3rd Workshop on High-pT Physics at LHC
Tokaj, 16 March, 2008
EPS08 - An improved global analysis
of nuclear PDFs including RHIC data
Kari J. Eskola
Department of Physics, University of Jyväskylä
Helsinki Institute of Physics
KJE, Hannu Paukkunen, Carlos Salgado,
arXiv:0802.0139 [hep-ph]
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Collinear QCD factorization & PDFs
Inclusive hard process cross sections in hadronic and nuclear collisions,
e.g. A+B  k+l + anything (LO below) :
Parton Distribution Functions
• number density distributions (in LO at least)
• universal = process-independent, specific to A and B
• contain nonpertubative input at an initial scale Q02
• obey DGLAP scale evolution equations of pQCD:
Calculable in pQCD
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Global analysis of PDFs
= DGLAP-evolved PDFs
+ constraints from hard pQCD process data
+ constraints from sum rules (momentum, charge, baryon#)
Procedure: iterate until best fit, best set of initial parameters {ai} found
{ fi(x,{aj}) } at Q0,
model independent
Vary {aj}
no
Min(chi2) ?
Impose sum rules
DGLAP
{ fi(x) } at Q>Q0
Comparison with
data at various x & Q 3
Difficulties in extracting nonperturbative input for PDFs at fixed Q02
- data not at one fixed Q2 but correlated in x and Q2
- kinematic ranges & data precision vary from one experiment to another
- how to account for systematic uncertainties, for overall-normalization errors?
- nPDF analysis more complicated than free proton PDFs:
▪ not enough data at small x & perturbative Q2 !
▪ A-dependence [under control], spatial dependence [open question],…
fi/A(x,Q2) =/ fi/p(x,Q2)
perturbative
nonperturbative
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Global analyses for…
Free proton PDFs: CTEQ, MRST, GRV,…
Nuclear PDFs: 1. EKS98 (Eskola, Kolhinen, Ruuskanen, Salgado)
[hep-ph/9802350,hep-ph/9807297]
- 1st global analysis for nPDFs
- very good fits to nuclear DIS & DY data obtained
with sum rules imposed – it works!
2. HKN, HKM (Hirai, Kumano, Nagai, Miyama)
[LO hep-ph/0103208,hep-ph/0404093; HKN_NLO 0709.3038 hep-ph]
- automated chi2 minimization
- first uncertainty estimates for the nPDFs
3. nDS (de Florian, Sassot)
[hep-ph/0311227]
- first NLO global analysis for nPDFs
4. EPS08 (Eskola, Paukkunen, Salgado)
[0802.0139 hep-ph]
- first global analysis with RHIC data included
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EKS98: ▪ pioneering analysis Nucl. Phys. B535 (1998) 351, [hep-ph/9802350]
▪ (x, Q2,A)-dependent modifications; parametrization for general use:
Eur. Phys. J. C9 (1999) 61 [hep-ph/9807297]
gluons
sea
quarks
valence
quarks
Got the Q2-slopes right!
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Last year in the High-pT LHC workshop in Jyväskylä:
- reported uncertainty estimates for EKS98-type of global analysis,
with automated chi2 minimization and DIS&DY data
[EKPS, hep-ph/0703104]
- discussed the need to include RHIC data in the global analysis
valence
sea
gluons
F2(A)/F2(D)
- Need stronger gluon shadowing at x<0.03 ?
- Uncertainty estimates tied to the fit function forms
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Now, for the EPS08
1. Include RHIC high-pT pion & negative-h data from d+Au
- forward-rapidity data  constrained region extended
down to x~10-3
2. Improve the chi2 minimization procedure
- introduce weighting of different data sets
 emphasize the constraints for gluons
- account for given overall normalization errors of the data
3. Answer Q: Can the strong gluon shadowing suggested by
BRAHMS forward data be accommodated together with the
DIS&DY data in a global DGLAP analysis?
= can a good global fit still be obtained?
