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Di ec pho on p oduc ion a low ans e se momen um in p o on-p o on collisions a √s
= 2.76 and 8 TeV
Published e sion
ALICE Collabo a ion
ALICE Collabo a ion. (2019). Di ec pho on p oduc ion a low ans e se momen um in p o on-
p o on collisions a √s = 2.76 and 8 TeV. Physical Re iew C, 99(2), A icle 024912.
h ps://doi.o g/10.1103/PhysRe C.99.024912
2019
PHYSICAL REVIEW C 99, 024912 (2019)
Di ec pho on p oduc ion a low ans e se momen um in p o on-p o on
collisions a √s=2.76 and 8 TeV
S. Acha ya e al.∗
(ALICE Collabo a ion)
(Recei ed 30 Ma ch 2018; published 21 Feb ua y 2019)
Measu emen s o inclusi e and di ec pho on p oduc ion a mid apidi y in pp collisions a √s=2.76 and
8 TeV a e p esen ed by he ALICE expe imen a he LHC. The esul s a e epo ed in ans e se momen um
anges o 0.4<pT<10 GeV/cand 0.3<pT<16 GeV/c, espec i ely. Pho ons a e de ec ed wi h he
elec omagne ic calo ime e (EMCal) and ia econs uc ion o e+e−pai s om con e sions in he ALICE
de ec o ma e ial using he cen al acking sys em. Fo he inal measu emen o he inclusi e pho on spec a
he esul s a e combined in he o e lapping pTin e al o bo h me hods. Di ec pho on spec a, o hei uppe
limi s a 90% C.L. a e ex ac ed using he di ec pho on excess a io Rγ, which quan i ies he a io o inclusi e
pho ons o e decay pho ons gene a ed wi h a decay-pho on simula ion. An addi ional hyb id me hod, combining
pho ons econs uc ed om con e sions wi h hose iden i ied in he EMCal, is used o he combina ion o he
di ec pho on excess a io Rγ, as well as he ex ac ion o di ec pho on spec a o hei uppe limi s. While no
signi ican signal o di ec pho ons is seen o e he ull pT ange, Rγ o pT>7 GeV/cis a leas one σabo e
uni y and consis en wi h expec a ions om nex - o-leading o de pQCD calcula ions.
DOI: 10.1103/PhysRe C.99.024912
I. INTRODUCTION
Majo expe imen al e o s a e unde aken a he Rela i is-
ic Hea y Ion Collide (RHIC) [1–4] and he La ge Had on
Collide (LHC) [5–13] o s udy he condi ions o he c e-
a ion and he p ope ies o he qua k-gluon plasma (QGP),
a decon ined pa onic s a e p edic ed by he heo y o s ong
in e ac ion, quan um ch omodynamics (QCD) [14,15]. Di ec
pho ons, which a e de ined as all pho ons ha a e p oduced
di ec ly in sca e ing p ocesses and he e o e do no o igina e
om had onic decays, a e a powe ul ool o explo ing he
QGP. They a e p oduced du ing all s ages o he collision and
a e basically una ec ed by inal-s a e in e ac ions as hey only
pa icipa e in elec omagne ic in e ac ions [16]. Hence, hey
a e sensi i e o he ea ly s ages o he collision’s e olu ion.
Since a a ie y o QGP signa u es a e also p esen in high mul-
iplici y p-Pb o pp collision a he LHC [17], i is in e es ing
o s udy i a di ec pho on signal a low pTcan be obse ed
al eady in minimum bias pp collisions, as p edic ed o √s=
7TeV[18]. Expe imen ally, howe e , he main challenge o
di ec pho on measu emen s is o dis inguish hem om he
la ge backg ound o decay pho ons.
Depending on hei p oduc ion mechanism, di ec pho ons
a e usually classi ied in o wo main ca ego ies: p omp and
he mal pho ons. P omp pho ons ca y in o ma ion abou
∗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.
pa on dis ibu ions in nuclei [19,20] as hey a e p oduced
in ha d sca e ings o incoming pa ons, such as Comp on
sca e ing q+g→q+γo annihila ion q+q→g+γ,as
well as b emss ahlung emission om qua ks, which unde go
a ha d sca e ing [21–23]. These p ocesses a e desc ibed by
pe u ba i e QCD (pQCD) in leading and nex - o-leading o -
de , which a e dominan a LHC ene gies. One o he pu poses
o di ec pho on measu emen s is o imp o e he accu acy o
such calcula ions in a ious collision sys ems. A RHIC a
cen e o mass ene gies pe nucleon-nucleon pai o √sNN =
0.2 TeV and a he LHC a √sNN =2.76 TeV, di ec pho ons
wi h ans e se momen a (pT) abo e abou 3 and 15 GeV/c,
espec i ely, we e ound o be domina ed by p omp pho ons
and o ollow a powe -law spec al shape in small sys ems (pp,
pA,dA)[24–27] as well as in hea y-ion collisions [27–30], as
desc ibed by pQCD.
In hea y-ion collisions, addi ionally, he mal pho ons a e
expec ed o be adia ed o he locally he malized, ho QGP
and had onic ma e , which p o ide in o ma ion abou he
empe a u e, collec i e expansion, as well as he space- ime
e olu ion o he medium [31], and a e expec ed o domi-
na e he di ec pho on spec um a low ans e se momen a
(pT3GeV/c)[32,33]. Fu he di ec pho on p oduc ion
mechanisms, such as in e ac ions o ha d sca e ed pa ons
wi h dense pa onic ma e (je -pho on con e sion) [21,22], as
well as p oduc ion o pho ons om nonequilib a ed phases
[34], may also play a ole in he low and in e media e pT
egion om 3 o ∼10 GeV/c.
In he ollowing, we p esen i s esul s om he mea-
su emen o di ec pho on p oduc ion a mid apidi y in 0.4<
pT<10 GeV/cand 0.3<pT<16 GeV/cin ppcollisions a
√s=2.76 and 8 TeV, espec i ely. These da a, which a e he
i s di ec pho on da a below 15 GeV/cin ppcollisions a he
2469-9985/2019/99(2)/024912(19) 024912-1 ©2019 CERN, o he ALICE Collabo a ion
S. ACHARYA e al. PHYSICAL REVIEW C 99, 024912 (2019)
LHC, enable pQCD calcula ions o be es ed in his low pT
egime. Fu he mo e, hey p o ide an impo an baseline o
he in e p e a ion o ini ial- and inal-s a e e ec s obse ed in
di ec pho on da a om hea y-ion collisions [35,36], because
e en gene a o s and pe u ba i e calcula ions a e gene ally
no eliable a pT3.
The di ec pho on yield is ex ac ed by compa ing he mea-
su ed inclusi e pho on spec um o he spec um o pho ons
om had on decays ia a double a io, ob ained om he
so-called di ec pho on excess a io Rγ[37,38]. The double
a io, de ined on he le el o ully co ec ed quan i ies, can be
w i en as
Rγ=Yγincl
Yγdecay ≈Yγincl
Yπ0measYγdecay
Yπ0sim
,(1)
whe e he nume a o deno es he measu ed inclusi e pho on
yield, Yγincl , di ided by he measu ed neu al pion yield, Yπ0,
and he denomina o is cons uc ed in he same way, bu wi h
he pho on yield ob ained by a decay-pho on simula ion and a
pa ame iza ion o he neu al pion yield. Wi h Rγ, he di ec
pho on yield can hen be ob ained om he inclusi e pho on
yield as
Yγdi =Yγincl −Yγdecay =1−1
RγYγincl .(2)
The yields in Eqs. (1) and (2) a e implici ly de ined a
mid apid y as a unc ion o pTo he co esponding pa icle.
The c oss sec ions can be ob ained by eplacing he inclusi e
pho on yield wi h he inclusi e pho on c oss sec ion in Eq. (2).
The ad an age o using Rγ( a he han ying o di ec ly
quan i y he di e ence o inclusi e and decay pho ons) is he
pa ial o ull cancella ion o se e al sys ema ic unce ain ies
in he double a io. The pho on econs uc ion is pe o med
independen ly using ei he con e sions in he inne de ec o
ma e ial econs uc ed wi h he cen al acking sys em and o
he i s ime wi h he Elec omagne ic Calo ime e (EMCal).
Combined inclusi e and di ec pho on spec a a e de e mined
based on he indi idual inclusi e pho on spec a and di ec
pho on excess a ios. The di ec pho on spec a, o espec-
i ely hei uppe limi s a 90% C.L., a e inally compa ed o
nex - o-leading o de pQCD calcula ions.
The pape is s uc u ed as ollows. Sec ion II desc ibes he
pho on-decay simula ion a gene a o le el, usually known as
cock ail simula ion. Sec ion III desc ibes he ele an ALICE
de ec o s o he pho on and neu al meson measu emen s, he
da a aking condi ions, and he e en selec ion. Sec ion IV
desc ibes he da a analysis wi h emphasis on he pho on econ-
s uc ion ia he Pho on Con e sion Me hod (PCM) and using
he EMCal. The sys ema ic unce ain ies a e summa ized in
Sec. V, whe eas Sec. VI p esen s he esul s. Sec ion VII
concludes wi h a sho summa y.
