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nPDF cons ain s om he la ge had on elec on collide
Helenius, Ilkka; Paukkunen, Hannu; A mes o, Nes o
Helenius, I., Paukkunen, H., & A mes o, N. (2016). nPDF cons ain s om he la ge
had on elec on collide . In DIS 2016 : P oceedings o he 24 h In e na ional
Wo kshop on Deep-Inelas ic Sca e ing and Rela ed Subjec s (A icle 276). SISSA. PoS
: P oceedings o Science, DIS2016. h ps://doi.o g/10.22323/1.265.0276
2016
PoS(DIS2016)276
nPDF cons ain s om he La ge Had on Elec on
Collide
Ilkka Helenius∗a, Hannu Paukkunenbcd and Nes o A mes od
aDepa men o As onomy and Theo e ical Physics, Lund Uni e si y, Söl ega an 14A, SE-223 62
Lund, Sweden
bUni e si y o Jy askyla, Depa men o Physics, P.O. Box 35, FI-40014 Uni e si y o Jy askyla,
Finland
cHelsinki Ins i u e o Physics, P.O. Box 64, FI-00014 Uni e si y o Helsinki, Finland
dIGFAE, Uni e sidade de San iago de Compos ela, E-15782 Galicia, Spain
E-mail: [email p o ec ed],[email p o ec ed],
[email p o ec ed]
An upda ed analysis ega ding he expec ed nuclea PDF cons ain s om he u u e La ge Had on
Elec on Collide (LHeC) expe imen is p esen ed. The new s udy is based on a mo e lexible
small-xpa ame iza ion which p o ides less biased unce ain y es ima es in he egion whe e
he e a e cu en ly no da a cons ain s. The e ec o he LHeC is quan i ied by di ec ly including
a sample o pseudoda a acco ding o he expec ed p ecision o his planned expe imen . As a
esul , a signi ican educ ion o he small-xunce ain ies in sea qua ks and gluons is obse ed.
XXIV In e na ional Wo kshop on Deep-Inelas ic Sca e ing and Rela ed Subjec s
11-15 Ap il, 2016
DESY Hambu g, Ge many
∗Speake .
c
Copy igh owned by he au ho (s) unde he e ms o he C ea i e Commons
A ibu ion-NonComme cial-NoDe i a i es 4.0 In e na ional License (CC BY-NC-ND 4.0). h p://pos.sissa.i /
PoS(DIS2016)276
nPDF cons ain s om he LHeC Ilkka Helenius
1. In oduc ion
The La ge Had on Elec on Collide (LHeC) p ojec consis s on he cons uc ion o a new
elec on accele a o p o iding an elec on beam ha would collide wi h he had on beam om he
La ge Had on Collide (LHC). The design also allows a synch onous ope a ion o e-p collisions a
he LHeC and p-p collisions a he LHC, as well as eplacing he p o on beam wi h hea y ions. A
de ailed desc ip ion abou he design can be ound in he concep ual design epo [1].
Accu a ely de e mined pa on dis ibu ion unc ions (PDFs) a e essen ial o all pe u ba i e
QCD (pQCD) based heo y p edic ions. This holds also o nuclea collisions, whe e he nuclea
modi ica ions o he PDFs a e needed o ob ain a p ecise pQCD baseline o hea y-ion physics a
he LHC, and also o u u e high-ene gy collide s, such as he Fu u e Ci cula Collide (FCC) [2].
In his alk we ocus on he cu en s a us o he nuclea PDFs (nPDFs), and quan i y he po en ial o
e-Pb collisions a he LHeC o imp o e he accu acy o he u u e nPDF analyses. O he in e es ing
e-Aphysics a e desc ibed e.g. in Re s. [1,3].
2. New baseline nPDF i
The nPDFs can be de e mined ia a simila global analysis as he ee p o on PDFs. The scale
e olu ion is gi en by he DGLAP equa ions, bu a non-pe u ba i e inpu unc ion (x,Q2
0)a he
ini ial scale Q2
0o he i is equi ed o he xdependence. The ansa z o (x,Q2
0)should include
enough eedom o cap u e all he ele an ea u es o da a used in he analysis bu , on he o he
hand, keep he numbe o pa ame e s easonable o ensu e he con e gence o he i and no o be
sensi i e o he luc ua ions o he indi idual da a poin s.
The da a used in he cu en i s comes om deep inelas ic sca e ing (DIS), D ell-Yan dilep-
on p oduc ion and inclusi e pion p oduc ion in d-Au collisions a RHIC. Since mos o he da a
a e om ixed- a ge expe imen s, he limi ed collision ene gy es ic s he kinema ic each o he
da a, as discussed e.g. in Re . [3]. The e o e, he cu en i s NCTEQ15 [4], KA15 [5], DSSZ [6],
EPS09 [7] and HKN07 [8] include da a ha a e es ic ed o x&5·10−3and Q2.100 GeV2.
