Event-by-event mean pT fluctuations in pp and Pb–Pb collisions at the LHC

Eu . Phys. J. C (2014) 74:3077
DOI 10.1140/epjc/s10052-014-3077-y
Regula A icle - Expe imen al Physics
E en -by-e en mean pT luc ua ions in pp and Pb–Pb collisions
a he LHC
ALICE Collabo a ion
CERN, 1211 Gene a 23, Swi ze land
Recei ed: 22 July 2014 / Accep ed: 12 Sep embe 2014 / Published online: 15 Oc obe 2014
© CERN o he bene i o he ALICE collabo a ion 2014. This a icle is published wi h open access a Sp inge link.com
Abs ac E en -by-e en luc ua ions o he mean ans-
e se momen um o cha ged pa icles p oduced in pp colli-
sions a √s=0.9, 2.76 and 7 TeV, and Pb–Pb collisions a
√sNN =2.76 TeV a e s udied as a unc ion o he cha ged-
pa icle mul iplici y using he ALICE de ec o a he LHC.
Dynamical luc ua ionsindica i eo co ela edpa icleemis-
sion a e obse ed in all sys ems. The esul s in pp collisions
show li le dependence on collision ene gy. The Mon e Ca lo
e en gene a o s PYTHIA and PHOJET a e in quali a i e
ag eemen wi h heda a. Pe iphe alPb–Pb da aexhibi a sim-
ila mul iplici y dependence as ha obse ed in pp. In cen al
Pb–Pb, he esul s de ia e om his end, ea u ing a signi -
ican educ ion o he luc ua ion s eng h. The esul s in Pb–
Pb a e in quali a i e ag eemen wi h p e ious measu emen s
in Au–Au a lowe collision ene gies and wi h expec a ions
om models ha inco po a e collec i e phenomena.
1 In oduc ion
The s udy o e en -by-e en luc ua ions was p oposed as a
p obe o he p ope ies o he ho and dense ma e gene a ed
in high-ene gy hea y-ion collisions [1–9]. The occu ence o
a phase ansi ion om he Qua k-Gluon Plasma o a Had on
Gas o he exis ence o a c i icalpoin in he phase diag am o
s ongly in e ac ing ma e may go along wi h c i ical luc-
ua ions o he modynamic quan i ies such as empe a u e.
This could be e lec ed in dynamical e en -by-e en luc ua-
ions o he mean ans e se momen um pTo inal-s a e
cha ged pa icles.
E en -by-e en pT luc ua ions ha e been s udied in
nucleus-nucleus (A–A) collisions a he Supe P o on Syn-
ch o on (SPS) [10–14] and a he Rela i is ic Hea y-Ion
Collide (RHIC) [15–20], whe e dynamical luc ua ions ha e
been obse ed. Fluc ua ions o pTwe e ound o dec ease
wi h collision cen ali y, as gene ally expec ed in a dilu ion
scena io caused by supe posi ion o pa ially independen
e-mail: [email p o ec ed]
pa icle-emi ing sou ces. In de ail, howe e , de ia ions om
a simple supe posi ion scena io ha e been epo ed. In pa -
icula , wi h espec o a e e ence ep esen ing independen
supe posi ion – i.e.a dec ease o luc ua ions acco ding o
dNch/dη−0.5, whe e dNch/dηis he a e age cha ged-
pa icle densi y in a gi en in e al o collision cen ali y
and pseudo apidi y (η) – he obse ed luc ua ions inc ease
sha ply om pe iphe al o semi-pe iphe al collisions, ol-
lowed by a shallow dec ease owa ds cen al collisions [18].
A numbe o possible mechanisms ha e been p oposed o
explain his beha io , such as s ing pe cola ion [21]o he
onse o he maliza ionandcollec i i y[22,23],bu nos ong
connec ion o c i ical beha io could be made. I was ecen ly
sugges ed [24,25] ha ini ial s a e densi y luc ua ions [26]
could a ec he inal s a e ans e se momen um co ela ions
and hei cen ali y dependence.
Fluc ua ions o pTa ise om many kinds o co ela ions
among he pTo he inal-s a e pa icles, such as esonance
decays, je s, o quan um co ela ions. To accoun o hese
con ibu ions om con en ional mechanisms simila s ud-
ies can be pe o med in pp, whe e such co ela ions a e also
p esen . The esul s om pp could hus be used o cons uc a
model-independen baseline o sea ch o non- i ial luc u-
a ions in A–A which mani es hemsel es in a modi ica ion
o he luc ua ion pa e n wi h espec o he pp e e ence.
In his pape , we p esen esul s o a mul iplici y-
dependen s udy o e en -by-e en pT luc ua ions o
cha ged pa icles in pp collisions a √s=0.9, 2.76 and
7 TeV, and Pb–Pb collisions a √sNN =2.76 TeV measu ed
wi hALICEa heLHC.Theexpe imen alda aa ecompa ed
o di e en Mon e Ca lo (MC) e en gene a o s.
2 ALICE de ec o and da a analysis
The da a used in his analysis we e collec ed wi h he ALICE
de ec o a he CERN La ge Had on Collide (LHC) [27]
du ing he Pb–Pb un in 2010 and he pp uns in 2010 and
2011.
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3077 Page 2 o 15 Eu . Phys. J. C (2014) 74:3077
Fo ade aileddesc ip iono heALICEappa a ussee[28].
The analysis is based on 19 ×106Pb–Pb e en s a √sNN =
2.76 TeV, and 6.9×106,66×106and 290×106pp e en s a
√s=0.9, 2.76 and 7 TeV, espec i ely. The s anda d ALICE
coo dina e sys em is used, in which he nominal in e ac ion
poin is he o igin o a igh -handed Ca esian coo dina e
sys em. The z-axis is along he beam pipe, he x-axis poin s
owa ds he cen e o he LHC, ϕis he azimu hal angle
a ound he z-axis and θis he pola angle wi h espec o
his axis. The de ec o s in he cen al ba el o he expe -
imen a e ope a ed inside a solenoidal magne ic ield wi h
B=0.5 T. Abou hal o he Pb–Pb da a se was eco ded
wi h nega i e (Bz<0) and posi i e (Bz>0) ield pola i y,
espec i ely.
A minimum bias (MB) igge condi ion was applied o
selec collision e en s. In pp, his igge was de ined by a
leas one hi in he Silicon Pixel De ec o (SPD) o in one o
he wo o wa d scin illa o sys ems VZERO-A (2.8<η<
5.1) and VZERO-C (−3.7<η<−1.7). In Pb–Pb, he MB
igge condi ion is de ined as a coincidence o hi s in bo h
VZERO de ec o s.
In his analysis, he Time P ojec ion Chambe (TPC) [29]
is used o cha ged-pa icle acking in |η|<0.8. In he
momen um ange selec ed o his analysis, 0.15 <pT<
2GeV/c, he momen um esolu ion σ(pT)/pTis be e han
2%. The acking e iciency is la ge han 90% o pT>
0.3GeV/cand d ops o abou 70% a pT=0.15 GeV/c.