II. GENERATOR-LEVEL DECAY-PHOTON SIMULATION
The decay-pho on spec a a e ob ained by a pa icle de-
cay simula ion, also called cock ail simula ion, needed o
he seconda y decay-pho on co ec ion as well as o he
calcula ion o Rγ. The decay simula ion is based on he
PYTHIA6.4 pa icle decaye [43] wi h andom gene a ion o
mo he pa icles uni o m in azimu h and pT. Pa ame iza ions
o he ans e se momen um spec a o he mo he pa icles
measu ed by ALICE a e used as weigh s in o de o ob ain he
co ec abundances.
Fo he √s=2.76 TeV cock ail, measu ed pTdi e en ial
yields pe inelas ic e en o π0[39], K±,p[40], φ[41], and
ρ0[42], as well as he η/π0[39] a io a e pa ame ized as
inpu s, and a e shown in he le panel o Fig. 1. Neu al kaons,
which cons i u e an impo an backg ound o seconda y de-
cay pho ons, a e app oxima ed by he a e age o he cha ged
kaon yields. The pa icle decay simula ion o √s=8TeV
uses measu ed pTdi e en ial yields om π0and η[44]as
inpu . Fu he mo e, pTdi e en ial yields o K±,φ, and p
a e ex apola ed using he measu ed spec a a √s=2.76
and 7 TeV [45–47] as inpu s. The ex apola ion is done on a
bin-by-bin basis in pTassuming a powe -law e olu ion o he
pa icle yields wi h inc easing cen e -o -mass ene gy. Fo he
pa ame iza ion, he pTdi e en ial pa icle yields a e i ed
wi h a modi ied Hagedo n unc ion [48,49] whose unc ional
o m is gi en by
d2N
dydpT=pT·A·exp apT+bp2
T+pT
p0−n
.(3)
In o de o ob ain a s able pa ame iza ion o he ηpa icle
yields up o high pT, heη/π0 a ios a √s=2.76 and
8 TeV a e i ed wi h an empi ical unc ion ha desc ibes
con ibu ions om so and ha d p ocesses [49], gi en as
η
π0(pT)=
A·exp βpT−mη
T
T√1−β2+N·B·1+pT
p02−n
exp βpT−mπ0
T
T√1−β2+B·1+pT
p02−n,
(4)
wi h a ela i e no maliza ion ac o Bbe ween he so and
ha d pa o he pa ame iza ion and he cons an a io alue
Nbe ween he wo pa icle species ha is app oached a high
pT. All spec a a e desc ibed by hei pa ame iza ion wi hin a
maximum o 10% de ia ion o e he ull ans e se momen-
um ange. Fo pa icles ha a e nei he measu ed no ex ap-
ola ed, he pa ame iza ion is ob ained ia ans e se mass
scaling, mT=√p2
T+m2
0, wi h he neu al pion as basis (B)
o mesons and he p o on as basis o ba yons. The mTscaling
ac o s, CX
mT=(dNX/dmT)/(dNB/dmT), o each pa icle X
a e de i ed om he espec i e spec a in PYTHIA. These
pa icles a e η(CmT=0.4), (CmT=1.0), 0(CmT=0.49),
0,+(CmT=1.0), and ω(CmT=0.85) a √s=2.76 TeV and
addi ionally ρ0(CmT=1.0) a √s=8 TeV. The limi a ions
o ans e se mass scaling [49]a lowpTcan be neglec ed
o his measu emen as he ans e se mass scaled pa icles
con ibu e only a iny ac ion o he o al decay-pho on yield
as seen in Fig. 1.
Fo he pa icle decay simula ion, pa icles a e gene a ed
uni o mly in he ans e se momen um ange o 0 ⩽pT⩽
50 GeV/c, o he apidi y ange o |y|<1.0aswellas he ull
azimu h o 0 <φ<2π. Fo each pa icle, he ull decay chain
is simula ed, which allows he decay simula ion o be used
o he seconda y pho on co ec ion o pho ons p oduced
ollowing weak decays o p ima y had ons as well as he
024912-2
DIRECT PHOTON PRODUCTION AT LOW TRANSVERSE … PHYSICAL REVIEW C 99, 024912 (2019)
)c (GeV/
T
p
1 10
decay
γ /
sou ce
γ
6−
10
5−
10
4−
10
3−
10
2−
10
1−
10
1
10
0
π η ω ’η0
ρ±
ρ
φ0
ΣS
0
KL
0
KΛ0/+
Δ
ALICE simula ion = 2.76 TeVspp,
omγ
(b)
)c (GeV/
T
p
1 10
)
-1
)c ((GeV/
yd
T
pd
2
Nd
inel
N
1
9−
10
8−
10
7−
10
6−
10
5−
10
4−
10
3−
10
2−
10
1−
10
1mod. Hagedo n i
0
π η
)/2
-
π+
+
π( )/2
-
+K
+
(K
)/2p(p+ φ
0*
K0
ρ
= 2.76 TeVsALICE, pp,
(a)
FIG. 1. (a) Measu ed iden i ied pa icle yields pe inelas ic e en in pp collisions a √s=2.76 TeV [39–42] including hei modi ied
Hagedo n pa ame iza ion used as inpu o he cock ail simula ion. S a is ical unce ain ies a e shown wi h e ical lines and sys ema ic
unce ain ies wi h boxes. See he ex o e e ences o he da a. (b) Ra io o p ima y decay pho ons om di e en sou ces o all p ima y decay
pho ons in he decay-pho on simula ion o pp collisions a √s=2.76 TeV. F om op o bo om a high pT he di e en sou ces a e π0,η,ω,
η,ρ0,φ,K
0
L,ρ±,K
0
S,0/+,0,and.
ex ac ion o he decay-pho on spec um. A e gene a ion,
only decay pho ons a e kep , which ul ill |y|<0.9, o ma ch
he had on apidi y ange ha is used in he measu emen s.
Fu he mo e, he mo he pa icles as well as all decay p oduc s
a e weigh ed wi h he pa ame iza ion o he mo he pa icle.
The con ibu ion o each indi idual decay-pho on sou ce o
all decay pho ons o he cock ail simula ion is shown in he
igh panel o Fig. 1. Decay pho ons o igina ing om π0
decays a e he dominan con ibu ion wi h ∼86% o o al
decay pho ons a high pT. Con ibu ions om he ηmeson
decay pho ons ep esen ∼10% whe eas decay pho ons om
ωand ηmesons con ibu e below 3% and 1.5%, espec i ely.
All o he emaining sou ces a e basically negligible as shown
in Fig. 1.
III. EXPERIMENTAL SETUP AND DATA
TAKING CONDITIONS
Two di e en me hods using independen de ec o sys ems
o ALICE [50] a e employed o measu e pho ons in his
analysis. In he i s me hod, PCM, pho ons a e econs uc ed
om e+e−pai s, which a e c ea ed by pho on con e sions in
he inne de ec o ma e ial. The inne ma e ial includes he
ull ac i e and passi e ma e ial o he beam pipe, he Inne
T acking Sys em (ITS), as well as he inne ield cage essel o
he Time P ojec ion Chambe (TPC) and pa o he TPC gas.
The main acking sys ems in ALICE a mid apidi y, he ITS
and he TPC, a e used o he econs uc ion o hese elec on-
posi on pai s, which o igina e om seconda y e ices (V0).
In he second pho on econs uc ion me hod, EMC, he ene gy
deposi in he EMCal is used o measu e pho ons. Wi h PCM,
a high momen um esolu ion a low pTis achie ed, bu he
me hod is limi ed by s a is ics a high ans e se momen a.
The EMC me hod bene i s om la ge s a is ics up o high pT
bu has a dec easing esolu ion owa ds low pT. The necessa y
de ec o sys ems a e desc ibed in he ollowing wi h emphasis
on he de ec o con igu a ions in bo h pp da a aking pe iods
o √s=2.76 TeV in 2011 and √s=8 TeV in 2012.
The ITS [51] consis s o h ee subde ec o s each wi h wo
laye s o measu e he ajec o ies o cha ged pa icles and
o econs uc p ima y [52] and seconda y e ices [53]. The
wo inne mos laye s a e he Silicon Pixel De ec o s (SPD)
posi ioned a adial dis ances o 3.9 cm and 7.6 cm ela i e
o he beam line, ollowed by wo laye s o he Silicon D i
De ec o s (SDD) a 15.0 cm and 23.9 cm, and comple ed by
wo laye s o he Silicon S ip De ec o s (SSD) a 38 cm and
43 cm. The wo laye s o SPD co e pseudo apidi y anges o
|η|<2 and |η|<1.4, espec i ely. The SDD and SSD co e
|η|<0.9 and |η|<1.0, acco dingly.
