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P obing nuclea PDFs wi h dije s in ul a-pe iphe al Pb+Pb collisions
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Helenius, I.
Helenius, I. (2019). P obing nuclea PDFs wi h dije s in ul a-pe iphe al Pb+Pb collisions. In D.
d'En e ia, A. Mo sch, & P. C oche (Eds.), Ha d P obes 2018 : In e na ional Con e ence on Ha d
and Elec omagne ic P obes o High-Ene gy Nuclea Collisions (A icle 118). Sissa Medialab s l.
POS P oceedings o Science, 345. h ps://doi.o g/10.22323/1.345.0118
2019
PoS(Ha dP obes2018)118
P obing nuclea PDFs wi h dije s in ul a-pe iphe al
Pb+Pb collisions
Ilkka Helenius∗
Uni e si y o Jy askyla, Depa men o Physics, P.O. Box 35, FI-40014 Uni e si y o Jy askyla,
Finland
Ins i u e o Theo e ical Physics, Tübingen Uni e si y, Au de Mo gens elle 14, 72076
Tübingen, Ge many
E-mail: [email p o ec ed]
In his alk we apply he pho op oduc ion amewo k ecen ly implemen ed in o he PYTHIA 8
Mon e Ca lo e en gene a o o s udy he po en ial o pho o-nuclea dije s in ul a-pe iphe al
Pb+Pb collisions a he LHC o u he cons ain he nuclea PDFs. These e en s can be desc ibed
as γA collisions whe e he ele an pa o he lux o quasi- eal pho ons om hea y-ions is ob-
ained by using he equi alen pho on app oxima ion and cu ing ou impac -pa ame e alues
which would lead o had onic in e ac ions be ween he beam pa icles. In pa icula , we quan-
i y he small-x each wi h di e en je kinema ics and show how well he alues o xde i ed
om econs uc ed je momen a a e co ela ed wi h he ac ual alues o pa onic momen um ac-
ions p obed in hese measu emen s. Also he con ibu ions om di ec and esol ed pho ons a e
sepa a ely p esen ed. To demons a e he po en ial, we compa e he expec ed expe imen al un-
ce ain ies o he cu en nuclea -PDF e o s and discuss o he heo e ical unce ain ies including
he unce ain y a ising om poo ly-cons ained pho on PDFs. We ind ha such a measu emen
would po en ially p o ide a conside able educ ion o he nuclea PDF unce ain ies in a egion
10−4.x.10−2.
In e na ional Con e ence on Ha d and Elec omagne ic P obes o High-Ene gy Nuclea Collisions
30 Sep embe - 5 Oc obe 2018
Aix-Les-Bains, Sa oie, F ance
∗Speake .
c
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PoS(Ha dP obes2018)118
P obing nuclea PDFs wi h dije s in ul a-pe iphe al Pb+Pb collisions Ilkka Helenius
1. In oduc ion
The unce ain ies in he cu en nuclea PDF (nPDF) analyses [
1
,
2
] a e conside able especially
a small alues o
x
due o lack o da a cons ain s. The mos p ecise way o pin down he nPDF
unce ain ies would be o measu e he s uc u e unc ions in deep inelas ic sca e ing (DIS) p ocess
in a high-ene gy elec on-ion collide whe e a i ual pho on p obes he pa onic s uc u e o a
hea y nucleus [
3
]. Such collide s a e being conside ed (see e.g. Re . [
4
]) bu o some ex en simila
measu emen s could be pe o med also in ul a-pe iphe al Pb+Pb collisions a he LHC.
In ul a-pe iphe al collisions (UPCs) [
5
] he beam pa icles pass wi hou any s ong in e ac ions
be ween he cons i u ing pa ons bu a quasi- eal pho on emi ed by one beam pa icle collide wi h a
pa icle om he o he beam o wi h a pho on om he o he beam. Unlike in DIS p ocesses he
i uali y o hese in e media e pho ons is small so he ha d scale jus i ying he use o pe u ba i e
QCD mus be p o ided by a high-
pT
obse able. Fu he mo e, hese quasi- eal pho ons may luc ua e
in o a had onic s a e wi h he same quan um numbe s. The pa onic s uc u e o hese esol ed
pho ons can be desc ibed wi h PDFs and, simila ly as in he case o pu ely had onic collisions,
gi es ise o mul iple pa onic in e ac ions (MPIs). Due o he ine i able con ibu ion o esol ed
pho ons, he measu emen s in his low-
Q2
(pho op oduc ion) egime a e no as clean as in high-
Q2
(DIS) bu due o p esence o he di ec -pho on -pa on sca e ing, and di e en pa onic s uc u e,
he unde lying e en is signi ican ly supp essed compa ed o had onic collisions.