= can the nuclear effects be factorized into the nPDFs?8
EPS08 framework = similar to EKS98
• Define the PDFs of bound protons w.r.t. the known free proton PDFs:
• PDFs of the bound neutrons from isospin symmetry: un/A=dp/A, dn/A=up/A
• Similarly to EKS98, parametrize initial distributions at Q0=1.3 GeV
in terms of three different initial modifications Ri(x,Q0):
valence, sea & gluons
• piecewise construction:
• Sum rules imposed
baryon # conservation  constrains mainly valence
momentum conservation  constrains mainly gluons
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EPS08 framework
- A-dependence is in the parameters e.g. ya=ya(C) (A/12) p(ya)
- new: more flexible small-x fit function, with no saturation of shadowing
fA/fp ~ x-dA/x-dP 0 when x0 (dA<dP)
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- [almost] no constraints for large-x sea&gluon modifications
 fix gluons to valence RV in the EMC-effect region
[support from (yet unpublished) PHENIX photon data in Au+Au]
- Fast DGLAP solver now our own [HannuP] -- earlier we used CTEQ’s
- Lots of manual labour to figure out which parameters are important [HannuP] !
 Minimize chi2 for 15 free fit parameters
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The data used in EPS08
DIS: l+A
(484 points)
SLAC-E-139
NMC 95, 95re, 96
+ EMC
- leave E665 out
Drell-Yan in p+A
E772
E866
(92)
+ new input
RHIC pi and h- in d+Au (51)
BRAHMS, fwd
PHENIX, mid-rap.
STAR, mid-rap.
Include only the
region pT>2 GeV
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#datapoints = 627
Inclusive single hadron production at high pT: selection of RHIC data
pQCD:
KKP
p+pbar, pp:
LO pQCD with K(s)
works ~OK
[KJE & H. Honkanen,
hep-ph/0205048 ]
d+Au at RHIC:
To avoid the Cronin effect
complications with protons
(assumed to be related to
hadronization), we include
in the EPS08 fit only pion
data, and fwd-rap. h- data
We also exclude the region
qT< 2 GeV from the global fit
at pT< 2 GeV too steep slopes
- also at NLO; FF uncertainties
13 ?
New elements in EPS08 – improvements in chi2 minimization
usual definition
now define
1. Weights wN for data sets N
with these, we emphasize those data sets which provide important
constraints but whose number of data points is small
2. Treatment of the additional overall normalization errors σnorm
given by the experiment – similar procedure used also by CTEQ:
- fN is determined by minimizing the chi2N for each data set N, i.e. for each
parameter-set candidate during the overall chi2 minimization
- ”penalty factor” (…)2 accounts for the fact that fN=1 should be
the optimal value  the normalization given by the experiment
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The results from EPS08
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DIS & EPS08
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Constraints for gluons from
the first 3 panels of
F2(Sn)/F2(C) in DIS
EPS08 has the strongest
gluon shadowing which
still agrees with the F2
Q2-slopes !
>0
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DY & EPS08
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EPS08 and RHIC pion data from d+Au: good agreement obtained when
the given additional overall-normalization errors are accounted for: fN ≠ 1 !
PHENIX
σnorm=10%
STAR
σnorm=17%
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EPS08 and forward-rapidity negative hadron RHIC data:
Good agreement obtained for pT>2 GeV
BRAHMS
σnorm=5%
here fN=0
From the EPS08 fit
fN=1.02
not a big effect
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The EPS08 nuclear effects at the initial scale Q=1.3 GeV
Note the strong gluon shadowing!
Unconstrained
region
Constrained region
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Comparison with earlier global analyses
Much more gluon shadowing in EPS08
-- correspondingly more antishadowing
EKPS
EPS08: chi2/N = 0.71
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Conclusions
- RHIC data now in the global analysis of nPDFs, for the 1st time
- the constrained x-region has been extended from x>0.01 to x>0.001
- chi2 analysis improved by introducing
+ weights for data sets
+ treatment of overall normalization errors
- very good agreement obtained with DIS and DY data,
and also with the pT>2 GeV RHIC pion data at midrapidity
and with h- data at fwd rapidity
 universal nPDFs and factorization seem OK
- treatment of normalization errors led to a good simultaneous
agreement w. PHENIX and STAR pion data
- pT<2 GeV region in hadron production in d+Au at RHIC still difficult
 need FF improvements, impact parameter dependent nPDFs,… 23
- thanks to the weights given to the RHIC data, the EPS08 results
correspond to the strongest shadowing which is still in agreement
with the Q2-slopes of F2 measured at DIS
- gluon shadowing in EPS08 is much stronger than in earlier global
analyses!
- More data needed !
next:
include RHIC photons from Au+Au
hope to have D production in d+Au at RHIC
hope for a p+Pb program at LHC, too
- EPS08 now available at
http://www.jyu.fi/science/laitokset/fysiikka/en/research/highenergy/urhic/nPDFs
- Gluon shadowing still under debate…
 use EPS08 parallel with EKS98
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