The TPC [54]isala ge(90m
3) cylind ical d i de ec o
illed wi h Ne-CO2(90%–10%) gas mix u e. I co e s a pseu-
do apidi y ange o |η|<0.9 o e he ull azimu h, p o iding
up o 159 econs uc ed space poin s pe ack. A magne ic
ield o B=0.5 T is gene a ed by a la ge solenoidal magne
su ounding he cen al ba el de ec o s. Cha ged acks o ig-
ina ing om he p ima y e ex can be econs uc ed down
o pT≈100 MeV/cand cha ged seconda ies down o pT≈
50 MeV/cwi h a acking e iciency o ≈80% o acks wi h
024912-3
S. ACHARYA e al. PHYSICAL REVIEW C 99, 024912 (2019)
pT>1GeV/c[55]. In addi ion, he TPC p o ides pa icle
iden i ica ion ia he measu emen o ene gy loss dE/dx wi h
a esolu ion o ≈5%. The ITS and TPC a e complemen ed
by he T ansi ion Radia ion De ec o (TRD) [56] and he
Time-O -Fligh (TOF) [57] de ec o .
The EMCal de ec o [58] is an elec omagne ic sampling
calo ime e co e ing φ =100◦in azimu h and |η|<0.7in
pseudo apidi y, loca ed a a adial dis ance o 4.28 m om
he nominal collision e ex. Du ing he da a aking pe iods
in 2011 and 2012, i consis ed o a o al o 11520 ac i e
elemen s, o cells, each o which comp ise 77 al e na ing
laye s o lead and plas ic scin illa o p o iding a adia ion
leng h o 20.1X0. A ached pe pendicula o he ace o each
cell a e wa eleng h shi ing ibe s ha collec he scin illa ion
ligh in each laye . A alanche pho o diodes (APDs) wi h
an ac i e a ea o 5 ×5mm
2a e connec ed o he ib es
o de ec he gene a ed scin illa ion ligh . The size o each
cell is η ×φ =0.0143 ×0.0143 ad (≈6.0×6.0cm
2),
co esponding o app oxima ely wice he Moliè e adius. The
EMCal consis s o en supe modules, whe e each supe mod-
ule is composed o 12 ×24 modules, consis ing o 2 ×2
cells apiece. I has an in insic ene gy esolu ion o σE/E=
4.8%/E⊕11.3%/√E⊕1.7% whe e he ene gy Eis gi en
in uni s o GeV [59]. The ene gy calib a ion o he de ec o
is pe o med by measu ing, in each cell, he econs uc ed
π0mass in he wo-pho on in a ian mass dis ibu ion wi h
one pho on associa ed wi h he gi en cell. An es ima ed
calib a ion le el o be e han 3% is achie ed wi h his
me hod, which adds up quad a ically o he cons an e m o
he ene gy esolu ion. Be ween 2011 and 2012 an addi ional
TRD module in on o EMCal was ins alled, which esul s
in a sligh ly di e en ou e ma e ial budge be ween he 2.76
and 8 TeV da a se s. The ma e ial budge di e ences due o
he TRD will be s udied in de ail o he es ima ion o he
associa ed sys ema ic unce ain ies.
As igge o minimum bias pp collisions and o educe
beam-induced backg ound and pileup e en s he V0 de ec o
[60] is used. I consis s o wo scin illa o a ays (V0A and
V0C) co e ing 2.8<η<5.1 and −3.7<η<−1.7. The
p obabili y o collision pileup pe igge ed e en was below
2.5% and below 1% a √s=2.76 and 8 TeV, espec i ely.
Backg ound e en s om beam-gas in e ac ions o de ec o
noise a e ejec ed based on he iming in o ma ion om V0A
and V0C [55]. E en s con aining mo e han one pp collision
wi hin a single bunch c ossing a e ejec ed based on he
in o ma ion econs uc ed in he SPD. In hese e en s, ei he
mul iple p ima y e ices could be econs uc ed wi hin he
accep ance [55] o an excess o SPD clus e s wi h espec o
he numbe o SPD ackle s could be obse ed. In addi ion,
he p ima y e ex is equi ed o be econs uc ed wi hin
|z|<10 cm om he nominal in e ac ion poin . In 2011, he
minimum bias igge condi ion equi ed a hi in ei he he
SPD, he V0A o he V0C (MBOR condi ion), whe eas in
2012 a hi in he V0A and he V0C (MBAND condi ion)
was equi ed. The la e was necessa y due o he highe
beam in ensi ies in 2012. The co esponding c oss sec ion o
he minimum bias igge s a e ob ained om an de Mee
scans [61] yielding σMBOR =55.4±3.9s a +sys mb [62] and
σMBAND =55.8±1.2s a ±1.5sys mb [63] o he da a aking
campaigns a √s=2.76 TeV and √s=8 TeV, espec i ely.
Fo he con e sion-based measu emen s, in eg a ed luminosi-
ies o Lin =0.96 ±0.07no m nb−1a √s=2.76 TeV and
Lin =2.17 ±0.06no m nb−1a √s=8 TeV a e analyzed.
The calo ime e -based measu emen s sample 50% and, e-
spec i ely, 10.6% smalle in eg a ed luminosi ies, since he
EMCal was no always ac i e du ing da a aking. Fu he
in o ma ion abou he pe o mance o hese and o he de ec o
sys ems can be ound in Re . [55].
IV. PHOTON RECONSTRUCTION
Inclusi e pho ons a e econs uc ed in wo ways; ei he
using pho on con e sions be ween 0.4 (0.3) and 8 (16) GeV/c
o using he EMCal be ween 1.5 and 10 (16) GeV/c o
√s=2.76 (8) TeV. Pho ons con e wi hin he inne de ec o
ma e ial o ALICE wi h a p obabili y o abou 8.9%, and
a e econs uc ed wi h he PCM me hod as ollows: (i) ack-
ing o cha ged pa icles and seconda y e ex inding [53];
(ii) pa icle iden i ica ion; and (iii) pho on candida e econ-
s uc ion and subsequen selec ion. The seconda y e ices
used in his analysis a e ob ained du ing da a econs uc ion
by employing he ull acking capabili ies o ITS and TPC.
Fo he daugh e acks, a minimum o 60% o he maxi-
mum possible indable TPC clus e s, ha a pa icle ack can
c ea e in he TPC along i s pa h, and a minimum ack pT
o 50 MeV/ca e equi ed. The con amina ion om Dali z
decays is educed by ejec ing con e sion candida es wi h
econs uc ed e ices wi h a adial dis ance o less han
5 cm wi h espec o he nominal cen e o he de ec o .
Fu he mo e, only seconda y acks and e ices wi h |η|<
0.9 a e accep ed. In addi ion, we es ic he geome ical η
dis ibu ion o he V0s in o de o emo e pho on candida es
ha would o he wise appea ou side he angula dimensions o
he de ec o . To do so, he condi ion Rcon >|Zcon |SZR −7cm
is applied wi h SZR = an {2a c an[exp(−ηmax)]}≈0.974 o
ηmax =0.9, whe e Rcon and Zcon deno e he adial and longi-
udinal coo dina e o he con e sion poin , espec i ely. The
coo dina es Rcon and Zcon a e de e mined wi h espec o
he cen e o he de ec o and a e se o Rcon <180 cm and
|Zcon |<240 cm o ensu e a high quali y seconda y ack
econs uc ion inside he TPC.
Elec ons and posi ons a e iden i ied ia hei ene gy
deposi in he TPC, dE/dx, by employing he di e ence
o he measu ed dE/dx o he expec ed alue o elec ons
and posi ons [55]. Fo he measu emen a √s=2.76 TeV,
he dE/dx o he cha ged acks is equi ed o be wi hin
−4<nσe<5 o he expec ed elec on/posi on ene gy loss,
whe e nσe=(dE/dx −dE/dxe)/σeis pTdependen wi h
he a e age ene gy loss o he elec on/posi on, dE/dxe,
and he Gaussian wid h o he i o he measu ed dE/dx dis-
ibu ion, σe. This condi ion is igh ened o he measu emen
a √s=8TeV o−3<nσe<5. To educe he con amina ion
om pions, an addi ional selec ion based on he sepa a ion
om he cha ged pion ene gy loss hypo hesis is equi ed in
nσπ. A ejec ion o acks wi h ene gy losses close o he
pion line han |nσπ|<1isappliedup oapTo 3.5 GeV/c.
In he √s=2.76 TeV analysis, his ejec ion is con inued
abo e pT>3.5GeV/cwi h an |nσπ|<0.5 in o de educe
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DIRECT PHOTON PRODUCTION AT LOW TRANSVERSE … PHYSICAL REVIEW C 99, 024912 (2019)
he con amina ion e en u he in he momen um egion whe e
he wo dE/dx bands o he pion and elec on me ge.