The ecen dije , cha ged had on and W±/Zda a om p-Pb collisions a he LHC p o ide some
addi ional cons ain s o he nPDF analyses [9], bu in p ac ice do no inc ease he small-x each.
Wi h he LHeC, he kinema ic each o e-ADIS c oss sec ion could be ex ended by mo e han h ee
o de s o magni ude in bo h xand Q2p o iding a kinema ic each compa able o he cu en p o on
PDF i s.
The nPDF unce ain ies a e usually quan i ied ia he Hessian me hod [10], which allows a
simple way o s udy how he unce ain ies p opaga e in o physical obse ables. Wi hin his me hod
he pa ame e s (in a diagonalized basis) a e allowed o a y wi hin some ∆χ2 alue (he e, ∆χ2=
17). The unce ain y es ima es a e always ied o he unc ional o m o (x,Q2
0), especially in he
egion whe e he e a e no guidance om he da a. In he EPS09 analysis [7] he a ios Ro pa on
densi ies in a bound p o on inside a nucleus o e ha in a ee p o on we e pa ame ized wi h a
piecewise unc ion,
REPS09(x) = 




a0+(a1+a2x)(e−x−e−xa),x≤xa
b0+b1x+b2x2+b3x3,xa≤x≤xe
c0+(c1−c2x)(1−x)−β,xe≤x≤1
.(2.1)
1
PoS(DIS2016)276
nPDF cons ain s om he LHeC Ilkka Helenius
This unc ional o m does no allow much eedom o he small-xbeha iou , as shown in he le -
hand panel o Figu e 1— he unc ion a small xis mono onic. Theo e ically, his kind o beha iou
appea s easonable bu since global i s should a he indica e he unce ain y o igina ing om he
used da a, a mo e lexible o m should be used o s udy he ealis ic po en ial o he LHeC. The
small-x o m used in his s udy is
R(x≤xa) = a0+a1(x−xa)2+√x(xa−x)a2logx
xa+a3log2x
xa+a4log3x
xa,(2.2)
which p o ides much mo e eedom o he small-xbeha iou educing he bias due o he ansa z
signi ican ly. This is illus a ed in he igh -hand panel o Figu e 1, showing he R(x<xa,Q2
0)wi h
a ew di e en possible pa ame e alues.
Figu e 1: The i unc ion beha iou om he EPS09-s yle ansa z (le ) and om he new ansa z wi h mo e
eedom a small alues o xused in his s udy ( igh ).
To ha e a mo e ealis ic es ima e o he cu en unce ain ies, a new baseline i was pe -
o med. The se up o he baseline i was e y simila as in he EPS09 analysis, bu now including
he mo e lexible o m om Eq. (2.2) a low x. The new baseline i e lec s he lack o con ol
a small alues o x om he da a by p o iding as ly la ge unce ain ies han he o iginal EPS09
analysis, as shown in Figu e 2, e en hough he da a cons ain s a e he same.
3. Fi o pseudoda a
The impac o he LHeC pseudoda a on he nPDF unce ain ies was s udied by pe o ming
a new nPDF analysis using pseudoda a gene a ed acco ding o LHeC expec a ions, bu o he wise
keeping he de ails as in he baseline i . The pseudoda a we e gene a ed o neu al cu en (NC)
DIS assuming pe -nucleon luminosi ies Lep =10 b and LePb =1 b. The kinema ical window
s udied was 10−5<x<1 and 2 <Q2<105GeV2and he da a we e based on he EPS09 nPDFs,
including also ealis ic luc ua ions wi h he ci ed luminosi ies [11]. A compa ison be ween he
baseline i and he gene a ed pseudoda a is shown in Figu e 3displaying a ios o educed c oss
sec ions be ween e-Pb and e-p collisions. Figu e 3shows also he co esponding compa ison a e
including he pseudoda a in o he i . A d as ic educ ion o he nPDF unce ain ies is obse ed
once he pseudoda a a e included o he analysis.
2
PoS(DIS2016)276
nPDF cons ain s om he LHeC Ilkka Helenius
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
10-5 10-4 10-3 10-2 10-1
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
10-5 10-4 10-3 10-2 10-1
EPS09
EPS09 EPS09
x
R alence
(Pb)
x
Rsea
(Pb)
x
Rgluon
(Pb)
Ri(x,Q2=1.69 GeV2)
Pb
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
10-5 10-4 10-3 10-2 10-1
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
10-5 10-4 10-3 10-2 10-1
EPS09 EPS09 EPS09
x
R alence
(Pb)
x
Rsea
(Pb)
x
Rgluon
(Pb)
Ri(x,Q2=10 GeV2)
Pb
Figu e 2: The nPDF modi ica ions o alence (le ) and sea (middle) qua ks, and gluons ( igh ) a
Q2=1.69 GeV2(uppe panels) and Q2=10 GeV2(lowe panels). The dashed lines show he unce ain y
acco ding o he EPS09 analysis and he colou band he esul o he new baseline i wi h he mo e lexible
low-xpa ame iza ion.