In his wo k we s udy he possibili y o u he cons ain he nPDFs using dije p oduc ion in
UPCs a he LHC as p oposed in Re . [
6
]. The i s expe imen al esul s o he p ocess ha e been
ecen ly published by he ATLAS collabo a ion [
7
]. Dije p oduc ion in p+Pb collisions a he LHC
has al eady been conside ed as a p obe o nPDFs (see e.g. Re . [
8
]) bu he UPC measu emen
would allow o s udy je p oduc ion in a cleane
γA
in e ac ion ha should enable je econs uc ion
a lowe alues o
pT
. This inc eases he small-
x
each o he obse able and also lowe s he scale a
which he nPDFs a e p obed whe e he unce ain ies a e la ge . In his s udy he dije c oss sec ions
a e calcula ed applying he ecen pho op oduc ion amewo k o PYTHIA 8 [
9
] Mon e Ca lo e en
gene a o ha has been alida ed agains a ious HERA da a [10].
2. Ul a-pe iphe al Pb+Pb collisions a he LHC
The pho on lux om hea y ions can be ob ained acco ding o he equi alen pho on app oxi-
ma ion. Since he con igu a ions whe e he wo ions would in e ac had onically mus be ejec ed,
i is con enien o de ine he pho on lux in impac -pa ame e (
b
) space. To a good p ecision, he
ele an pa o he pho on lux can be calcula ed by in eg a ing he lux o e impac pa ame e s
la ge han he sum o adii o he colliding ions (RA), gi ing
xγ A
γ(xγ) = 2αEMZ2
πξK1(ξ)K0(ξ)−ξ2
2K2
1(ξ)−K2
0(ξ),(2.1)
whe e
xγ
is he momen um ac ion o he pho on w . he beam pa icle,
ξ=2RAxγm/(¯
hc)
,
m
(pe -nucleon) mass and
Z
he elec ic cha ge o he nucleus. Compa ed o he lux o pho ons om
lep ons he lux om hea y ions is ampli ied by a ac o o
Z2
bu , due o he ini e size o he
nuclei aken in o accoun wi h he impac -pa ame e based ejec ion, he pho on spec um is so e as
1
PoS(Ha dP obes2018)118
P obing nuclea PDFs wi h dije s in ul a-pe iphe al Pb+Pb collisions Ilkka Helenius
shown in Fig. 1. The in a ian mass dis ibu ions o he
γ
-nucleon sys em,
Wγp
, o e en s ha ha e a
pa onic je wi h
pT>10 GeV/c
is shown in Fig. 1 o se ups co esponding o he pho op oduc ion
measu emen s a HERA and he UPCs a he LHC. As he pho on spec um om nuclei is a he
so , la ge con ibu ion o he dije c oss sec ion in UPCs is coming om
Wγp
alues p obed a
HERA bu due o highe
√sNN
a he LHC, he
Wγp
dis ibu ion ex ends s ill up o a ac o o wo
highe ene gies han wha was eached a HERA. Fo he UPC e en s he pa on showe s and MPIs
a e gene a ed o he
γ
-nucleon sys em so u he sca e ings o he pho on emnan wi h he o he
nucleons a e no conside ed.
10 410 310 210 1100
x
10 2
10 1
100
101
102
103
104
105
x i
(
x
) * / EM
lep ons
Pb nucleus
a bi . uni s
Wγp[GeV]
HERA: ep@318 GeV
LHC: PbPb@5000 GeV
E en s wi h
pje
T>10 GeV
Figu e 1: Le :
The pho on lux om lep ons (o ange) and om Pb-nucleus (blue) as a unc ion o pho on
momen um ac ion
xγ
.
Righ :
In a ian -mass dis ibu ions o
γ
-nucleon sys em in e+p collisions a HERA
(o ange) and ul a-pe iphe al Pb+Pb collisions a he LHC (blue) o e en s ha ha e a pa onic je wi h
pT>10 GeV/c.
3. Dije sensi i i y o nPDFs
We s udy he pho o-nuclea dije p oduc ion in wo di e en je kinema ics. Fi s is based on
he p elimina y ATLAS s udy [
7
] whe e he
pT
o he leading je was abo e
20 GeV/c
and he
sub-leading je s had
pT>15 GeV/c
. In he second case he co esponding limi s o he
pT
o he
leading and sub-leading je s a e
8 GeV/c
and
6 GeV/c
which esembles he je kinema ics analyzed
a HERA [
11
]. In bo h cases he je s a e econs uc ed wi h he an i-
kT
algo i hm wi h
R=0.4
and
a e equi ed o be wi hin
|η|<4.4
and e en s wi h a leas wo accep ed je s a e conside ed. As in
he ATLAS s udy we cons uc he ollowing e en -le el a iables om he ou momen a o he
econs uc ed je s
mje s =q(ΣiEi)2−|Σi~pi|2HT=ΣipTi
yje s =1
2logΣiEi+Σipzi
ΣiEi−Σipzi xA=mje s
√se−yje s ,
whe e he sums un o e accep ed je s. Fo he nPDF s udies pa icula ly in e es ing obse able is he
xA
a iable, which, in leading o de pa on-le el kinema ics would co espond o
x2
, he momen um
ac ion o he pa on in he nucleus. Howe e , his connec ion is smea ed due o pa on-showe
emissions, had oniza ion e ec s and unde lying e en om he MPIs. To s udy he co ela ion
be ween
xA
and
x2
wi hin he applied MC amewo k we plo he wo-dimensional c oss sec ion in
2
PoS(Ha dP obes2018)118
P obing nuclea PDFs wi h dije s in ul a-pe iphe al Pb+Pb collisions Ilkka Helenius
e ms o hese a iables in Fig. 2. Fo a mo e quan i a i e esul we also plo he c oss sec ion as a
unc ion o x2in one xAbin in linea scale in Fig. 2. The esul s show a s ong co ela ion be ween
xAand x2.