Fu he con amina ion om nonpho onic V0candida es is
supp essed by a iangula wo-dimensional selec ion ange
o |pai |<
pai ,max(1 −χ2
ed/χ2
ed,max) wi h χ2
ed,max =30 and
pai ,max =0.1 ad. As explained in Re . [39], his selec-
ion is based on he educed χ2o he Kalman-Fil e hy-
po hesis [64,65] o hee+e−pai and on he angle pai
be ween he plane pe pendicula o he magne ic ield o
he ALICE magne and he e+e−pai plane ex apola ed
50 cm beyond he econs uc ed con e sion poin . An ad-
di ional selec ion based on he cosine o he poin ing an-
gle wi h cos(θPA )>0.85 is applied, whe e he poin ing
angle, θPA, is he angle be ween he econs uc ed pho-
on momen um ec o and he ec o joining he colli-
sion e ex and he con e sion poin . A selec ion in he
A men e os-Podolanski plo [66], which con ains he dis i-
bu ion o qT=pdaugh e ×sin θmo he −daug he e sus he longi-
udinal momen um asymme y [α=(p+
L−p−
L)/(p+
L+p−
L)]
wi h qT<qT,max1−α2/α2
max whe e qT,max =0.05 GeV/c
and αmax =0.95 emo es he emaining con amina ion om
K0
S,, and . Addi ionally, as explained in Re . [67], an ou -
o -bunch pileup co ec ion is equi ed o he PCM measu e-
men , which es ima es he con amina ion o pho on candida es
om mul iple o e lapping e en s in he TPC. The co ec ion
is ob ained om a s udy o he longi udinal dis ance o
closes app oach (DCA) o he con e sion pho on candida es,
which is he smalles dis ance in beam di ec ion (z) be ween
he p ima y e ex and he momen um ec o o he pho on
candida e. Pho on candida es om di e en e en s gene a e
a b oad unde lying Gaussian-like DCA dis ibu ion, which
is desc ibed wi h a backg ound es ima o o desc ibe he
ou -o -bunch pileup con ibu ion. This co ec ion is ound o
be ans e se momen um dependen and anges om 12% a
low pT(≈0.5GeV/c) o4%a highpT(≈7GeV/c) a bo h
cen e -o -mass ene gies.
Pho ons and elec ons/posi ons p oduce elec omagne ic
showe s as hey en e an elec omagne ic calo ime e and hei
deposi ed ene gy can be measu ed. By design, hese showe s
usually sp ead o e se e al adjacen calo ime e cells in he
EMCal. The e o e, he econs uc ion o he ull ene gy o
pa icles equi es he g ouping o such adjacen cells in o clus-
e s, o which a clus e iza ion algo i hm is used. The cell wi h
he highes deposi ed ene gy, exceeding a gi en seed ene gy,
Eseed, is used by he algo i hm as a s a ing poin . The clus e
is hen o med by addi ion o all adjacen cells wi h indi idual
ene gy abo e a minimum ene gy, Emin. This agg ega ion o
cells con inues as long as he ene gy o an adjacen cell is
smalle han he ene gy o he p e ious cell. O he wise he
clus e iza ion algo i hm s ops he agg ega ion p ocess. The
clus e ing p ocedu e is epea ed un il all cells a e g ouped
in o clus e s. The ene gy deposi ed in he indi idual cells o
he clus e is summed o ob ain he o al clus e ene gy. Fo
he p esen ed EMC analyses, he alues o Eseed =500 MeV
and Emin =100 MeV a e chosen, which a e de e mined o
supp ess ou -o -bunch backg ound, as well as he gene al
noise le el o he on -end elec onics. Finally, a co ec ion
o he di e ence o ela i e ene gy scale and posi ion o he
EMCal be ween da a and simula ion is applied, which was
ob ained by econs uc ing in da a and simula ion he a e age
neu al pion mass peak as a unc ion o he EMCal pho on
ene gy, pai ing pho on candida es om PCM wi h hose o
he EMCal [39,44].
To selec ue pho on candida es om he sample o e-
cons uc ed clus e s, pho on iden i ica ion c i e ia a e applied.
Clus e s a e equi ed o ha e a minimum ene gy Eclus e >
0.7 GeV and should consis o a leas wo cells. EMCal
clus e s a e accep ed only i hey a e wi hin |η|<0.67 and
1.40 ad <ϕ<3.15 ad. A clus e iming selec ion ela i e
o he collision ime o −35 < clus e <30 ns a √s=8TeV
(| clus e |<50 ns a √s=2.76 TeV) is imposed o emo e
pileup om mul iple e en s ha may occu wi hin he eadou
in e al o he on -end elec onics. This cons ain emo es
pho on candida es om di e en bunch c ossings wi h an
e iciency o be e han 99%.
Clus e s, which may ha e a signi ican con ibu ion om
ene gy deposi ed by cha ged had ons, a e ejec ed by p op-
aga ing cha ged pa icle acks o he EMCal su ace and
associa ing hem o clus e s based on geome ical c i e ia,
gene ally called ack ma ching in wha ollows. T ack ma ch-
ing is applied in ηand ϕdepending on ack momen um,
om |η|<0.04 and |ϕ|<0.09 ad o lowes pT o
|η|<0.01 and |ϕ|<0.015 ad a highes pT. Pa ame e -
ized as |η|<0.01 +(pT+4.07)−2.5and |ϕ|<0.015 +
(pT+3.65)−2 ad, wi h pTin uni s o GeV/c, hese c i e-
ia esul in a ack ma ching e iciency o mo e han 95%
o e he ull pT ange. Fu he mo e, he pho on pu i y is
signi ican ly imp o ed by he applica ion o a clus e shape
selec ion o 0.1<σ
2
long <(0.32 +0.0072 ·E2
clus/GeV2) o
Eclus ⩽5 GeV and 0.1<σ
2
long <0.5 o Eclus >5GeV,
used o supp ess he con amina ion caused by o e lapping
clus e s. He e, σ2
long s ands o he la ge eigen alue o he
dispe sion ma ix o he showe shape ellipse de ined by
he co esponding cell indices in he supe module and hei
ene gy con ibu ions o he clus e [39,68]. In addi ion, by
applying σ2
long >0.1 he con amina ion caused by neu ons
hi ing he APDs o he eadou elec onics is emo ed.
Co ec ions o econs uc ion e iciencies, con e sion
p obabili y and pu i y a e e alua ed using he PYTHIA8[69]
and PHOJET [70] MC e en gene a o s. Pa icles gene a ed by
he e en gene a o a e p opaga ed h ough he ALICE de ec-
o using GEANT3[71]. The same econs uc ion algo i hms
and analysis selec ion anges a e applied as hose in da a. The
co ec ion ac o s o bo h MC p oduc ions a e ound o be
consis en , and a e he e o e combined o educe he s a is-
ical unce ain ies. Be o e he e iciency co ec ion, pT-scale
and esolu ion e ec s a e co ec ed using Bayesian un olding
[72] wi h he de ec o esponse is used o con e om he
econs uc ed o he ue pTo he pho ons. Consequen ly,
he econs uc ion e iciency is calcula ed as a unc ion o
he ue ans e se momen um by di iding he econs uc ed
Mon e Ca lo (MC) alida ed pho on spec um by all pho ons
om he simula ion. The econs uc ion e iciency is ound o
be la ges a pT≈3GeV/cwi h 73% o PCM and 56% a
pT≈5GeV/c o EMC in he espec i e de ec o accep ance,
dec easing wi h lowe and highe pT o bo h me hods. Fo he
pho ons econs uc ed wi h PCM, a u he co ec ion based
on MC in o ma ion is applied o accoun o he con e sion
024912-5
S. ACHARYA e al. PHYSICAL REVIEW C 99, 024912 (2019)
TABLE I. Summa y o ela i e sys ema ic unce ain ies in pe cen o selec ed pTbins o he econs uc ion o inclusi e pho ons and he
Rγmeasu emen a √s=2.76 TeV. The hyb id me hod PCM-EMC is abb e ia ed as P-E in his able. The s a is ical unce ain ies a e gi en in
addi ion o he o al sys ema ic unce ain y as well as he unce ain ies a e combina ion o he independen measu emen s. The isible c oss
sec ion unce ain y o σMBOR o 2.5% is independen om epo ed measu emen s and is sepa a ely indica ed in he igu es below.
pTin e al (GeV/c)0.4–0.61.6–1.86.0–8.0
Me hod PCM PCM P-E EMC PCM P-E EMC
Measu emen Yγincl RγYγincl RγRγYγincl RγYγincl RγRγYγincl Rγ
Inne ma e ial 4.5 4.5 4.5 4.5 – – – 4.5 4.5 – – –
Ou e ma e ial – – – – 2.1 2.1 3.0 – – 2.1 2.1 3.0
PCM ack ec. 0.3 3.3 0.3 1.6 1.3 – – 0.3 8.4 1.3 – –
PCM elec on PID 0.5 1.4 0.6 1.8 0.4 – – 1.3 13.4 3.8 – –
PCM pho on PID 0.4 5.4 0.6 2.5 1.1 – – 2.2 11.4 3.1 – –
Clus e desc ip ion – – – – 2.6 2.7 4.1 – – 5.5 2.7 4.0
Clus e ene gy calib. – – – – 2.0 1.4 2.0 – – 2.6 2.0 2.5
T ack ma ch o clus e – – – – 1.5 0.7 0.7 – – 5.7 0.7 1.4
E iciency – – – – 2.0 1.5 2.5 – – 2.0 1.5 2.5
Signal ex ac ion π0– 5.0 – 2.7 2.1 – 2.5 – 4.9 3.7 – 2.4
Cock ail – 0.9 – 2.2 1.3 – 1.4 – 3.4 3.1 – 2.3
Pileup 2.4 2.6 1.1 1.2 0.9 0.3 – 1.6 1.7 0.9 0.3 –
To al sys . unce ain y 5.1 9.7 4.7 6.7 5.6 4.0 6.7 5.4 20.9 11.3 4.3 7.1
S a is ical unce ain y 0.2 7.8 0.7 4.3 4.4 0.5 5.0 6.3 23.1 18.3 4.6 8.6
Measu emen Yγincl RγYγincl RγYγincl Rγ
Comb sys . unce ain y 5.1 9.7 3.1 4.6 2.9 7.1
Comb s a . unce ain y 0.2 7.8 0.4 2.7 3.9 7.2
p obabili y o he pho ons in he de ec o ma e ial, which
inc eases om 5.6% a he lowes o 8.9% a he highes
measu ed pT, mainly due o he minimum elec on ack
momen um equi emen .
