tomáš ježo - imperial college londonwascko/nuint14/talks/2.1.3_jezo_20140520.pdf · the cteq...
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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
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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)
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Introduction to PDFsNeutrino physics
Collider physics
Nuclear physics
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IntroductionNeutrino physics
Introduction to PDFs
small
heavy targets
nPDFs
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Introduction to PDFsNuclear physicsnuclear effects
Pauli principleFermi motionMultiple scattering
nuclear correctionsPDFs => nPDFs
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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
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Introduction to PDFsNeutrino physics
Collider physicsnPDFs
nPDFs
nPDFs
Nuclear physics
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Neutrino-nucleon interactions
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Neutrino-nucleon interactions
DIS coss section dominates above a few GeV
[hep-ph/0207172v1]
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Deep Inelastic Scattering (DIS)
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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
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Available nuclear PDFs
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[PRD 80, 094004 (2009), arXiv: 0907.2357]
framework framework
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Data sets
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Schematics of Global Analysis
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Fit details
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Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
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Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
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Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
χ2
χ0
2
χ0
2+Δχ2
zi
(eigen-vector direction)
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Hessian method[JHEP 07 (2002) 012, arXiv: hep-ph/0201195]
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results impact of single production data
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results comparison with other nPDF fits
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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]
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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
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Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
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Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
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Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
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Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
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Neutrino DIS
PRELI
MINARY
PRELI
MINARY
when correlated errors taken into account and prefer different nuclear corrections
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Summary and outlook
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Thank you!Thank you!
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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
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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
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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
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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
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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
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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
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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
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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
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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
![Page 41: Tomáš Ježo - Imperial College Londonwascko/nuint14/talks/2.1.3_jezo_20140520.pdf · The CTEQ Nuclear PDFs Tomáš Ježo Member of University of Liverpool in collaboration with](https://reader030.vdocuments.net/reader030/viewer/2022040913/5e88a2fca8c685408e7ef5af/html5/thumbnails/41.jpg)
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
![Page 42: Tomáš Ježo - Imperial College Londonwascko/nuint14/talks/2.1.3_jezo_20140520.pdf · The CTEQ Nuclear PDFs Tomáš Ježo Member of University of Liverpool in collaboration with](https://reader030.vdocuments.net/reader030/viewer/2022040913/5e88a2fca8c685408e7ef5af/html5/thumbnails/42.jpg)
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
![Page 43: Tomáš Ježo - Imperial College Londonwascko/nuint14/talks/2.1.3_jezo_20140520.pdf · The CTEQ Nuclear PDFs Tomáš Ježo Member of University of Liverpool in collaboration with](https://reader030.vdocuments.net/reader030/viewer/2022040913/5e88a2fca8c685408e7ef5af/html5/thumbnails/43.jpg)
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]
![Page 44: Tomáš Ježo - Imperial College Londonwascko/nuint14/talks/2.1.3_jezo_20140520.pdf · The CTEQ Nuclear PDFs Tomáš Ježo Member of University of Liverpool in collaboration with](https://reader030.vdocuments.net/reader030/viewer/2022040913/5e88a2fca8c685408e7ef5af/html5/thumbnails/44.jpg)
Neutrino DIS[Phys.Rev.Lett. 106(2011) 122301, arXiv: 1012.1178]