P ima y e ex in o ma ion is ob ained om bo h he
Inne T acking Sys em (ITS) and he TPC. E en s a e used
in he analysis when a leas one accep ed cha ged-pa icle
ack con ibu es o he p ima y e ex econs uc ion. I is
equi ed ha he econs uc ed e ex is wi hin ±10 cm om
he nominal in e ac ion poin along he beam di ec ion o
ensu eauni o m pseudo- apidi yaccep ance wi hin heTPC.
Addi ionally, he e en e ex is econs uc ed using only
TPC acks. The e en is ejec ed i he z-posi ion o ha e -
ex is di e en by mo e han 10 cm om ha o he s anda d
p ocedu e.
In Pb–Pb, a leas 10 econs uc ed acks inside he accep-
ance a e equi ed. The con amina ion by non-had onic in e -
ac ions is negligible in he e en sample ha ul ills he a o e-
men ioned selec ion c i e ia. The cen ali y in Pb–Pb is es i-
ma ed om he signal in he VZERO de ec o s using he
p ocedu e desc ibed in [30,31].
The cha ged-pa icle acks used o his analysis a e
equi ed o ha e a leas 70 ou o a maximum o 159 econ-
s uc ed space poin s in he TPC, and he maximum χ2pe
space poin in he TPC om he momen um i mus be less
han 4. Daugh e acks om econs uc ed seconda y weak-
decay opologies (kinks) a e ejec ed. The dis ance o closes
app oach (DCA) o he ex apola ed ajec o y o he p ima y
e ex posi ionis es ic ed oless han3.2 cmalong he beam
di ec ion and less han 2.4 cm in he ans e se plane. The
numbe o acks in an e en ha a e accep ed by hese selec-
ion c i e ia is deno ed by Nacc.
E en -by-e en measu emen s o he mean ans e se
momen um a e subjec o he ini e econs uc ion e iciency
o hede ec o .Whilee iciencyco ec ionscanbe appliedon
as a is ical basis ode i e heinclusi epTo cha gedpa i-
cles in a gi en kinema ic accep ance ange, such an app oach
is no adequa e o e en -by-e en s udies. The e en -by-
e en mean ans e se momen um is he e o e app oxima ed
by he mean alue MEbE(pT)ko he ans e se momen a
pT,io he Nacc,kaccep ed cha ged pa icles in e en k:
MEbE(pT)k=1
Nacc,k
Nacc,k

i=1
pT,i.(1)
E en -by-e en luc ua ions o MEbE(pT)kin hea y-ion col-
lisions a e composed o s a is ical and dynamical con i-
bu ions. The wo-pa icle ans e se momen um co ela o
C=pT,i,pT,jis a measu e o he dynamical compo-
nen σ2
dyn o hese luc ua ions and he e o e well sui ed o
an e en -by-e en analysis [13,18,32]. The co ela o Cmis
he mean o co a iances o all pai s o pa icles iand jin he
same e en wi h espec o he inclusi e M(pT)min a gi en
mul iplici y class mand is de ined as
Cm=1
ne ,m
k=1Npai s
k·
ne ,m

k=1
Nacc,k

i=1
Nacc,k

j=i+1
(pT,i−M(pT)m)·(pT,j−M(pT)m),
(2)
whe e ne ,mis he numbe o e en s in mul iplici y class m,
Npai s
k=0.5·Nacc,k·(Nacc,k−1)is he numbe o pa icle
pai s in e en kand M(pT)mis he a e age pTo all acks
in all e en s o class m:
M(pT)m=1
ne ,m
k=1Nacc,k
ne ,m

k=1
Nacc,k

i=1
pT,i
=1
ne ,m
k=1Nacc,k
ne ,m

k=1
Nacc,k·MEbE(pT)k.(3)
By cons uc ion, Cm anishes in he case o unco ela ed pa -
icle emission, when only s a is ical luc ua ions a e p esen .
The esul s in his pape a e p esen ed in e ms o he
dimensionless a io √Cm/M(pT)mwhich quan i ies he
s eng h o he dynamical luc ua ions in uni s o he a e age
ans e se momen um M(pT)min he mul iplici y class m.
The co ela o is compu ed in in e als o he e en mul i-
plici y Nacc. In pp collisions, in e als o Nacc =1a eused
o he calcula ion o Cmand M(pT)m. In Pb–Pb collisions,
Cmis calcula ed in he mul iplici y in e als Nacc =10
o Nacc <200, Nacc = 25 o 200 ≤Nacc <1000 and
123
Eu . Phys. J. C (2014) 74:3077 Page 3 o 15 3077
Table 1 Con ibu ions o he
o al sys ema ic unce ain y on
√Cm/M(pT)min pp and Pb–Pb
collisions. Ranges a e gi en
when he unce ain ies depend
on dNch/dηo cen ali y
Collision sys em pp pp pp Pb–Pb
√sNN 0.9 TeV 2.76 TeV 7 TeV 2.76 TeV
Ve ex z-posi ion cu 0–0.5% <0.1% <0.1% 0.5–1%
Ve ex calcula ion 0–2% 0.5–2% 0.5–2% <0.1%
Ve ex di e ence cu 0–1.5% 0–3% 0–2% 0–2%
Min.TPC space poin s 1.5–3% 1–2% 1–3% 2–3%
TPC χ2/ d.o. . <0.1% <0.1% <0.1% <0.1%
DCA o e ex 1% 1–1.5% 0.5–1% 0.5–1%
B- ield pola i y 0.5% 0.5% 0.5% 0.5%
Cen ali y in e als – – – 1–3%
TPC-only s.hyb id 4% 4% 4% 1–5%
MC gene a o s. ull sim. 0–6% 0–6% 0–6% 0–4%
To al 4.4–7.7% 4.4–7.6% 4.4–7.9% 4.2–7.4%
Nacc = 100 o Nacc ≥1000. To accoun o he s eep
inc ease o M(pT)mwi h mul iplici y in pe iphe al colli-
sions, he calcula ion o he co ela o in (2) uses alues
o M(pT)mwhich a e calcula ed in bins o Nacc =1 o
Nacc <1000. A highe mul iplici ies, M(pT)changes only
mode a ely and M(pT)mis calcula ed in he same in e als
as Cm, i.e.Nacc = 100.