To s udy he imp o emen s in mo e de ail, Figu e 4compa es he nPDF unce ain ies o
alence qua ks, sea qua ks and gluons om he baseline i and om he new i including also
he pseudoda a. The la ge-x alence qua ks a e al eady well cons ained by he cu en da a bu
he imp o emen is signi ican o he small-xsea qua ks and gluons. Imp o emen like his would
subs an ially solidi y he pQCD baseline o he hea y-ion physics a he LHC, and also a he FCC,
al eady om pT∼3 GeV/c on.
4. Summa y
The impac o he NC DIS da a om he LHeC o he nPDFs has been s udied. To ob ain
a mo e ealis ic es ima es han he p esen nPDF unce ain ies, a new baseline i was pe o med
applying a mo e lexible o m o he small-xbeha iou ha is included in he cu en i s. Due o
he new pa ame iza ion, he baseline analysis possesses signi ican ly la ge small-xunce ain ies
han he cu en public analyses. A se o pseudoda a was gene a ed acco ding o he expec ed
LHeC speci ica ions, and a new i including he pseudoda a was pe o med and he unce ain ies
we e compa ed o he baseline i wi hou he pseudoda a. The esul s show a subs an ial educ ion
o small-xunce ain ies o sea qua ks and gluons, imp o ing he accu acy o pQCD baseline o
hea y-ion collisions in he kinema ic egion ele an o he LHC and he FCC.
Acknowledgmen s
This esea ch was suppo ed by he Eu opean Resea ch Council g an Ho LHC ERC-2011-
3

PoS(DIS2016)276
nPDF cons ain s om he LHeC Ilkka Helenius
0.6
0.8
1.0
1.2
Q2=2GeV2Q2=5GeV2Q2=10GeV2Q2=20GeV2Q2=50GeV2
0.4
0.6
0.8
1.0
1.2
0.4
0.6
0.8
1.0
1.2
10-6 10-4 10-2 1
Q2=100GeV2
10-4 10-2 1
Q2=200GeV2
10-4 10-2 1
Q2=500GeV2
10-4 10-2 1
Q2=1000GeV2
10-4 10-2 1
Q2=2000GeV2
LHeC pseudoda a Baseline i
xxxxx
Ra io o he educed c oss-sec ions
0.6
0.8
1.0
1.2
Q2=2GeV2Q2=5GeV2Q2=10GeV2Q2=20GeV2Q2=50GeV2
0.4
0.6
0.8
1.0
1.2
0.4
0.6
0.8
1.0
1.2
10-6 10-4 10-2 1
Q2=100GeV2
10-4 10-2 1
Q2=200GeV2
10-4 10-2 1
Q2=500GeV2
10-4 10-2 1
Q2=1000GeV2
10-4 10-2 1
Q2=2000GeV2
LHeC pseudoda a LHeC i
xxxxx
Ra io o he educed c oss-sec ions
Figu e 3: Ra ios o he educed NC DIS c oss sec ion be ween e-Pb and e-p collisions. The gene a ed
pseudoda a a e shown wi h ed ma ke s and compa ed o he baseline i (uppe panels) and o a new i
using he LHeC pseudoda a (lowe panels). The i unce ain ies a e shown wi h yellowish colou bands.
S G-279579 and by Xun a de Galicia (Conselle ia de Educacion) — H. P. and N. A. a e pa o he
S a egic Uni AGRUP2015/11. N. A. is suppo ed by he People P og amme (Ma ie Cu ie Ac ions)
o he Eu opean Union Se en h F amewo k P og amme FP7/2007-2013/ unde REA g an ag ee-
men #318921 and Minis e io de Ciencia e Inno aciónn o Spain unde p ojec FPA2014-58293-
C2-1-P. I .H. has been suppo ed by he MCne ITN FP7 Ma ie Cu ie Ini ial T aining Ne wo k,
con ac PITN-GA-2012-315877 and has ecei ed unding om he Eu opean Resea ch Council
(ERC) unde he Eu opean Union Ho izon 2020 esea ch and inno a ion p og amme (g an ag ee-
men No 668679).
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4
PoS(DIS2016)276
nPDF cons ain s om he LHeC Ilkka Helenius
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
0.2
0.6
1.0
1.4
10-5 10-4 10-3 10-2 10-1
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0.2
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x
R alence
(Pb)
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Rsea
(Pb)
x
Rgluon
(Pb)
Ri(x,Q2=1.69 GeV2)
Pb
Baseline LHeC
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10-5 10-4 10-3 10-2 10-1
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R alence
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Rsea
(Pb)
x
Rgluon
(Pb)
Ri(x,Q2=10 GeV2)
Pb
Baseline LHeC
Figu e 4: The nuclea modi ica ion o he PDFs o alence qua ks (le ), sea qua ks (middle) and gluons
( igh ) o wo scales Q2=1.69 GeV2(uppe panels) and Q2=10 GeV2(lowe panels). The baseline i is
shown as yellowish colou bands and he i including also LHeC pseudoda a as da k ed bands.
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5