The CTEQ Nuclear PDFsTomáš JežoMember of University of Liverpool
in collaboration withA. Kusina, K. Kovařík, F. I. Olness, I. Schienbein, J. Y. Yu, B. Clark,J. Owens, J. Morfín, C. Keppel
Introduction to PDFs
PDF: f(x,Q), x momentum fraction, Q scale
PDF = parton distribuion (density) function
=
describe how nucleons compose of partons
x-dep. not calculable in perturbative QCD
evolution in Q accodring to DGLAP
generalization to nuclei: nuclear PDFs (nPDFs)
Introduction to PDFsNeutrino physics
Collider physics
Nuclear physics
IntroductionNeutrino physics
Introduction to PDFs
small
heavy targets
nPDFs
Introduction to PDFsNuclear physicsnuclear effects
Pauli principleFermi motionMultiple scattering
nuclear correctionsPDFs => nPDFs
hardon collider predictions require PDFs
Introduction to PDFs
Collider physics
data from collisions of nuclei usedalso in free-proton analysis
collisions ... free-proton PDFs
collisions ... nPDFs
Introduction to PDFsNeutrino physics
Collider physicsnPDFs
nPDFs
nPDFs
Nuclear physics
Neutrino-nucleon interactions
Neutrino-nucleon interactions
DIS coss section dominates above a few GeV
[hep-ph/0207172v1]
Deep Inelastic Scattering (DIS)
Goal for this talk
extraction of nPDFs from experiment
estimation of uncertainities
present:
explain:
most recent fit including uncertainities
previous fit including neutrino data
the compatibility of neutrino DIS data with other data sets
Available nuclear PDFs
[PRD 80, 094004 (2009), arXiv: 0907.2357]
framework framework
Data sets
Schematics of Global Analysis
Fit details
Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
χ2
χ0
2
χ0
2+Δχ2
zi
(eigen-vector direction)
Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
results impact of single production data
results comparison with other nPDF fits
results
0.01 0.1 1x
0.80
0.85
0.90
0.95
1.00
1.05
1.10 Q2 =5GeV2
nCTEQ - l AHKN07EPS09
R[F
lA
2]
0.01 0.1 1x
0.80
0.85
0.90
0.95
1.00
1.05
1.10 Q2 =20GeV2
nCTEQ - l AHKN07EPS09
R[F
lA
2]
results production
2 4 6 8 10 12 14 16pT [GeV]
0.7
0.8
0.9
1.0
1.1
1.2
1.3
RdAu
nCTEQ
EPS09NLO
PHENIX 2007 π0
STAR 2010 π0
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
Neutrino DIS
PRELI
MINARY
PRELI
MINARY
when correlated errors taken into account and prefer different nuclear corrections
Summary and outlook
Thank you!Thank you!
Assumptions entering the nuclear PDF analysis
1. Factorization & DGLAP evolution
I allow for definition of universal PDFsI make the formalism predictiveI needed even if it is broken
2. Isospin symmetry
{un/A(x) = dp/A(x)dn/A(x) = up/A(x)
3. x ∈ (0, 1) like in free-proton PDFs [instead of (0, A)]
Then observables OA can be calculated as:
OA = ZOp/A + (A− Z)On/A
With the above assumptions we can use the free proton framework toanalyze nuclear data
2 / 20
nCTEQ results
Nuclear PDFs (Q = 10GeV)
xfPbi (x,Q)
Compare nCTEQ fits:
I with π0 data (violet)
I without π0 data (gray)
10 3 10 2 10 1 1x0
5
10
15
20
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
nCTEQ no PionnCTEQ with Pion
nCTEQ with π0
nCTEQ no π0
PREL
IMIN
ARY
9 / 20
nCTEQ results
Nuclear correction factors(Q = 10GeV)
Ri(Pb) =fPbi (x,Q)
fpi (x,Q)
Compare nCTEQ fits:
I with π0 data (violet)
I without π0 data (gray)
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
=(
,)/
(,
)
nCTEQ no PionnCTEQ with Pion
10 3 10 2 10 1 1x
nCTEQ no PionnCTEQ with Pion
nCTEQ with π0
nCTEQ no π0