Addi ionally, he Pb–Pb da a a e also analyzed in 5%
in e als o he collision cen ali y. The esul s a e shown in
bins o he mean numbe o pa icipa ing nucleons Npa as
de i ed om he cen ali y pe cen ile using a Glaube MC
calcula ion [30]. Fo he esul s p esen ed as a unc ion
o he mean cha ged-pa icle densi y dNch/dη, he mean
alue Naccin each cen ali y bin is associa ed wi h he
measu ed alue o dNch/dη om [30]. A linea ela ion
be ween Naccand dNch/dηis obse ed o e he ull cen-
ali y ange, allowing in e pola ion o assign a alue o
dNch/dη o any in e al o Nacc. In pp, dNch/dηis cal-
cula ed o each in e al o Nacc employing he ull de ec o
esponse ma ix om MC and un olding o he measu ed
Nacc dis ibu ions ollowing he p ocedu e ou lined in [33].
The sys ema ic unce ain ies a e es ima ed sepa a ely o
each collision sys em (Pb–Pb and pp) and a each collision
ene gy. The ela i e unce ain ies on √Cm/M(pT)ma e gen-
e ally smalle han hose on Cmbecause mos o he sou ces
o unce ain ies lead o co ela ed a ia ions o M(pT)mand
Cm ha end o cancel in he a io √Cm/M(pT)m. The e o e,
all quan i a i e esul s shown below a e p esen ed in e ms
o √Cm/M(pT)m. The con ibu ions o he o al sys ema ic
unce ain y on √Cm/M(pT)min pp and Pb–Pb collisions a e
summa ized in Table 1. Ranges a e gi en when he unce ain-
ies depend on dNch/dηo cen ali y.
The la ges con ibu ion o he o al sys ema ic unce ain y
esul s om he compa ison o √Cm/M(pT)m om ull MC
simula ions employing a GEANT3 [34] implemen a ion o
he ALICE de ec o se up [35] o he MC gene a o le el.
P ocessing he e en s h ough he ull simula ion chain al e s
he esul o √Cm/M(pT)mwi h espec o he MC gene -
a o le el by up o 6% in high mul iplici y pp collisions.
This includes e ec s o acking e iciency dependence on
he ans e se momen um. The s udies in pp a e pe o med
using he Pe ugia-0 une o PYTHIA6[36,37],simila esul s
a e ob ained wi h PHOJET [38]. HIJING [39]isused o
Pb–Pb collisions, whe e he di e ences a e sligh ly smalle ,
eaching up o 4% in mos cen al collisions.
Since hese de ia ions a e in gene al dependen on he
e en cha ac e is ics assumed in he model, in pa icula on
he na u e o he unde lying pa icle co ela ions, no co -
ec ion o expe imen al esul s is pe o med. Ins ead, hese
de ia ions a e added o he sys ema ic da a unce ain ies o
allow o a compa ison o he expe imen al esul s o model
calcula ions on he MC e en gene a o le el.
Ano he majo con ibu ion o he o al sys ema ic unce -
ain y eme ges om he di e ence be ween he s anda d
analysis using only TPC acks and an al e na i e analysis
employing a hyb id acking scheme. The hyb id acking
combines TPC and ITS acks when ITS de ec o in o ma-
ion is a ailable, and hus p o ides mo e powe ul supp es-
sion o seconda y pa icles ( emaining con amina ion 4–5%)
as compa ed o he s anda d TPC-only acking (∼12%).
The TPC, on he o he hand, ea u es e y s able ope a ional
condi ions h oughou he analyzed da a se s. The di e -
ences be ween he esul s om he wo analyses each 5% in
√Cm/M(pT)m.
A he e en le el, mino con ibu ions o he o al sys-
ema ic unce ain y a ise om he cu on he maximum dis-
ance o he econs uc ed e ex o he nominal in e ac ion
poin along he beam axis. In he s anda d analysis global
acks ha combine TPC and ITS ack segmen s a e used
o he e ex calcula ion. Al e na i ely, we s udied also he
esul s when only TPC acks o only ackle s om he SPD
a e used o econs uc he p ima y e ex. The e ec om
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3077 Page 4 o 15 Eu . Phys. J. C (2014) 74:3077
using he di e en e ex es ima o s is negligible in Pb–
Pb collisions. In pp collisions, his e ec is small wi h he
excep ion o he lowes mul iplici y bin, whe e i eaches
2% in √Cm/M(pT)m. Addi ionally, he cu on he di e -
ence be ween he z-posi ions o he econs uc ed e ices
ob ained om global acks and TPC-only acks is a ied.
This shows a sizable e ec only in pe iphe al Pb–Pb and
low-mul iplici y pp collisions (2–3% in √Cm/M(pT)m).
In addi ion, a ia ions o he ollowing ack quali y cu s
a e pe o med: he numbe o space poin s pe ack in he
TPC, he χ2pe deg ee o eedom o he momen um i , and
he DCA o each ack o he p ima y e ex, bo h along he
beam di ec ion and in he ans e se plane. Nei he o hese
con ibu ions o he o al sys ema ic unce ain y exceeds 3%
in √Cm/M(pT)m.
The di e ence be ween he esul s ob ained om Pb–Pb
da a aken a he wo magne ic ield pola i ies is included
in o he sys ema ic unce ain ies. The e ec is small (0.5%
in √Cm/M(pT)m). The co esponding unce ain y in pp is
assumed o be he same as in Pb–Pb collisions. Finally, he
e ec o ini e cen ali y in e als in Pb–Pb, and he co e-
sponding a ia ion o M(pT)wi hin hese in e als, is aken
in oaccoun byincluding he di e encebe ween he analyses
in 5 and 10% cen ali y in e als [30,31] in o he sys ema ic
unce ain y. The o al unce ain y on √Cm/M(pT)m o each
da a se was ob ained by adding in quad a u e he indi idual
con ibu ions in Table 1.
3 Resul s in pp collisions
The ela i e dynamical luc ua ion √Cm/M(pT)mas a unc-
iono hea e agecha ged-pa iclemul iplici ydNch/dηin
pp collisions a √s=0.9, 2.76 and 7 TeV is shown in Fig. 1.
The non-ze o alues o √Cm/M(pT)mindica e signi ican
dynamical e en -by-e en M(pT) luc ua ions. The luc ua-
ion s eng h eaches a maximum o 12–14% in low mul-
iplici y collisions and dec eases o abou 5% a he high-
es mul iplici ies. No signi ican beam ene gy dependence is
obse ed o he ela i e luc ua ion √Cm/M(pT)m.