A co ec ion based on MC in o ma ion o he con am-
ina ion o he pho on sample om alsely iden i ied and
subsequen ly combined acks o elec ons, pions, kaons, o
muons is applied o he con e sion me hod. The pu i y o
he pho on sample econs uc ed wi h PCM is ound o be
99% up o 3 GeV/cand dec eases down o 96% a high
ans e se momen um due o he inc easing con amina ion
om elec on-pion pai s. Fo he calo ime e -based me hod,
a simila pu i y co ec ion is applied bu o alsely iden i ied
pho on candida es mainly om clus e s c ea ed by neu ons
and an ineu ons a low pTand by neu al kaons a high pT.
The pu i y co ec ion is he la ges o pT<3GeV/cwhe e
pu i ies be ween 87% and 97% ising wi h pTwe e ound,
while a high pT he pu i ies each alues o 97%.
Fo he inclusi e pho on measu emen s, con ibu ions o
seconda y pho ons om weak decays and had onic in e ac-
ions a e es ima ed and emo ed. The main sou ce o pho ons
om weak decays a e K0
Sdecays, howe e , con ibu ions
om K0
Land a e also conside ed. The co ec ion uses he
decay-pho on cock ail simula ion desc ibed in Sec. II, which
p o ides he seconda y pho on yields. Taking in o accoun
he de ec o esponse and de ec ion e iciency o he di -
e en econs uc ion echniques, hese pho ons a e emo ed
om he pho on sample. The emaining co ec ion ac o o
seconda y pho ons, o example due o in e ac ions wi h he
de ec o ma e ial, a e ob ained pu ely om MC in o ma ion.
The seconda y co ec ions a e o he o de o 1–3% o K0
S,
0.05–0.2% o K0
L,0.02% o and 0.1–2.5% o ma e-
ial in e ac ions depending on pTand on he pho on econ-
s uc ion echnique wi hin he gi en anges. In gene al he
co ec ion ac o s end o be la ge o he EMC econs uc ion
echnique, due o he wo se poin ing esolu ion o he pho ons.
The neu al pion and ηmeson measu emen s, which a e
needed o ex ac Rγ om Eq. (1), a e desc ibed in de ail
in Re s. [39,44]. The meson yields a e ob ained o PCM,
EMC, and a hyb id me hod (PCM-EMC), in which pho on
candida es econs uc ed wi h PCM a e pai ed wi h hose
econs uc ed in he EMCal. Fo he measu emen o Rγwi h
he PCM-EMC me hod, i is bene icial o measu e he inclu-
si e pho ons wi h PCM. Howe e , o be consis en wi h he
co esponding meson measu emen s [44], a wide selec ion
ange o −4<nσe<5 on he ene gy loss hypo hesis o he
elec on/posi on in he √s=8 TeV measu emen is used, and
he cha ged pion dE/dx-based ejec ion is applied indepen-
den o pTin bo h collision sys ems o he co esponding
inclusi e pho on measu emen wi h PCM.
V. SYSTEMATIC UNCERTAINTIES
Sys ema ic unce ain ies a e summa ized o he measu e-
men s o Yγincl and Rγin Table I o √s=2.76 TeV and in
Table II o √s=8TeV and shown o h ee ans e se mo-
men um bins used in he analyses. The unce ain ies a e gi en
in pe cen and o each econs uc ion me hod indi idually.
The de ailed desc ip ion o unce ain ies ela ed o he π0
meson measu emen s ha en e in o he calcula ion o he
di ec pho on excess a ios Rγcan be ound in Re . [39]
o √s=2.76 TeV and in Re . [44] o √s=8TeV. All
024912-6
DIRECT PHOTON PRODUCTION AT LOW TRANSVERSE … PHYSICAL REVIEW C 99, 024912 (2019)
TABLE II. Summa y o ela i e sys ema ic unce ain ies in pe cen o selec ed pTbins o he econs uc ion o inclusi e pho ons and he
Rγmeasu emen a √s=8 TeV. The hyb id me hod PCM-EMC is abb e ia ed as P-E in his able. The s a is ical unce ain ies a e gi en in
addi ion o he o al sys ema ic unce ain y as well as he unce ain ies a e combina ion o he independen measu emen s. The isible c oss
sec ion unce ain y o 2.6% is independen om epo ed unce ain ies and is sepa a ely indica ed in he igu es below.
pTin e al (GeV/c)0.4–0.61.6–1.89.0–12.0
Me hod PCM PCM P-E EMC PCM P-E EMC
Measu emen Yγincl RγYγincl RγRγYγincl RγYγincl RγRγYγincl Rγ
Inne ma e ial 4.5 4.5 4.5 4.5 – – – 4.5 4.5 – – –
Ou e ma e ial – – – – 2.1 2.1 3.0 – – 2.1 2.1 3.0
PCM ack ec. 0.2 0.5 0.1 0.5 0.2 – – 0.1 0.5 0.2 – –
PCM elec on PID 1.1 2.4 0.6 0.8 0.3 – – 0.7 0.8 0.8 – –
PCM pho on PID 1.8 1.2 1.3 1.0 1.0 – – 2.3 5.5 1.7 – –
Clus e desc ip ion – – – – 2.5 2.6 3.0 – – 3.0 2.6 1.9
Clus e ene gy calib. – – – – 2.3 1.4 2.3 – – 1.8 0.9 1.8
T ack ma ch o clus e – – – – 0.2 1.8 1.5 – – 1.9 1.8 1.6
E iciency 0.5 0.5 0.5 0.5 2.1 1.8 2.7 0.5 0.5 2.1 1.8 2.7
Signal ex ac ion π0– 4.9 – 1.6 1.8 – 2.7 – 6.6 3.1 – 1.9
Cock ail 0.2 1.7 0.1 0.7 1.0 0.3 0.8 0.1 0.5 1.9 0.3 1.4
Pileup 3.8 4.3 2.7 4.2 2.7 0.1 – 4.3 4.4 3.0 0.1 –
To al sys . unce ain y 6.3 8.5 5.4 6.6 5.7 4.4 6.4 6.4 10.7 7.1 4.3 5.6
S a is ical unce ain y 0.1 4.3 0.3 2.2 2.1 0.2 2.7 3.3 17.2 9.9 2.1 4.7
Measu emen Yγincl RγYγincl RγYγincl Rγ
Comb sys . unce ain y 6.3 8.5 3.5 4.5 3.6 5.9
Comb s a . unce ain y 0.1 4.3 0.2 1.4 1.8 4.3
unce ain ies a e e alua ed on he ully co ec ed spec a o
Yγincl o di ec ly on Rγ. In case o Rγ, he sys ema ic unce ain-
ies he e o e also con ain he e ec s o he sys ema ic a ia-
ions on he measu ed neu al pion spec um, hus bene i ing
om pa ial cancella ions o common unce ain ies.
Fo he PCM measu emen s, he ma e ial budge unce -
ain y is he main con ibu o o he o al unce ain y and i s
alue o 4.5% was p e iously de e mined in Re s. [55,73].
Sys ema ic unce ain ies associa ed wi h ack econs uc ion
a e he unce ain ies ha a e es ima ed om a ia ions o
equi ed TPC clus e s as well as minimum ans e se mo-
men um equi emen s o acks. Pa icle iden i ica ion (PID)
unce ain ies a e de e mined by a ia ion o he PID selec ion
anges o elec ons and pho ons as desc ibed in Sec. IV. A sys-
ema ic unce ain y is es ima ed o he pileup co ec ions ha
a e applied in he analyses. I is domina ed by he con ibu ion
om he DCA backg ound desc ip ion o he ou -o -bunch
pileup es ima ion bu also con ains he unce ain y om he
SPD in-bunch pileup ejec ion due o i s limi ed e iciency.
The sys ema ic unce ain y o he EMC measu emen con-
ains a la ge con ibu ion om he limi ed knowledge o he
ou e ma e ial budge , which is composed by all de ec o com-
ponen s om he adial cen e o he TPC up o he EMCal.
This unce ain y is de e mined by compa ing he e ec s on
he co ec ed spec a using inpu s om da a aking campaigns
wi h and wi hou TRD modules in on o he EMCal. This
could be done as he EMCal was masked only pa ially by he
TRD du ing he da a aking in 2011 and 2012. The ma e ial
budge s o TRD and TOF a e oughly simila and he e o e
he quo ed unce ain y is aken as √2 imes he di e ence o
he co ec ed spec a wi h and wi hou TRD modules in on
o he EMCal. Sys ema ic unce ain ies con ibu ing o he
clus e desc ip ion ca ego y a e he unce ain ies associa ed
o he desc ip ion o clus e s in simula ion, which in luence
he econs uc ion e iciencies. The associa ed a iables a e
he minimum clus e ene gy, showe shape, numbe o cells,
ime, and clus e iza ion seed, as well as minimum ene gy
selec ion a ia ions. The unce ain y o nonlinea i y e ec s as
well as he ene gy scale o clus e s a e inco po a ed in he
clus e ene gy calib a ion. To assess his unce ain y di e en
pa ame iza ions o he MC π0mass peak posi ion co ec ion
a e conside ed o accoun o he esidual di e ences be ween
da a and MC. The e iciency unce ain y e lec s he di e -
ences be ween he MC gene a o s ha a e used o he e i-
ciency calcula ion. The pileup sys ema ic unce ain y e lec s
he ini e e iciency o he SPD o in-bunch pileup ejec ion.