PREL
IMIN
ARY
10 / 20
nCTEQ vs. EPS09
nCTEQ
xup/Av (Q0) = x
cu1 (1− x)cu2 e
cu3 x(1 + ecu4 x)
cu5
xdp/Av (Q0) = x
cd1 (1− x)cd2 e
cd3x(1 + ecd4 x)
cd5
cuvk
= cuvk,0
+ cuvk,1
(1− A
−cuvk,2)
cdvk
= cdvk,0
+ cdvk,1
(1− A
−cdvk,2)
EPS09
up/Av (Q0) = Rv(x,A, Z)u(x,Q0)
dp/Av (Q0) = Rv(x,A, Z) d(x,Q0)
Rv =
a0 + (a1 + a2x)(e−x − e−xa ) x ≤ xab0 + b1x + b2x
2 + b3x3 xa ≤ x ≤ xe
c0 + (c1 − c2x)(1− x)−β xe ≤ x ≤ 1
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
(,
)
nCTEQNP14EPS09
10 3 10 2 10 1 1x0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7nCTEQNP14EPS09
nCTEQnCTEQ with const.on uval, dvalEPS09
we set: {cdv1 = cuv1
cdv2 = cuv213 / 20
Variables: DIS of nuclear target eA→ e′X
I DIS variables in case on nucleons
in nucleus
{Q2 ≡ −q2
xA ≡ Q2
2 pA·q
I pA – nucleus momentumI xA ∈ (0, 1) – analog of Bjorken variable
(fraction of the nucleus momentum carried by a nucleon)
I Analogue variables for partons:
I pN = pAA – average nucleon momentum
I xN ≡ Q2
2 pN ·q = AxA – parton momentum fraction withrespect to the avarage nucleon momentum pN
I xN ∈ (0, A) – parton can carry more than the averagenucleon momentum pN .
22 / 20
ee′
q
A X
nCTEQ results
Pion production, ratio
RπdAu =1
2Ad2σdAuπ /dpTdy
d2σppπ /dpTdy
I good data description,however big experimentaluncertainities do not allow forstrong constraints on PDFs
I despite different u-valence &d-valence ratios are similar toEPS09
2 4 6 8 10 12 14 16pT [GeV]
0.7
0.8
0.9
1.0
1.1
1.2
1.3
RdAu
nCTEQ
EPS09NLO
PHENIX 2007 π0
STAR 2010 π0
2 4 6 8 10 12 14 16pT [GeV]
0.7
0.8
0.9
1.0
1.1
1.2
1.3
RdAu
nCTEQ
EPS09NLO
STAR 2006 π+ +π−
31 / 20
20
NuTeV & di-muon
CHORUS
Neutrino DIS cross-section data
� + N � l + X
V
}N X
� l
N = Fe
N = Pb
→ 2310 data points
→ 824 data points
All charged lepton
DIS & Drell-Yan data
→ 708 data points
Challenges in combining the neutrino & charged lepton data
deal with the disparity of number of data points - assigning weights to neutrino data
neutrino DIS data only with 2 heavy nuclei - insufficient to get a reliable A-dependance
do all neutrino data show the different behavior or only NuTeV ?
NEUTRINO DIS
Different neutrino observablesd�
⌫A
dxdQ
2
d�
⌫̄A
dxdQ
2F
⌫+⌫̄2 (x,Q2) xF
⌫+⌫̄3 (x,Q2)vs.& &
Nuclear correction factors we show correction factors defined e.g. as R[F ⌫
2 ] = F ⌫A2 /F ⌫A,free
2
needs theory assumptions to extract
from free proton PDF
23
NEUTRINO DIS NLO QCD calculation of in the ACOT-VFN schemeF ⌫A
2 + F ⌫̄A2
2
comparison of nCTEQ - only neutrino fit against extracted NuTeV data at different Q2
charge lepton fit undershoots low-x data & overshoots mid-x data
low-Q2 and small-x data cause tension with the shadowing observed in charged lepton data
24
NEUTRINO DIS NLO QCD calculation of in the ACOT-VFN schemeF ⌫A
2 + F ⌫̄A2
2
comparison of nCTEQ - only neutrino fit against extracted NuTeV data at different Q2
charge lepton fit undershoots low-x data & overshoots mid-x data
low-Q2 and small-x data cause tension with the shadowing observed in charged lepton data
25
NEUTRINO DIS NLO QCD calculation of in the ACOT-VFN schemeF ⌫A
2 + F ⌫̄A2
2
comparison of nCTEQ - only neutrino fit against extracted NuTeV data at different Q2
charge lepton fit undershoots low-x data & overshoots mid-x data
low-Q2 and small-x data cause tension with the shadowing observed in charged lepton data
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