The beam ene gy dependence o ela i e dynamical
mean ans e se momen um luc ua ions in pp collisions
was s udied a lowe collision ene gies by he Spli Field
Magne (SFM) de ec o a he In e sec ion S o age Rings
(ISR). The SFM expe imen measu ed ela i e luc ua-
ions in inclusi e pp collisions a √s=30.8, 45, 52,
and 63 GeV [40]. The luc ua ions a e exp essed by he
quan i y R ha is ex ac ed om he mul iplici y depen-
dence o he e en -by-e en M(pT)dispe sion. The mea-
su e R=[D(MEbE(pT)k)/M(pT)]n→∞ is ob ained om
an ex apola ion o he mul iplici y-dependen dispe sion
D(MEbE(pT)k) o in ini e mul iplici y, no malized by he
inclusi e mean ans e se momen um. I is an al e na i e
〉
η
/d
ch
Nd〈
0 1020304050
m
)
T
p(
M
/
m
C
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16 ALICE pp
= 7 TeVs
= 2.76 TeVs
= 0.9 TeVs
ALICE pp
= 7 TeVs
= 2.76 TeVs
= 0.9 TeVs
ALICE pp
= 7 TeVs
= 2.76 TeVs
= 0.9 TeVs
ALICE pp
= 7 TeVs
= 2.76 TeVs
= 0.9 TeVs
ALICE pp
= 7 TeVs
= 2.76 TeVs
= 0.9 TeVs
| < 0.8
η
|
c < 2 GeV/
T
p0.15 <
Fig. 1 Rela i e luc ua ion √Cm/M(pT)mas a unc ion o dNch/dη
in pp collisions a √s=0.9, 2.76 and 7 TeV
(GeV)s
2
10 3
10 4
10
) luc ua ions
T
p
(M
Rela i e
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
pp
)
T
p(M / CALICE:
RISR:
pp
C
ALICE:
RISR:
Fig. 2 Rela i e dynamical mean ans e se momen um luc ua ions in
ppcollisionsasa unc ion o √s.TheALICE esul s o √C/M(pT)a e
compa ed o he quan i y Rmeasu ed a he ISR (see ex and [40])
app oach o ex ac dynamical ans e se momen um luc-
ua ions in inclusi e pp collisions.
To allow o a compa ison o ISR esul s, an inclu-
si e analysis o ALICE pp da a is pe o med. The ela-
i e luc ua ion √C/M(pT)is compu ed a each collision
ene gy as in (2), howe e , wi hou subdi ision in o mul i-
plici y classes m. Mon e Ca lo s udies o pp collisions a
√s=7 TeV using PYTHIA8 ha e shown ha esul s o R
and √C/M(pT)ag ee wi hin 10–15%. The ALICE esul s
o he inclusi e √C/M(pT)as a unc ion o √sa e shown
in Fig. 2, along wi h he ISR esul s o R om [40]. No
signi ican dependence o he ela i e ans e se momen um
luc ua ionson hecollision ene gyisobse edo e his la ge
ene gy ange.
The esul s in pp a √s=7 TeV a e compa ed wi h esul s
om di e en e en gene a o s. In pa icula , PYTHIA6
123
Eu . Phys. J. C (2014) 74:3077 Page 5 o 15 3077
〉/d
ch
Nd〈
01020304050
)c (GeV/
m
〉
T
p〈
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
= 7 TeVspp:
PYTHIA6 Pe ugia-0
PHOJET
PYTHIA8.150
PYTHIA6 Pe ugia-11 de aul
PYTHIA6 Pe ugia-11 NOCR
| < 0.8
η
|
c < 2 GeV/
T
p0.15 <
η
Fig. 3 Resul s o pTmas a unc ion o dNch/dηin pp collisions
a √s=7 TeV om di e en e en gene a o s
( unes Pe ugia-0 and Pe ugia-11), PYTHIA8.150 and PHO-
JET ha e been used.
I has been poin ed ou ha high-mul iplici y e en s in pp
collisions a LHC ene gies a e d i en by mul i-pa on in e -
ac ions (MPIs) [41]. This pic u e is also sugges ed by ecen
s udies o he e en sphe ici y in pp collisions [42]. MPIs a e
independen p ocesses on he pe u ba i e le el. Howe e ,
he colo econnec ion mechanism be ween p oduced s ings
may lead o co ela ions in he had onic inal s a e. Colo
econnec ion is also he d i ing mechanism in PYTHIA o
he inc ease o pTas a unc ion o Nch [43,44].
The de aul PYTHIA6 Pe ugia-11 une including he
colo - econnec ion mechanism is compa ed o esul s o
he same une wi hou colo - econnec ion (NOCR). Fig-
u e 3shows model calcula ions o pTmas a unc ion o
dNch/dηin 0.15 <pT<2GeV/cand |η|<0.8inppcol-
lisions a √s=7 TeV. The MC gene a o s yield quali a i ely
di e en esul s o he mul iplici y dependence, in pa icula
PHOJET and he NOCR e sion o PYTHIA6 Pe ugia-11
show only li le inc ease o pTmwi h mul iplici y. Good
ag eemen be ween PYTHIA8 and ALICE esul s in pp col-
lisions a √s=7 TeV was demons a ed [44], albei in a
di e en ηand pTin e al.
Resul s o he ela i e dynamical luc ua ion measu e
√Cm/M(pT)min pp a √s=7 TeV a e compa ed o model
calcula ions in Fig. 4. The da a exhibi a clea powe -law
dependence wi h dNch/dηexcep o e y small mul i-
plici ies. A powe -law i o √Cm/M(pT)m∝dNch/dηb
in he in e al 5 <dNch/dη<30 yields b=−0.431 ±
0.001(s a .)±0.021(sys .). The de ia ion o he powe -law
index om b=−0.5 indica es ha he obse ed mul iplic-
i y dependence o M(pT) luc ua ions in pp does no ollow
a simple supe posi ion scena io, con a y o wha migh be
expec ed o independen MPIs. All PYTHIA unes unde
s udy ag ee wi h his inding o he ex en ha hey exhibi
a simila powe -law index as he da a. This is also ue o
he NOCR calcula ion which excludes he colo econnec-
ion mechanism in i s p esen implemen a ion in PYTHIA
as a dominan sou ce o co ela ions beyond he independen
supe posi ion scena io.