The hyb id me hod PCM-EMC equi es he same e alu-
a ion o unce ain ies as i s indi idual s and-alone me hods.
Howe e , mos sys ema ics show a di e en size o beha io
on Rγas he con ained inclusi e pho on measu emen is PCM
based whe eas o he neu al pion one pho on candida e o
each econs uc ion app oach is used. In addi ion, he ack
ma ching o clus e unce ain y includes he unce ain ies as-
socia ed wi h he ma ching o V0 acks o p ima y acks wi h
he clus e , which is an impo an ing edien o he hyb id
me hod.
The unce ain y on he decay-pho on simula ion is ob-
ained by a ying he pa ame iza ions o he neu al pion
and ηmeson o each econs uc ion echnique wi hin he
pT-unco ela ed sys ema ic and s a is ical unce ain ies. This
leads o an associa ed unce ain y o 0.9–3% and 0.5–2% o
pp collisions a √s=2.76 and 8 TeV, espec i ely, which
024912-7
S. ACHARYA e al. PHYSICAL REVIEW C 99, 024912 (2019)
s ongly depends on pT. Fu he mo e, a a ia ion o he
mTscaling cons an s has been conside ed o he emaining
mesons, which yields an unce ain y below 0.1%.
Pa ial sys ema ic unce ain y cancella ions a e p esen o
he di ec pho on excess a io Rγ. The ma e ial budge un-
ce ain y in he PCM measu emen , which en e s once in he
inclusi e pho on measu emen and wice in he neu al pion
measu emen , cancels once in Rγ. A simila cancella ion is
p esen in he EMC measu emen , whe e he ou e ma e ial
budge unce ain y cancels pa ially in he double a io as well.
Fo he hyb id me hod, he inne ma e ial budge unce ain y
cancels ully in he double a io and only he ou e ma e ial
budge unce ain y en e s once in he o al unce ain y, which
is he main ad an age o using his econs uc ion me hod
o Rγ.
The inal es ima ed sys ema ic unce ain ies on he inclu-
si e pho on c oss sec ion amoun o 5–7% o he con e sion
me hod and 4–9% o he EMC measu emen in he measu ed
pT ange. The ma e ial budge unce ain y o he con e sion
me hod is he dominan sou ce, whe eas he calo ime e -based
me hod shows a s ong dependence on he clus e desc ip ion
in he simula ion and he associa ed e iciency es ima es.
Wi h s a is ical unce ain ies below 1% o pT<3GeV/c
he inclusi e pho on measu emen is he e o e limi ed by he
sys ema ic unce ain ies.
The sys ema ic unce ain ies on he di ec pho on excess
a io Rγa e la ge han o he inclusi e pho ons due o he
addi ion o he neu al-pion- ela ed unce ain ies. Fo PCM,
he sys ema ic unce ain ies amoun o 6–20% domina ed by
he ma e ial budge unce ain y and he neu al pion signal
ex ac ion unce ain ies a low and high pT. Sys ema ic un-
ce ain ies o he EMC measu emen s a e smalle a high
ans e se momen um compa ed o PCM wi h alues o 7–9%
a √s=2.76 TeV and 6–8% a √s=8 TeV wi h dominan
con ibu ions o he ou e ma e ial budge , he clus e desc ip-
ion and neu al pion signal ex ac ion unce ain ies. Mos ly
due o he cancella ion o he inne ma e ial budge unce -
ain y, he hyb id me hod PCM-EMC exhibi s he smalles
sys ema ic unce ain y a in e media e pTwi h alues o 6%
a √s=2.76 TeV and 5.4% a √s=8TeV.
VI. RESULTS
The in a ian c oss sec ions o inclusi e pho ons a mid a-
pidi y (|y|<0.9) a e gi en as
Ed3σpp→γ+X
dp
3=1
2πpT
1
Lin
pu
Pcon  ecA
Fpile-up ·Nγ−Nγ
sec
ypT
,
(5)
whe e pu ,Pcon , and  ec a e he pu i y, con e sion p obabili y
and econs uc ion e iciency co ec ion ac o s, espec i ely,
and Lin is he in eg a ed luminosi y. The con e sion p ob-
abili y as well as he ou -o -bunch pileup co ec ion ac o
(Fpile-up) only apply o he PCM measu emen . The accep-
ance co ec ion ac o , A, is only applied o EMCal o
accoun o he limi ed azimu h co e age. In addi ion, he
inclusi e pho on aw yield is gi en by Nγand he summed
seconda y pho on aw yields by Nγ
sec. Fu he mo e, he in e al
anges in apidi y and ans e se momen um a e gi en by
ypT.
The double a ios a e measu ed by combining he indi id-
ual inclusi e pho on and neu al pion spec a om he same
econs uc ion me hods wi h a cock ail simula ion based on
he same neu al pion spec um. In his way, possible biases
can be emo ed, since hey would a ec bo h he inclusi e
pho on and he neu al pion measu emen s. The indi idually
measu ed inclusi e pho on in a ian di e en ial c oss sec-
ions o he PCM and EMC as well as he double a ios
o he PCM, PCM-EMC, and EMC econs uc ion me hods
a e combined o ob ain he inal spec a and double a ios,
espec i ely. Fo he combina ion, he bes linea unbiased
es ima es (BLUE) me hod [82–86] wi h ull ea men o
s a is ical and sys ema ic unce ain y co ela ions was used.
Fo he inclusi e pho on measu emen , he EMC measu emen
is assumed o be ully independen o he PCM measu emen
bo h s a is ically and sys ema ically. Howe e , o Rγ he
s a is ical unce ain ies show pa ial co ela ion be ween he
PCM and PCM-EMC, which a e de e mined o be ∼20–50%
depending on pT, since bo h measu emen s a e based on he
PCM inclusi e pho on measu emen using di e en subse s
o he da a; howe e , he s a is ical unce ain ies o he neu al
pion measu emen s a e ully independen due o hei di e en
econs uc ion me hods. The sys ema ic unce ain y co ela-
ions we e app oxima ed ia pTdependen co ela ion ac o s.
I has been ound ha he la ges co ela ions o he sys ema ic
unce ain ies a e among he PCM-EMC and he PCM o EMC
me hods, espec i ely. The ac ion o co ela ion among he
sys ema ic unce ain ies o he PCM-EMC and EMC me hod
has been es ima ed o be be ween 60–80%, which can be
a ibu ed o he common unce ain y ega ding he clus e
econs uc ion and e iciency unce ain ies as well as he ou e
ma e ial budge . Fo he PCM and PCM-EMC me hods he
unce ain ies ega ding he PCM pho on iden i ica ion and
selec ion a e la gely co ela ed and hus he co ela ion ac o
anges be ween 45–70% depending on ans e se momen um.
The combined in a ian c oss sec ions o inclusi e and
di ec pho ons, as well as he di ec pho on excess a ios Rγ,
co e ans e se momen um anges o 0.4<pT<10 GeV/c
and 0.3<pT<16 GeV/c o √s=2.76 and 8 TeV, espec-
i ely. The combined inclusi e pho on spec a a e shown in
Fig. 5 oge he wi h a wo-componen model (TCM) i [87],
whose unc ional o m is a combina ion o an exponen ial
unc ion a low pTand a powe law a high pT, gi en as
Ed3σ
dp
3=Aeexp −pT
Te+A1+p2
T
T2n−n
,(6)
wi h he ee pa ame e s Ae,A,Te,T, and n. The wo-
componen model is i ed o he inclusi e pho on spec a
by using he o al unce ain ies o he spec a, ob ained by
quad a ic combina ion o s a is ical and sys ema ic unce ain-
ies. I is used only o acili a e a compa ison o he me hods
in he a io o he i .
The a ios o he inclusi e pho on spec a measu ed in-
di idually by PCM and EMC ela i e o he TCM i a e
shown in Fig. 2, demons a ing ha he inclusi e spec a
measu ed wi h PCM and EMC ag ee wi hin he unce ain ies.
