesminis e ium ü Bildung, Wissenscha ,
Fo schung und Technologie (BMBF) and GSI Helmhol zzen-
um ü Schwe ionen o schung GmbH, Ge many; Gene al
Sec e a ia o Resea ch and Technology, Minis y o Edu-
ca ion, Resea ch and Religions, G eece; Na ional Resea ch,
De elopmen and Inno a ion O ice, Hunga y; Depa men o
A omic Ene gy Go e nmen o India (DAE), Depa men o
Science and Technology, Go e nmen o India (DST), Uni-
e si y G an s Commission, Go e nmen o India (UGC) and
Council o Scien i ic and Indus ial Resea ch (CSIR), India;
Indonesian Ins i u e o Science, Indonesia; Cen o Fe mi -
Museo S o ico della Fisica e Cen o S udi e Rice che En ico
Fe mi and Is i u o Nazionale di Fisica Nuclea e (INFN), I aly;
Ins i u e o Inno a i e Science and Technology, Nagasaki
Ins i u e o Applied Science (IIST), Japan Socie y o he
P omo ion o Science (JSPS) KAKENHI and Japanese Min-
is y o Educa ion, Cul u e, Spo s, Science and Technology
(MEXT), Japan; Consejo Nacional de Ciencia (CONACYT)
y Tecnología, h ough Fondo de Coope ación In e nacional
en Ciencia y Tecnología (FONCICYT) and Di ección Gen-
e al de Asun os del Pe sonal Academico (DGAPA), Mexico;
Nede landse O ganisa ie oo We enschappelijk Onde zoek
(NWO), Ne he lands; The Resea ch Council o No way, No -
way; Commission on Science and Technology o Sus ainable
De elopmen in he Sou h (COMSATS), Pakis an; Pon i icia
Uni e sidad Ca ólica del Pe ú, Pe u; Minis y o Science and
Highe Educa ion and Na ional Science Cen e, Poland; Ko ea
Ins i u e o Science and Technology In o ma ion and Na ional
Resea ch Founda ion o Ko ea (NRF), Republic o Ko ea;
Minis y o Educa ion and Scien i ic Resea ch, Ins i u e o
A omic Physics and Minis y o Resea ch and Inno a ion
and Ins i u e o A omic Physics, Romania; Join Ins i u e o
Nuclea Resea ch (JINR), Minis y o Educa ion and Science
o he Russian Fede a ion, Na ional Resea ch Cen e Ku cha-
o Ins i u e, Russian Science Founda ion and Russian Foun-
da ion o Basic Resea ch, Russia; Minis y o Educa ion,
Science, Resea ch and Spo o he Slo ak Republic, Slo-
akia; Na ional Resea ch Founda ion o Sou h A ica, Sou h
A ica; Swedish Resea ch Council (VR) and Knu & Alice
Wallenbe g Founda ion (KAW), Sweden; Eu opean O gani-
za ion o Nuclea Resea ch, Swi ze land; Na ional Science
and Technology De elopmen Agency (NSDTA), Su ana ee
Uni e si y o Technology (SUT) and O ice o he Highe
Educa ion Commission unde NRU p ojec o Thailand, Thai-
land; Tu kish A omic Ene gy Agency (TAEK), Tu key; Na-
ional Academy o Sciences o Uk aine, Uk aine; Science
and Technology Facili ies Council (STFC), Uni ed Kingdom;
Na ional Science Founda ion o he Uni ed S a es o Ame ica
(NSF) and Uni ed S a es Depa men o Ene gy, O ice o
Nuclea Physics (DOE NP), Uni ed S a es o Ame ica.
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[2] G. I. Kopylo and M. I. Podgo e sky, Co ela ions o iden ical
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ONE-DIMENSIONAL CHARGED KAON FEMTOSCOPY … PHYSICAL REVIEW C 100, 024002 (2019)
116Technical Uni e si y o Košice, Košice, Slo akia
117Technische Uni e si ä München, Excellence Clus e ‘Uni e se’, Munich, Ge many
118The Hen yk Niewodniczanski Ins i u e o Nuclea Physics, Polish Academy o Sciences, C acow, Poland
119The Uni e si y o Texas a Aus in, Aus in, Texas, Uni ed S a es
120Uni e sidad Au ónoma de Sinaloa, Culiacán, Mexico
121Uni e sidade de São Paulo (USP), São Paulo, B azil
122Uni e sidade Es adual de Campinas (UNICAMP), Campinas, B azil
123Uni e sidade Fede al do ABC, San o And e, B azil
124Uni e si y College o Sou heas No way, Tonsbe g, No way
125Uni e si y o Cape Town, Cape Town, Sou h A ica
126Uni e si y o Hous on, Hous on, Texas, Uni ed S a es
127Uni e si y o Jy äskylä, Jy äskylä, Finland
128Uni e si y o Li e pool, Li e pool, Uni ed Kingdom
129Uni e si y o Science and Techonology o China, He ei, China
130Uni e si y o Tennessee, Knox ille, Tennessee, Uni ed S a es
131Uni e si y o he Wi wa e s and, Johannesbu g, Sou h A ica
132Uni e si y o Tokyo, Tokyo, Japan
133Uni e si y o Tsukuba, Tsukuba, Japan
134Uni e si é Cle mon Au e gne, CNRS/IN2P3, LPC, Cle mon -Fe and, F ance
135Uni e si é de Lyon, Uni e si é Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeu banne, Lyon, F ance
136Uni e si é de S asbou g, CNRS, IPHC UMR 7178, F-67000 S asbou g, F ance, S asbou g, F ance
137Uni e si é Pa is-Saclay Cen e d’E udes de Saclay (CEA),
IRFU, Dépa men de Physique Nucléai e (DPhN), Saclay, F ance
138Uni e si à degli S udi di Foggia, Foggia, I aly
139Uni e si à degli S udi di Pa ia, Pa ia, I aly
140Uni e si à di B escia, B escia, I aly
141Va iable Ene gy Cyclo on Cen e, Homi Bhabha Na ional Ins i u e, Kolka a, India
142Wa saw Uni e si y o Technology, Wa saw, Poland
143Wayne S a e Uni e si y, De oi , Michigan, Uni ed S a es
144Wes älische Wilhelms-Uni e si ä Müns e , Ins i u ü Ke nphysik, Müns e , Ge many
145Wigne Resea ch Cen e o Physics, Hunga ian Academy o Sciences, Budapes , Hunga y
146Yale Uni e si y, New Ha en, Connec icu , Uni ed S a es
147Yonsei Uni e si y, Seoul, Republic o Ko ea
aDeceased.
bDipa imen o DET del Poli ecnico di To ino, Tu in, I aly.
cM.V. Lomonoso Moscow S a e Uni e si y, D.V. Skobel syn Ins i u e o Nuclea , Physics, Moscow, Russia.
dDepa men o Applied Physics, Aliga h Muslim Uni e si y, Aliga h, India.
eIns i u e o Theo e ical Physics, Uni e si y o W oclaw, Poland.
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