4 Resul s in Pb–Pb collisions
Resul s o he ela i e dynamical luc ua ion
√Cm/M(pT)min Pb–Pb collisions a √sNN =2.76 TeV
as a unc ion o dNch/dηa e shown in Fig. 5.As o
pp collisions, signi ican dynamical luc ua ions as well
〉
η
/d
ch
Nd〈
1 10
m
)
T
p(M /
m
C
0.05
0.06
0.07
0.08
0.09
0.1
0.2
= 7 TeVspp:
ALICE
PYTHIA6 Pe ugia-0
PHOJET
PYTHIA8.150
PYTHIA6 Pe ugia-11 de aul
PYTHIA6 Pe ugia-11 NOCR
| < 0.8
η
|
c < 2 GeV/
T
p0.15 <
〉
η
/d
ch
Nd〈
0 5 10 15 20 25 30 35 40
(ALICE)
m
)
T
p(M /
m
C (MC) /
m
)
T
p(M /
m
C
0.6
0.8
1
1.2
1.4
= 7 TeVs
PHOJET
PYTHIA8.150
= 7 TeVs
PHOJET
PYTHIA8.150
= 7 TeVspp:
PHOJET
PYTHIA8.150
= 7 TeVspp:
PHOJET
PYTHIA8.150
= 7 TeVspp:
PHOJET
PYTHIA8.150
= 7 TeVspp:
PYTHIA6 Pe ugia-0
PHOJET
PYTHIA8.150
PYTHIA6 Pe ugia-11 de aul
PYTHIA6 Pe ugia-11 NOCR
| < 0.8
η
|
c < 2 GeV/
T
p0.15 <
Fig. 4 Le Rela i e dynamical luc ua ion √Cm/M(pT)m o da a and di e en e en gene a o s in pp collisions a √s=7 TeV as a unc ion o
dNch/dη.Righ Ra io models o da a. The ed e o band indica es he s a is ical and sys ema ic da a unce ain ies added in quad a u e
123

3077 Page 6 o 15 Eu . Phys. J. C (2014) 74:3077
〉
η
/d
ch
Nd〈
1 10 2
10 3
10
m
)
T
p(M /
m
C
-2
10
-1
10
= 2.76 TeV
NN
s
ALICE pp
ALICE Pb-Pb
HIJING Pb-Pb
Powe -law i ALICE pp
Powe -law i HIJING
| < 0.8
η
|
c < 2 GeV/
T
p0.15 <
Fig. 5 Rela i e dynamical luc ua ion √Cm/M(pT)mas a unc ion
o dNch/dηin pp and Pb–Pb collisions a √sNN =2.76 TeV. Also
shown a e esul s om HIJING and powe -law i s o pp (solid line)and
HIJING (dashed line)(see ex )
as a s ong dec ease wi h mul iplici y a e obse ed. Also
shown in Fig. 5is he esul o a HIJING [39] simula ion
( e sion 1.36) wi hou je -quenching. A powe -law i in
he in e al 30 <dNch/dη<1500 desc ibes he HIJING
esul s e y well, excep a low mul iplici ies, and yields
b=−0.499 ±0.003(s a .)±0.005(sys .). The app oxima e
dNch/dη−0.5scaling e lec s he basic p ope y o HIJING
as a supe posi ion model o independen nucleon-nucleon
collisions. The HIJING calcula ion, in pa icula he mul-
iplici y dependence, is in ob ious disag eemen wi h he
da a.
In pe iphe al collisions dNch/dη<100, he Pb–
Pb esul s a e in e y good ag eemen wi h he ex apola-
ion o a powe -law i o pp da a a √s=2.76 TeV in
he in e al 5 <dNch/dη<25, wi h b=−0.405 ±
0.002(s a .)±0.036(sys .). This is ema kable because sig-
ni ican di e ences in pTa e obse ed be ween pp and
Pb–Pb in his mul iplici y ange [44]. A la ge mul iplic-
i ies, he Pb–Pb esul s de ia e om he pp ex apola ion.
An enhancemen in 100 <dNch/dη<500 is ollowed by
a p onounced dec ease a dNch/dη>500, co esponding
o cen ali ies <40%, which indica es a s ong educ ion o
luc ua ions owa ds cen al collisions.
Measu emen s o mean ans e se momen um luc ua-
ions in cen al A–A collisions a he SPS [13] and a
RHIC [18] a e compa ed o he ALICE esul in Fig. 6.As
in pp, he e is no signi ican dependence on √sNN obse ed
o e a wide ange o collision ene gies.
Figu e 7shows a compa ison o he ALICE esul s o
√Cm/M(pT)m o measu emen s in Au–Au collisions a
√sNN =200 GeV by he STAR expe imen a RHIC [18].
In he pe iphe al egion, he STAR da a show e y simila
(GeV)
NN
s
10 2
10 3
10
)
T
p(M /
C
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
ALICE Pb-Pb, 0-5%
STAR Au-Au, 0-5%
CERES Pb-Au, 0-6.5%
Fig. 6 Mean ans e se momen um luc ua ions in cen al hea y-ion
collisions as a unc ion o √sNN. The ALICE da a poin is compa ed
o da a om he CERES [13]andSTAR[18] expe imen s. Fo STAR
only s a is ical unce ain ies a e a ailable
scaling wi h dNch/dηas he ALICE da a, as shown on
he le panel o Fig. 7. Also shown a e he i o pp da a a
√s=2.76 TeV om Fig. 5and he esul o a powe -law
i o he STAR da a in dNch/dη<200 whe e he powe is
ixed o b=−0.405. Good ag eemen o he ALICE and
STAR da a wi h he i s is obse ed in pe iphe al collisions.
The dec ease o luc ua ions in cen al collisions is simila in
ALICE and STAR, howe e , no signi ican enhancemen in
semi-cen al e en s is obse ed in he STAR da a. In he igh
panel o Fig. 7, he esul s o √Cm/M(pT)min ALICE and
STAR a e shown as a unc ion o he mean numbe o pa ic-
ipa ing nucleons Npa . In his ep esen a ion, he measu e-
men s o √Cm/M(pT)m om ALICE and STAR a e com-
pa ible wi hin he a he la ge expe imen al unce ain ies on
Npa in STAR. A powe -law i √Cm/M(pT)m∝Npa b
o he ALICE da a in he in e al 10 <Npa <40 yields
b=−0.472 ±0.007(s a .)±0.037(sys .). The ag eemen
be weenALICEandSTARda aasa unc iono Npa poin s
o a ela ion be ween he obse ed luc ua ion pa e ns and
he collision geome y.
T ans e se momen um co ela ions and luc ua ions may
be modi ied as a consequence o collec i e low in A–A colli-
sions. I should be no ed, howe e , ha e en -a e aged adial
low and azimu hal asymme ies a e no expec ed o gi e ise
o s ong ans e se momen um luc ua ions in azimu hally
symme ic de ec o s [13,16]. On he o he hand, M(pT) luc-
ua ions may occu due o luc ua ing ini ial condi ions ha
a e also ela ed o e en -by-e en luc ua ions o adial low
and azimu hal asymme ies. We compa e ou esul s o cal-
cula ions om heAMPT model [45]which has beendemon-
s a ed ogi ea easonabledesc ip iono inclusi eande en -
a e aged bulk p ope ies in Pb–Pb collisions a LHC ene -
123
Eu . Phys. J. C (2014) 74:3077 Page 7 o 15 3077
m
)
T
p(M /
m
C
-2
10
-1
10
= 2.76 TeV
NN
sALICE, Pb-Pb:
= 0.2 TeV
NN
sSTAR, Au-Au:
-0.405
〉
η
/d
ch
Nd〈) * sFi : A (
c < 2 GeV/
T
p0.15 <
〉
η
/d
ch
Nd〈
10 2
10 3
10
Da a / Fi
0.7
0.8
0.9
1
1.1
= 2.76 TeV
NN
sALICE, Pb-Pb:
= 0.2 TeV
NN
sSTAR, Au-Au:
-0.472
〉
pa
N〈Fi : A *
c < 2 GeV/
T
p0.15 <
〉
pa
N〈
10 2
10
Fig. 7 Le Rela i e dynamical luc ua ion √Cm/M(pT)mas a unc-
ion o dNch/dηin Pb–Pb collisions a √sNN =2.76 TeV om
ALICE compa ed o esul s om STAR in Au–Au collisions a
√sNN =200 GeV [18]. Also shown as dashed lines a e esul s om
powe -law i s o he da a (see ex ). Righ same da a as a unc ion o
Npa 
〉
η
/d
ch
Nd〈
10 2
10 3
10
-0.5
〉
η
/d
ch
Nd〈 / A *
m
)
T
p(M /
m
C
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
= 2.76 TeV
NN
s
ALICE pp
ALICE Pb-Pb
HIJING
AMPT s ing mel ing
AMPT de aul
| < 0.8
η
|
c < 2 GeV/
T
p0.15 <
Fig. 8 Rela i e dynamical luc ua ion √Cm/M(pT)mno malized o
dNch/dη−0.5(see ex ) as a unc ion o dNch/dηin pp and Pb–Pb
collisions a √sNN =2.76 TeV. The ALICE da a a e compa ed o esul s
om HIJING and AMPT
gies [46,47], in pa icula o he measu ed ellip ic low coe -
icien 2. Figu e 8shows he a io o √Cm/M(pT)min da a
and models o he esul o a i o A·dNch/dη−0.5 o he
HIJING simula ion in he in e al 30 <dNch/dη<1500.