dσ/dx2[mb]
x2
Pb+Pb
√sNN = 5.0 TeV
an i-kT, R = 0.4
plead
T>20 GeV/c
mje s >35 GeV
10−2< xA<1.5·10−2
Figu e 2: Le :
Co ela ion be ween
xA
and he ac ual
x2
a which he nPDFs a e p obed wi h dije s in he
ATLAS kinema ics. Righ : C oss sec ion o e en s wi hin a gi en xAbin as a unc ion o x2.
To calcula e he dije c oss sec ion we apply NNPDF2.3 LO [
12
] p o on PDFs wi h EPPS16
NLO [
1
] nuclea modi ica ions. The esul ing c oss sec ions co esponding o he wo di e en cu s
o je
pT
’s a e p esen ed in Fig. 3as a unc ion o
xA
. The esol ed-pho on con ibu ion domina es
he c oss sec ion a la ge-
xA
egion bu he di ec con ibu ion akes o e a a ound
xA<0.01(0.002)
wi h he ha de (so e ) je cu s. The impac o nPDFs is quan i ied by showing a a io o he
calcula ion wi h he p o on PDFs only. The nPDF-o igina ing unce ain ies om EPPS16 analysis
a e o he o de 10% a
xA>0.01
bu g ow up o 30% a smalle alues o
xA
wi h he so e je
cu s. By de aul PYTHIA 8 akes he PDFs o he esol ed pho ons om CJKL analysis [
13
] bu we
ha e conside ed also wo o he widely-used se s, GRV [
14
] and SaSgam (1D V2) [
15
] o s udy he
unce ain ies ela ed o p ecision o he pho on PDFs. The esul ing unce ain y is up o 10% a he
highes alues o
xA
whe e he esol ed con ibu ion domina es bu is negligible a smalle alues o
xA
whe e he nuclea PDF unce ain ies a e la ge. In Fig. 3we also es ima e he expec ed s a is ical
p ecision o he so e
pT
je s assumming in eg a ed luminosi y o
L=1.0 nb−1
co esponding o
he hea y-ion p og am a he LHC and
L=13 nb−1
co esponding o he high-luminosi y LHC (HL-
LHC) p oposal. The expec ed s a is ical unce ain ies become la ge han he nPDF unce ain ies a
xA.2·10−4.
4. Conclusions
We ha e s udied he pho o-nuclea dije p oduc ion in ul a-pe iphe al Pb+Pb collisions a he
LHC and i s po en ial o u he cons ain he nPDFs. We ind ha
xA
de i ed om he econs uc ed
je s co ela e well wi h he ac ual alues o he
x
p obed in he nucleus and ha a small-
xA
egion
he dije p oduc ion is domina ed by he clean di ec -pho on con ibu ion. Compa ing he nPDF
unce ain ies wi h he expec ed s a is ical p ecision o he measu emen a he LHC show ha his
obse able could po en ially p o ide p ecise nPDF cons ain s down o x∼10−4.
3

PoS(Ha dP obes2018)118
P obing nuclea PDFs wi h dije s in ul a-pe iphe al Pb+Pb collisions Ilkka Helenius
dσ/dxA[nb]
PbPb,√sNN = 5.02 TeV
an i-kT, R = 0.4
plead
T>20 GeV/c
mje s >35 GeV
Py hia
NNPDF2.3
EPPS16
esol ed
di ec
Ra io o NNPDF2.3
xA
SaSgam
GRV
dσ/dxA[nb]
PbPb,√sNN = 5.5 TeV
an i-kT, R = 0.4
plead
T>8 GeV/c
mje s >14 GeV
Py hia
NNPDF2.3
EPPS16
esol ed
di ec
Ra io o NNPDF2.3
xA
L= 1 nb−15.0 TeV
L= 13 nb−15.5 TeV
Figu e 3:
Di e en ial c oss sec ion o pho o-nuclea dije p oduc ion in ul a-pe iphe al Pb+Pb collisions a
he LHC as a unc ion o
xA
. Resul s wi h (blue) and wi hou ( ed) EPPS16 nPDFs a e shown sepa a ely as
also he con ibu ions om di ec (o ange) and esol ed p ocesses (g een). The lowe panels show a ios o
he esul wi hou he EPPS16 nPDFs. Wi h he highe
pT
cu s (le ) also he a ios o di e en pho on PDFs
a e shown and he expec ed s a is ical unce ain ies co esponding o he in eg a ed luminosi ies o he LHC
and HL-LHC a e es ima ed o lowe pTcu s ( igh ).
Acknowledgmen s
The wo k has been suppo ed by he Ca l Zeiss Founda ion and he Academy o Finland, P ojec
308301.
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