024912-8
DIRECT PHOTON PRODUCTION AT LOW TRANSVERSE … PHYSICAL REVIEW C 99, 024912 (2019)
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M. Cha ie ,125 S. Cha opadhyay,138 S. Cha opadhyay,106 A. Chau in,114,102 C. Cheshko ,132 B. Cheynis,132
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024912-15

S. ACHARYA e al. PHYSICAL REVIEW C 99, 024912 (2019)
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W. Shaikh,106 A. Shanga ae ,90 A. Sha ma,97 A. Sha ma,98 N. Sha ma,97 A. I. Sheikh,138 K. Shigaki,45 M. Shimomu a,82
S. Shi inkin,64 Q. Shou,7,109 K. Sh eje ,28 Y. Sibi iak,87 S. Siddhan a,54 K. M. Sielewicz,36 T. Siemia czuk,84 D. Sil e my ,80
G. Sima o ic,89 G. Simone i,102,36 R. Singa aju,138 R. Singh,85 V. Singhal,138 T. Sinha,106 B. Si a ,15 M. Si a,34 T. B. Skaali,23
M. Slupecki,124 N. Smi no ,143 R. J. M. Snellings,63 T. W. Snellman,124 J. Song,20 F. So amel,31 S. So ensen,127 F. Sozzi,103
I. Spu owska,115 J. S achel,101 I. S an,68 P. S ankus,94 E. S enlund,80 D. S occo,111 M. M. S o e ed ,37 P. S men,15
A. A. P. Suaide,118 T. Sugi a e,45 C. Sui e,61 M. Suleymano ,16 M. Suljic,36,27 R. Sul ano ,64 M. Šumbe a,93
S. Sumowidagdo,50 K. Suzuki,110 S. Swain,66 A. Szabo,15 I. Sza ka,15 U. Tabassam,16 J. Takahashi,119 G. J. Tamba e,24
N. Tanaka,130 M. Ta hini,61,111 M. Ta iq,18 M. G. Ta zila,47 A. Tau o,36 G. Tejeda Muñoz,2A. Telesca,36 C. Te e oli,31
B. Teyssie ,132 D. Thaku ,49 S. Thaku ,138 D. Thomas,116 F. Tho esen,88 R. Tieulen ,132 A. Tikhono ,62 A. R. Timmins,123
A. Toia,69 N. Topilskaya,62 M. Toppi,51 S. R. To es,117 S. T ipa hy,49 S. T ogolo,28 G. T ombe a,35 L. T opp,39 V. T ubniko ,3
W. H. T zaska,124 T. P. T zcinski,139 B. A. T zeciak,63 T. Tsuji,129 A. Tumkin,105 R. Tu isi,56 T. S. T e e ,23 K. Ullaland,24
E. N. Umaka,123 A. U as,132 G. L. Usai,26 A. U obicic,96 M. Vala,113 J. W. Van Hoo ne,36 M. an Leeuwen,63
P. Vande Vy e,36 D. Va ga,142 A. Va gas,2M. Va gyas,124 R. Va ma,48 M. Vasileiou,83 A. Vasilie ,87 A. Vau hie ,78
O. Vázquez Doce,102,114 V. Veche nin,137 A. M. Veen,63 A. Velu e,24 E. Ve cellin,28 S. Ve ga a Limón,2L. Ve mun ,63
R. Ve ne ,8R. Vé esi,142 L. Vicko ic,126 J. Viinikainen,124 Z. Vilakazi,128 O. Villalobos Baillie,107 A. Villa o o Tello,2
A. Vinog ado ,87 L. Vinog ado ,137 T. Vi gili,32 V. Visla icius,80 A. Vodopyano ,75 M. A. Völkl,100 K. Voloshin,64
S. A. Voloshin,140 G. Volpe,35 B. on Halle ,36 I. Vo obye ,114,102 D. Voscek,113 D. V anic,103,36 J. V láko á,39 B. Wagne ,24
H. Wang,63 M. Wang,7Y. Wa anabe,130,129 M. Webe ,110 S. G. Webe ,103 A. Weg zynek,36 D. F. Weise ,101 S. C. Wenzel,36
J. P. Wessels,141 U. Wes e ho ,141 A. M. Whi ehead,122 J. Wiechula,69 J. Wikne,23 G. Wilk,84 J. Wilkinson,53
G. A. Willems,141,36 M. C. S. Williams,53 E. Willshe ,107 B. Windelband,101 W. E. Wi ,127 R. Xu,7S. Yalcin,77 K. Yamakawa,45
S. Yano,45 Z. Yin,7H. Yokoyama,130,78 I.-K. Yoo,20 J. H. Yoon,60 V. Yu chenko,3V. Zaccolo,58 A. Zaman,16 C. Zampolli,36
H. J. C. Zanoli,118 N. Za dosh i,107 A. Za ochen se ,137 P. Zá ada,67 N. Za iyalo ,105 H. Zb oszczyk,139 M. Zhalo ,95
X. Zhang,7Y. Zhang,7Z. Zhang,131,7C. Zhao,23 N. Zhiga e a,64 D. Zhou,7Y. Zhou,88 Z. Zhou,24 H. Zhu,7J. Zhu,7Y. Zhu,7
A. Zichichi,29,11 M. B. Zimme mann,36 G. Zino je ,3J. Zmeskal,110 and S. Zou7
(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
2Benemé i a Uni e sidad Au ónoma de Puebla, Puebla, Mexico
3Bogolyubo Ins i u e o Theo e ical Physics, Na ional Academy o Sciences o Uk aine, Kie , Uk aine
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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, Uni ed S a es
7Cen al China No mal Uni e si y, Wuhan, China
8Cen e de Calcul de l’IN2P3, Villeu banne, Lyon, F ance
9Cen o de Aplicaciones Tecnológicas y Desa ollo Nuclea (CEADEN), Ha ana, Cuba
10Cen o de In es igación y de Es udios A anzados (CINVESTAV), Mexico Ci y and Mé ida, Mexico
11Cen o Fe mi - Museo S o ico della Fisica e Cen o S udi e Rice che “En ico Fe mi’, Rome, I aly
12Chicago S a e Uni e si y, Chicago, Illinois, Uni ed S a es
13China Ins i u e o A omic Ene gy, Beijing, China
14Chonbuk Na ional Uni e si y, Jeonju, Republic o Ko ea
15Comenius Uni e si y B a isla a, Facul y o Ma hema ics, Physics and In o ma ics, B a isla a, Slo akia
16COMSATS Ins i u e o In o ma ion Technology (CIIT), Islamabad, Pakis an
17C eigh on Uni e si y, Omaha, Neb aska, Uni ed S a es
18Depa men o Physics, Aliga h Muslim Uni e si y, Aliga h, India
19Depa men o Physics, Ohio S a e Uni e si y, Columbus, Ohio, Uni ed S a es
20Depa men o Physics, Pusan Na ional Uni e si y, Pusan, Republic o Ko ea
21Depa men o Physics, Sejong Uni e si y, Seoul, Republic o Ko ea
22Depa men o Physics, Uni e si y o Cali o nia, Be keley, Cali o nia, Uni ed S a es
23Depa men o Physics, Uni e si y o Oslo, Oslo, No way
24Depa men o Physics and Technology, Uni e si y o Be gen, Be gen, No way
25Dipa imen o di Fisica dell’Uni e si à ’La Sapienza’ and Sezione INFN, Rome, I aly
26Dipa imen o di Fisica dell’Uni e si à and Sezione INFN, Caglia i, I aly
27Dipa imen o di Fisica dell’Uni e si à and Sezione INFN, T ies e, I aly
28Dipa imen o di Fisica dell’Uni e si à and Sezione INFN, Tu in, I aly
29Dipa imen o di Fisica e As onomia dell’Uni e si à and Sezione INFN, Bologna, I aly
30Dipa imen o di Fisica e As onomia dell’Uni e si à and Sezione INFN, Ca ania, I aly
31Dipa imen o di Fisica e As onomia dell’Uni e si à and Sezione INFN, Pado a, I aly
32Dipa imen o di Fisica ‘E.R. Caianiello’ dell’Uni e si à and G uppo Collega o INFN, Sale no, I aly
33Dipa imen o DISAT del Poli ecnico and Sezione INFN, Tu in, I aly
34Dipa imen o di Scienze e Inno azione Tecnologica dell’Uni e si à del Piemon e O ien ale and INFN Sezione di To ino, Alessand ia, I aly
35Dipa imen o In e a eneo di Fisica ‘M. Me lin’ and Sezione INFN, Ba i, I aly
36Eu opean O ganiza ion o Nuclea Resea ch (CERN), Gene a, Swi ze land
37Facul y o Enginee ing and Science, Wes e n No way Uni e si y o Applied Sciences, Be gen, No way
38Facul y o Nuclea Sciences and Physical Enginee ing, Czech Technical Uni e si y in P ague, P ague, Czech Republic
39Facul y o Science, P.J. Ša á ik Uni e si y, Košice, Slo akia
40F ank u Ins i u e o Ad anced S udies, Johann Wol gang Goe he-Uni e si ä F ank u , F ank u , Ge many
41Gangneung-Wonju Na ional Uni e si y, Gangneung, Republic o Ko ea
42Gauha i Uni e si y, Depa men o Physics, Guwaha i, India
43Helmhol z-Ins i u ü S ahlen- und Ke nphysik, Rheinische F ied ich-Wilhelms-Uni e si ä Bonn, Bonn, Ge many
44Helsinki Ins i u e o Physics (HIP), Helsinki, Finland
45Hi oshima Uni e si y, Hi oshima, Japan
46Hochschule Wo ms, Zen um ü Technologie ans e und Telekommunika ion (ZTT), Wo ms, Ge many
47Ho ia Hulubei Na ional Ins i u e o Physics and Nuclea Enginee ing, Bucha es , Romania
48Indian Ins i u e o Technology Bombay (IIT), Mumbai, India
49Indian Ins i u e o Technology Indo e, Indo e, India