Fo dNch/dη<30, HIJING ag ees well wi h he esul s
om pp and Pb–Pb. A la ge mul iplici ies, none o he mod-
els shows quan i a i e ag eemen wi h he Pb–Pb da a. The
de aul AMPT calcula ion gi es ise o inc eased luc ua ions
on op o he unde lying HIJING scena io exceeding hose
obse ed in he da a, excep o e y pe iphe al collisions. In
con as , he AMPT calcula ion wi h s ing mel ing, whe e
pa ons a e esca e ing a e ecombined by a had onic coa-
lescence scheme, p edic s smalle luc ua ions. On he o he
hand, bo h AMPT e sions exhibi a p onounced all-o in
cen al collisions which is in quali a i e ag eemen wi h he
da a.
In a ecen app oach [24], ini ial spa ial luc ua ions o
glasma lux ubes ha e been ela ed o mean ans e se
momen um luc ua ions o inal s a e had ons ia hei cou-
pling oa collec i e low ield.Acompa ison o hesecalcula-
ions o da a om ALICE and STAR is shown in [24]. Good
ag eemen is ound in he semi-cen al and cen al egion,
whe e he da a de ia e om he pp ex apola ion.
5 Summa y and conclusions
Fi s esul s on e en -by-e en luc ua ions o he mean ans-
e se momen um o cha ged pa icles in pp and Pb–Pb col-
lisions a he LHC a e p esen ed. Exp essed in e ms o he
ela i e dynamical luc ua ion √Cm/M(pT)m, li le ene gy
dependence o he mean ans e se momen um luc ua ions
is obse ed in pp a √s=0.9, 2.76 and 7 TeV. The esul s
a e also compa ible wi h simila measu emen s a he ISR.
Fo he i s ime, mean ans e se momen um luc ua ions
in pp a e s udied as a unc ion o dNch/dη. A cha ac e -
is ic dec ease o √Cm/M(pT)m ollowing a powe law is
obse ed.The dec easeisweake hanexpec ed omasupe -
posi ion o independen sou ces. The na u e o such sou ces
in pp is subjec o u u e s udies, bu a connec ion o he con-
123
3077 Page 8 o 15 Eu . Phys. J. C (2014) 74:3077
cep o mul i-pa on in e ac ions is sugges i e. Model s udies
using PYTHIA howe e indica e ha he e is no s ong sensi-
i i y o ans e se momen um luc ua ions o he mechanism
o colo econnec ion.
In pe iphe al Pb–Pb collisions dNch/dη<100, he
dependence o √Cm/M(pT)mon dNch/dηis e y simila
o ha obse ed in pp collisions a he co esponding colli-
sion ene gy. A la ge mul iplici ies, he Pb–Pb da a de ia e
signi ican ly om an ex apola ion o pp esul s and show
a s ong dec ease o dNch/dη>500. The esul s o he
mos cen al collisions a e o he same magni ude as p e ious
measu emen s a he SPS and a RHIC. The cen ali y depen-
dence o √Cm/M(pT)mis compa ible wi h ha obse ed in
Au–Au a √sNN =200 GeV.
The Pb–Pb da a can no be desc ibed by models based
on independen nucleon-nucleon collisions such as HIJING.
Models which include ini ial s a e densi y luc ua ions and
hei e ec on he de elopmen o collec i i y in he inal
s a e a e in quali a i e ag eemen wi h he da a. This sugges s
a connec ion be ween he obse ed luc ua ions o ans e se
momen um and azimu hal co ela ions, and hei ela ion o
luc ua ions in he ini ial s a e o he collision.
