EPS08 An improved global analysis of nuclear PDFs including RHIC data Kari J. Eskola Department of P

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EPS08 - An improved global analysis of nuclear
PDFs including RHIC dataKari J. Eskola
Department of Physics, University of
JyväskyläHelsinki Institute of Physics KJE,
Hannu Paukkunen, Carlos Salgado,arXiv0802.0139
hep-ph
3rd Workshop on High-pT Physics at LHC Tokaj, 16
March, 2008
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Collinear QCD factorization PDFs
Inclusive hard process cross sections in hadronic
and nuclear collisions, e.g. AB ? kl
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
no
Vary aj
Impose sum rules
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• 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,

perturbative
nonperturbative
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Global analyses for

• 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)

• Free proton PDFs CTEQ, MRST, GRV,
• Nuclear PDFs

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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 DISDY 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 xlt0.03 ? -
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 dAu -
forward-rapidity data ? constrained region
extended down to x10-3 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 DISDY data
in a global DGLAP analysis? can a good
global fit still be obtained? can the
nuclear effects be factorized into the nPDFs?
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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/Adp/A, dn/Aup/A
• Similarly to EKS98, parametrize initial
  distributions at Q01.3 GeV
• in terms of three different initial
  modifications Ri(x,Q0)
• valence, sea gluons
• piecewise construction
• Sum rules imposed
• baryon conservation ? constrains mainly
  valence

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EPS08 framework

• A-dependence is in the parameters e.g. yaya(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 (dAltdP)

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• almost no constraints for large-x seagluon
  modifications
• ? fix gluons to valence RV in the EMC-effect
  region
• support from (yet unpublished) PHENIX photon
  data in AuAu
• - Fast DGLAP solver now our own HannuP --
  earlier we used CTEQs
• - 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 lA
(484 points) SLAC-E-139 NMC 95, 95re, 96 EMC -
leave E665 out Drell-Yan in pA
(92) E772 E866 new input RHIC pi and h- in
dAu (51) BRAHMS, fwd PHENIX, mid-rap. STAR,
mid-rap. Include only the region pTgt2 GeV
datapoints 627
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Inclusive single hadron production at high pT
selection of RHIC data
KKP
pQCD
ppbar, pp LO pQCD with K(s) works OK KJE H.
Honkanen, hep-ph/0205048 dAu 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 qTlt 2 GeV from the
global fit
at pTlt 2 GeV too steep slopes - also at NLO FF
uncertainties ?
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New elements in EPS08 improvements in chi2
minimization
usual definition
now define

• 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 snorm
• 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 fN1 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 !

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DY EPS08
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EPS08 and RHIC pion data from dAu good
agreement obtained when the given additional
overall-normalization errors are accounted for
fN ? 1 !
PHENIX snorm10
STAR snorm17
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EPS08 and forward-rapidity negative hadron RHIC
data Good agreement obtained for pTgt2 GeV
BRAHMS snorm5 here fN0
From the EPS08 fit fN1.02 not a big effect
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The EPS08 nuclear effects at the initial scale
Q1.3 GeV
Unconstrained region
Note the strong gluon shadowing!
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
  xgt0.01 to xgt0.001
• 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 pTgt2 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
• - pTlt2 GeV region in hadron production in dAu at
  RHIC still difficult
• ? need FF improvements, impact parameter
  dependent nPDFs,

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• 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 AuAu
• hope to have D production in dAu at RHIC
• hope for a pPb program at LHC, too
• - EPS08 now available at

http//www.jyu.fi/science/laitokset/fysiikka/en/r
esearch/highenergy/urhic/nPDFs

• Gluon shadowing still under debate
• ? use EPS08 parallel with EKS98