50Indonesian Ins i u e o Sciences, Jaka a, Indonesia
51INFN, Labo a o i Nazionali di F asca i, F asca i, I aly
52INFN, Sezione di Ba i, Ba i, I aly
53INFN, Sezione di Bologna, Bologna, I aly
54INFN, Sezione di Caglia i, Caglia i, I aly
55INFN, Sezione di Ca ania, Ca ania, I aly
56INFN, Sezione di Pado a, Pado a, I aly
57INFN, Sezione di Roma, Rome, I aly
58INFN, Sezione di To ino, Tu in, I aly
59INFN, Sezione di T ies e, T ies e, I aly
60Inha Uni e si y, Incheon, Republic o Ko ea
61Ins i u de Physique Nucléai e d’O say (IPNO), Ins i u Na ional de Physique Nucléai e e de Physique des Pa icules (IN2P3/CNRS),
Uni e si é de Pa is-Sud, Uni e si é Pa is-Saclay, O say, F ance
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62Ins i u e o Nuclea Resea ch, Academy o Sciences, Moscow, Russia
63Ins i u e o Suba omic Physics, U ech Uni e si y/Nikhe , U ech , Ne he lands
64Ins i u e o Theo e ical and Expe imen al Physics, Moscow, Russia
65Ins i u e o Expe imen al Physics, Slo ak Academy o Sciences, Košice, Slo akia
66Ins i u e o Physics, Bhubaneswa , India
67Ins i u e o Physics o he Czech Academy o Sciences, P ague, Czech Republic
68Ins i u e o Space Science (ISS), Bucha es , Romania
69Ins i u ü Ke nphysik, Johann Wol gang Goe he-Uni e si ä F ank u , F ank u , Ge many
70Ins i u o de Ciencias Nuclea es, Uni e sidad Nacional Au ónoma de México, Mexico Ci y, Mexico
71Ins i u o de Física, Uni e sidade Fede al do Rio G ande do Sul (UFRGS), Po o Aleg e, B azil
72Ins i u o de Física, Uni e sidad Nacional Au ónoma de México, Mexico Ci y, Mexico
73iThemba LABS, Na ional Resea ch Founda ion, Some se Wes , Sou h A ica
74Johann-Wol gang-Goe he Uni e si ä F ank u Ins i u ü In o ma ik, Fachbe eich In o ma ik und Ma hema ik, F ank u , Ge many
75Join Ins i u e o Nuclea Resea ch (JINR), Dubna, Russia
76Ko ea Ins i u e o Science and Technology In o ma ion, Daejeon, Republic o Ko ea
77KTO Ka a ay Uni e si y, Konya, Tu key
78Labo a oi e de Physique Suba omique e de Cosmologie, Uni e si é G enoble-Alpes, CNRS-IN2P3, G enoble, F ance
79Law ence Be keley Na ional Labo a o y, Be keley, Cali o nia, Uni ed S a es
80Lund Uni e si y Depa men o Physics, Di ision o Pa icle Physics, Lund, Sweden
81Nagasaki Ins i u e o Applied Science, Nagasaki, Japan
82Na a Women’s Uni e si y (NWU), Na a, Japan
83Na ional and Kapodis ian Uni e si y o A hens, School o Science, Depa men o Physics, A hens, G eece
84Na ional Cen e o Nuclea Resea ch, Wa saw, Poland
85Na ional Ins i u e o Science Educa ion and Resea ch, HBNI, Ja ni, India
86Na ional Nuclea Resea ch Cen e , Baku, Aze baijan
87Na ional Resea ch Cen e Ku cha o Ins i u e, Moscow, Russia
88Niels Boh Ins i u e, Uni e si y o Copenhagen, Copenhagen, Denma k
89Nikhe , Na ional ins i u e o suba omic physics, Ams e dam, Ne he lands
90NRC Ku cha o Ins i u e IHEP, P o ino, Russia
91NRNU Moscow Enginee ing Physics Ins i u e, Moscow, Russia
92Nuclea Physics G oup, STFC Da esbu y Labo a o y, Da esbu y, Uni ed Kingdom
93Nuclea Physics Ins i u e o he Czech Academy o Sciences, ˇ
Rež u P ahy, Czech Republic
94Oak Ridge Na ional Labo a o y, Oak Ridge, Tennessee, Uni ed S a es
95Pe e sbu g Nuclea Physics Ins i u e, Ga china, Russia
96Physics depa men , Facul y o science, Uni e si y o Zag eb, Zag eb, C oa ia
97Physics Depa men , Panjab Uni e si y, Chandiga h, India
98Physics Depa men , Uni e si y o Jammu, Jammu, India
99Physics Depa men , Uni e si y o Rajas han, Jaipu , India
100Physikalisches Ins i u , Ebe ha d-Ka ls-Uni e si ä Tübingen, Tübingen, Ge many
101Physikalisches Ins i u , Rup ech -Ka ls-Uni e si ä Heidelbe g, Heidelbe g, Ge many
102Physik Depa men , Technische Uni e si ä München, Munich, Ge many
103Resea ch Di ision and Ex eMe Ma e Ins i u e EMMI, GSI Helmhol zzen um ü Schwe ionen o schung GmbH, Da ms ad , Ge many
104Rudje Boško i´c Ins i u e, Zag eb, C oa ia
105Russian Fede al Nuclea Cen e (VNIIEF), Sa o , Russia
106Saha Ins i u e o Nuclea Physics, Kolka a, India
107School o Physics and As onomy, Uni e si y o Bi mingham, Bi mingham, Uni ed Kingdom
108Sección Física, Depa amen o de Ciencias, Pon i icia Uni e sidad Ca ólica del Pe ú, Lima, Pe u
109Shanghai Ins i u e o Applied Physics, Shanghai, China
110S e an Meye Ins i u ü Suba oma e Physik (SMI), Vienna, Aus ia
111SUBATECH, IMT A lan ique, Uni e si é de Nan es, CNRS-IN2P3, Nan es, F ance
112Su ana ee Uni e si y o Technology, Nakhon Ra chasima, Thailand
113Technical Uni e si y o Košice, Košice, Slo akia
114Technische Uni e si ä München, Excellence Clus e ’Uni e se’, Munich, Ge many
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, Aus in, Texas, Uni ed S a es
117Uni e sidad Au ónoma de Sinaloa, Culiacán, Mexico
118Uni e sidade de São Paulo (USP), São Paulo, B azil
119Uni e sidade Es adual de Campinas (UNICAMP), Campinas, B azil
120Uni e sidade Fede al do ABC, San o And e, B azil
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121Uni e si y College o Sou heas No way, Tonsbe g, No way
122Uni e si y o Cape Town, Cape Town, Sou h A ica
123Uni e si y o Hous on, Hous on, Texas, Uni ed S a es
124Uni e si y o Jy äskylä, Jy äskylä, Finland
125Uni e si y o Li e pool, Depa men o Physics Oli e Lodge Labo a o y, Li e pool, Uni ed Kingdom
126Uni e si y o Spli , Facul y o Elec ical Enginee ing, Mechanical Enginee ing and Na al A chi ec u e, Spli , C oa ia
127Uni e si y o Tennessee, Knox ille, Tennessee, Uni ed S a es
128Uni e si y o he Wi wa e s and, Johannesbu g, Sou h A ica
129Uni e si y o Tokyo, Tokyo, Japan
130Uni e si y o Tsukuba, Tsukuba, Japan
131Uni e si é Cle mon Au e gne, CNRS/IN2P3, LPC, Cle mon -Fe and, F ance
132Uni e si é de Lyon, Uni e si é Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeu banne, Lyon, F ance
133Uni e si é de S asbou g, CNRS, IPHC UMR 7178, F-67000 S asbou g, F ance, S asbou g, F ance
134Uni e si é Pa is-Saclay Cen e d’É udes de Saclay (CEA), IRFU, Depa men de Physique Nucléai e (DPhN), Saclay, F ance
135Uni e si à degli S udi di Pa ia, Pa ia, I aly
136Uni e si à di B escia, B escia, I aly
137V. 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
138Va iable Ene gy Cyclo on Cen e, Kolka a, India
139Wa saw Uni e si y o Technology, Wa saw, Poland
140Wayne S a e Uni e si y, De oi , Michigan, Uni ed S a es
141Wes älische Wilhelms-Uni e si ä Müns e , Ins i u ü Ke nphysik, Müns e , Ge many
142Wigne Resea ch Cen e o Physics, Hunga ian Academy o Sciences, Budapes , Hunga y
143Yale Uni e si y, New Ha en, Connec icu , Uni ed S a es
144Yonsei Uni e si y, Seoul, Republic o Ko ea
aDipa imen o DET del Poli ecnico di To ino, Tu in, I aly.
bM.V. Lomonoso Moscow S a e Uni e si y, D.V. Skobel syn Ins i u e o Nuclea , Physics, Moscow, Russia.
cDepa men o Applied Physics, Aliga h Muslim Uni e si y, Aliga h, India.
dIns i u e o Theo e ical Physics, Uni e si y o W oclaw, Poland.
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