Acknowledgmen s The ALICE Collabo a ion would like o hank
all i s enginee s and echnicians o hei in aluable con ibu ions o he
cons uc ion o he expe imen and he CERN accele a o eams o he
ou s anding pe o mance o he LHC complex. The ALICE Collabo a-
ion g a e ully acknowledges he esou ces and suppo p o ided by all
G id cen es and he Wo ldwide LHC Compu ing G id (WLCG) collab-
o a ion. The ALICE Collabo a ion acknowledges he ollowing unding
agencies o hei suppo in building and unning he ALICE de ec-
o : S a e Commi ee o Science, Wo ld Fede a ion o Scien is s (WFS)
and Swiss Fonds Kidagan, A menia, Conselho Nacional de Desen ol i-
men oCien í ico eTecnológico(CNPq),Financiado a deEs udos e P o-
je os (FINEP), Fundação de Ampa o à Pesquisa do Es ado de São Paulo
(FAPESP); Na ional Na u al Science Founda ion o China (NSFC), he
ChineseMinis yo Educa ion(CMOE)and heMinis yo Scienceand
Technology o China (MSTC); Minis y o Educa ion and You h o he
Czech Republic; Danish Na u al Science Resea ch Council, he Ca ls-
be g Founda ion and he Danish Na ional Resea ch Founda ion; The
Eu opean Resea ch Council unde he Eu opean Communi y’s Se en h
F amewo k P og amme; Helsinki Ins i u e o Physics and he Academy
o Finland; F ench CNRS-IN2P3, he ‘Region Pays de Loi e’, ‘Region
Alsace’, ‘Region Au e gne’ and CEA, F ance; Ge man BMBF and he
Helmhol z Associa ion; Gene al Sec e a ia o Resea ch and Technol-
ogy, Minis y o De elopmen , G eece; Hunga ian OTKA and Na ional
O ice o Resea ch and Technology (NKTH); Depa men o A omic
Ene gy and Depa men o Science and Technology o he Go e n-
men o India; Is i u o Nazionale di Fisica Nuclea e (INFN) and Cen o
Fe mi - Museo S o ico della Fisica e Cen o S udi e Rice che “En ico
Fe mi”, I aly; MEXT G an -in-Aid o Specially P omo ed Resea ch,
Japan; Join Ins i u e o Nuclea Resea ch, Dubna; Na ional Resea ch
Founda ion o Ko ea (NRF); CONACYT, DGAPA, México, ALFA-EC
and he EPLANET P og am (Eu opean Pa icle Physics La in Ame -
ican Ne wo k) S ich ing oo Fundamen eel Onde zoek de Ma e ie
(FOM) and he Nede landse O ganisa ie oo We enschappelijk Onde -
zoek (NWO), Ne he lands; Resea ch Council o No way (NFR); Polish
Minis y o Science and Highe Educa ion; Na ional Science Cen e,
Poland; Minis y o Na ional Educa ion/Ins i u e o A omic Physics
and CNCS-UEFISCDI-Romania; Minis y o Educa ion and Science
o Russian Fede a ion, Russian Academy o Sciences, Russian Fed-
e al Agency o A omic Ene gy, Russian Fede al Agency o Science
and Inno a ions and The Russian Founda ion o Basic Resea ch; Min-
is y o Educa ion o Slo akia; Depa men o Science and Technology,
Sou h A ica; CIEMAT, EELA, Minis e io de Economía y Compe i i i-
dad (MINECO) o Spain, Xun a de Galicia (Conselle ía de Educación),
CEADEN,Cubaene gía,Cuba,andIAEA(In e na ionalA omicEne gy
Agency); Swedish Resea ch Council (VR) and Knu & Alice Wallen-
be g Founda ion (KAW); Uk aine Minis y o Educa ion and Science;
Uni ed Kingdom Science and Technology Facili ies Council (STFC);
The Uni ed S a es Depa men o Ene gy, he Uni ed S a es Na ional
Science Founda ion, he S a e o Texas, and he S a e o Ohio; Min-
is y o Science, Educa ion and Spo s o C oa ia and Uni y h ough
Knowledge Fund, C oa ia.
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Re e ences
1. S. Jeon, V. Koch, E en by e en luc ua ions.
a Xi :hep-ph/0304012 [hep-ph]
2. S. M owczynski, Plasma ins abili y a he ini ial s age o ul a el-
a i is ic hea y ion collisions. Phys. Le . B 314, 118–121 (1993)
3. L. S odolsky, Tempe a u e luc ua ions in mul ipa icle p oduc ion.
Phys.Re .Le .75, 1044–1045 (1995)
4. E.V. Shu yak, E en pe e en analysis o hea y ion collisions
and he modynamical luc ua ions. Phys. Le . B 423, 9–14 (1998).
a Xi :hep-ph/9704456 [hep-ph]
5. M.A. S ephano , K. Rajagopal, E.V. Shu yak, Signa u es o he
ic i ical poin in QCD. Phys. Re . Le . 81, 4816–4819 (1998).
a Xi :hep-ph/9806219 [hep-ph]
6. M.A. S ephano , K. Rajagopal, E.V. Shu yak, E en -by-e en luc-
ua ions in hea y ion collisions and he QCD c i ical poin . Phys.
Re . D 60, 114028 (1999). a Xi :hep-ph/9903292 [hep-ph]
7. H. Heiselbe g, E en -by-e en physics in ela i is ic hea y ion col-
lisions. Phys. Rep . 351, 161–194 (2001). a Xi :nucl- h/0003046
[nucl- h]
8. A. Dumi u, R.D. Pisa ski, E en -by-e en luc ua ions om decay
o a Polyako loop condensa e. Phys. Le . B 504, 282–290 (2001).
a Xi :hep-ph/0010083 [hep-ph]
9. Z. Fodo , S. Ka z, C i ical poin o QCD a ini e T and mu, la -
ice esul s o physical qua k masses. JHEP 0404, 050 (2004).
a Xi :hep-la /0402006 [hep-la ]
10. NA49 Collabo a ion, H. Appelshäuse e al., E en -by-e en luc-
ua ions o a e age ans e se momen um in cen al Pb + Pb colli-
sions a 158 GeV pe nucleon, Phys. Le . B 459, 679–686 (1999).
a Xi :hep-ex/9904014 [hep-ex]
11. CERES Collabo a ion, D. Adamo á e al., E en by e en luc-
ua ions o he mean ans e se momen um in 40, 80 and 158 A
GeV / c Pb–Au collisions, Nucl. Phys. A 727, 97–119 (2003).
a Xi :nucl-ex/0305002 [nucl-ex]
12. NA49 Collabo a ion, T. An icic e al., T ans e se momen um luc-
ua ions in nuclea collisions a 158-A GeV. Phys. Re . C70,
034902 (2004). a Xi :hep-ex/0311009 [hep-ex]
13. CERES Collabo a ion, D. Adamo á e al., Scale-dependence o
ans e se momen um co ela ions in Pb-Au collisions a 158A
GeV/c, Nucl. Phys. A 811, 179–196 (2008). a Xi :0803.2407
[nucl-ex].
123
Eu . Phys. J. C (2014) 74:3077 Page 9 o 15 3077
14. NA49 Collabo a ion, T. An icic e al., Ene gy dependence o ans-
e se momen um luc ua ions in Pb+Pb collisions a he CERN
Supe P o on Synch o on (SPS) a 20A o 158A GeV. Phys. Re .
C79, 044904 (2009). a Xi :0810.5580 [nucl-ex]
15. PHENIX Collabo a ion, K. Adcox e al., E en -by-e en luc u-
a ions in mean p(T) and mean e(T) in √sNN = 130 GeV Au+Au
collisions,Phys.Re . C 66,024901 (2002).a Xi :nucl-ex/0203015
[nucl-ex]
16. PHENIX Collabo a ion, S. Adle e al., Measu emen o non an-
dom e en by e en luc ua ions o a e age ans e se momen um
in √sNN = 200 GeV Au+Au and p+p collisions, Phys. Re . Le .
93 092301 (2004). a Xi :nucl-ex/0310005 [nucl-ex]
17. STAR Collabo a ion, J. Adams e al., E en by e en mean-p( )
luc ua ions in Au-Au collisions a √sNN = 130 GeV, Phys. Re .
C71 064906 (2005). a Xi :nucl-ex/0308033 [nucl-ex]
18. STAR Collabo a ion, J. Adams e al., Inciden ene gy dependence
o p co ela ions a RHIC, Phys. Re . C 72, 044902 (2005).
a Xi :nucl-ex/0504031 [nucl-ex]
19. STAR Collabo a ion, J. Adams e al., T ans e se-momen um p( )
co ela ions on (e a, phi) om mean-p( ) luc ua ions in Au-Au
collisions a √sNN = 200 GeV, J. Phys. G 32, L37–L48 (2006).
a Xi :nucl-ex/0509030 [nucl-ex]
20. STAR Collabo a ion, J. Adams e al., The Ene gy dependence o
p angula co ela ions in e ed om mean-p( ) luc ua ion scale
dependence in hea y ion collisions a he SPS and RHIC, J. Phys.
G34, 451–466 (2007). a Xi :nucl-ex/0605021 [nucl-ex]
21. E. Fe ei o, F. del Mo al, C. Paja es, T ans e se momen um luc u-
a ions and pe cola ion o s ings. Phys. Re . C 69, 034901 (2004).
a Xi :hep-ph/0303137 [hep-ph]
22. S.A. Voloshin, T ans e se adial expansion in nuclea collisions
and wo pa icle co ela ions, Phys. Le . B 632, 490–494 (2006).
a Xi :nucl- h/0312065 [nucl- h]
23. S. Ga in, T aces o The maliza ion om p Fluc ua ions
in Nuclea Collisions. Phys. Re . Le . 92, 162301 (2004).
a Xi :nucl- h/0308067 [nucl- h]
24. S. Ga in, G. Moschelli, Fluc ua ion p obes o ea ly- ime co e-
la ions in nuclea collisions. Phys. Re . C 85, 014905 (2012).
a Xi :1107.3317 [nucl- h]
25. S. Ga in, G. Moschelli, Flow Fluc ua ions om Ea ly-Time Co -
ela ions in Nuclea Collisions. Phys. Re . C86, 034902 (2012).
a Xi :1205.1218 [nucl- h]
26. B. Al e , G. Roland, Collision geome y luc ua ions and iangu-
la low in hea y-ion collisions. Phys. Re . C 81, 054905 (2010).
a Xi :1003.0194 [nucl- h]. E a um: Phys. Re . C 82, 039903
(2010)
27. L. E ans, P. B yan , LHC machine. JINST 3, S08001 (2008)
28. ALICE Collabo a ion, K. Aamod e al., The ALICE expe imen
a he CERN LHC, JINST 3, S08002 (2008)
29. J. Alme e al., The ALICE TPC, a la ge 3-dimensional ack-
ing de ice wi h as eadou o ul a-high mul iplici y e en s.
Nucl. Ins um. Me h. A 622, 316–367 (2010). a Xi :1001.1950
[physics.ins-de ]
30. ALICE Collabo a ion, K. Aamod e al., Cen ali y dependence o
he cha ged-pa icle mul iplici y densi y a mid- apidi y in Pb-Pb
collisions a √sNN =2.76 TeV, Phys. Re . Le . 106, 032301
(2011). a Xi :1012.1657 [nucl-ex]
31. ALICE Collabo a ion, B. Abele e al., Cen ali y de e mina ion
o Pb-Pb collisions a √sNN = 2.76 TeV wi h ALICE, Phys. Re .
C88(4), 044909 (2013). a Xi :1301.4361 [nucl-ex]
32. S. Voloshin, V. Koch, H. Ri e , E en -by-e en luc ua ions
in collec i e quan i ies. Phys. Re . C 60, 024901 (1999).
a Xi :nucl- h/9903060 [nucl- h]
33. ALICE Collabo a ion, K. Aamod e al., Cha ged-pa icle mul i-
plici y measu emen in p o on-p o on collisions a √s=0.9and
2.36 TeV wi h ALICE a LHC, Eu . Phys. J. C 68, 89–108 (2010).
a Xi :1004.3034 [hep-ex]
34. R. B un, F. Ca mina i, S. Giani, GEANT De ec o Desc ip ion and
Simula ion Tool, CERN-W5013 (1994)
35. R. B un, P. Buncic, F. Ca mina i, A. Mo sch, F. Rademake s e
al., Compu ing in ALICE. Nucl. Ins um. Me h. A 502, 339–346
(2003)
36. T. Sjos and, S. M enna, P.Z. Skands, PYTHIA 6.4 Physics and
Manual, JHEP 05, 026 (2006). a Xi :hep-ph/0603175 [hep-ph]
37. P.Z. Skands, Tuning Mon e Ca lo Gene a o s: The Pe ugia Tunes.
Phys. Re . D82, 074018 (2010). a Xi :1005.3457 [hep-ph]
38. R. Engel, J. Ran , S. Roesle , Ha d di ac ion in had on had on
in e ac ions and in pho op oduc ion, Phys. Re . D 52, 1459–1468
(1995). a Xi :hep-ph/9502319 [hep-ph]
39. W.-T. Deng, X.-N. Wang, R. Xu, Gluon shadowing and had on
p oduc ion in hea y-ion collisions a LHC, Phys. Le . B 701, 133–
136 (2011). a Xi :1011.5907 [nucl- h]
40. CERN-Do mund-Heidelbe g-Wa saw-Ames-Bologna, CERN-
Heidelbe g-Lund Collabo a ion, K. B aune e al., Fluc ua ions in
he Had onic Tempe a u e in pp, pαand αα Collisions a ISR
Ene gies, Phys. Le . B 123 467 (1983)
41. P. Ba alini, E. Be ge , B. Blok, G. Calucci, R. Co ke, e al., Mul i-
pa on in e ac ions a he LHC. a Xi :1111.0469 [hep-ph]
42. ALICE Collabo a ion, B. Abele e al., T ans e se sphe ici y o
p ima y cha ged pa icles in minimum bias p o on-p o on colli-
sions a √s=0.9, 2.76 and 7 TeV, Eu . Phys. J. C 72 2124 (2012).
a Xi :1205.3963 [hep-ex]
43. T. Sjos and, Colou econnec ion and i s e ec s on p ecise mea-
su emen s a he LHC. a Xi :1310.8073 [hep-ph]
44. ALICE Collabo a ion, B. Abele e al., Mul iplici y dependence o
he a e age ans e se momen um in pp, p-Pb, and Pb-Pb collisions
a he LHC. Phys. Le . B 727, 371–380 (2013). a Xi :1307.1094
[nucl-ex]
45. Z.-W. Lin, C.M. Ko, B.-A. Li, B. Zhang, S. Pal, Mul iphase ans-
po model o ela i is ic hea y ion collisions. Phys. Re . C 72,
064901 (2005). a Xi :nucl- h/0411110 [nucl- h]
46. J. Xu, C.M. Ko, T iangula low in hea y ion collisions in a
mul iphase anspo model. Phys. Re . C 84, 014903 (2011).
a Xi :1103.5187 [nucl- h]
47. J. Xu, C.M. Ko, Highe -o de aniso opic lows and dihad on co -
ela ions in Pb-Pb collisions a √sNN =2.76 TeV in a mul iphase
anspo model. Phys. Re . C 84, 044907 (2011). a Xi :1108.0717
[nucl- h]
123