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EPS08 - An improved global analysis of nuclear PDFs including RHIC data

Kari J. Eskola

Department of Physics, University of JyväskyläHelsinki Institute of Physics

KJE, Hannu Paukkunen, Carlos Salgado,arXiv:0802.0139 [hep-ph]

3rd Workshop on High-pT Physics at LHCTokaj, 16 March, 2008

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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 Q0

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• 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

DGLAP

Comparison with data at various x & Q

noVary {aj}

{ fi(x) } at Q>Q0

Min(chi2) ?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

fi/A(x,Q2) = fi/p(x,Q2)/

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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

Global analyses for…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 DIS&DY data [EKPS, hep-ph/0703104]

- discussed the need to include RHIC data in the global analysis

- Need stronger gluon shadowing at x<0.03 ?- Uncertainty estimates tied to the fit function forms

valence sea

F2(A)/F2(D)gluons

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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?

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• 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

EPS08 framework = similar to EKS98

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- 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 x0 (dA<dP)

EPS08 framework

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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-139NMC 95, 95re, 96+ EMC- leave E665 out

Drell-Yan in p+A (92)E772E866

+ new input RHIC pi and h- in d+Au (51)BRAHMS, fwdPHENIX, mid-rap.STAR, mid-rap.Include only theregion pT>2 GeV

#datapoints = 627

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Inclusive single hadron production at high pT: selection of RHIC data

pQCD:

p+pbar, pp:LO pQCD with K(s)works ~OK[KJE & H. Honkanen, hep-ph/0205048 ]

d+Au at RHIC:

KKP

We also exclude the region qT< 2 GeV from the global fit

at pT< 2 GeV too steep slopes- also at NLO; FF uncertainties ?

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

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New elements in EPS08 – improvements in chi2 minimization

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

usual definition

now define

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The results from EPS08

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DIS & EPS08

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EPS08 has the strongestgluon shadowing which still agrees with the F2 Q2-slopes !

Constraints for gluons from the first 3 panels of F2(Sn)/F2(C) in DIS

> 0

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DY & EPS08

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EPS08 and RHIC pion data from d+Au: good agreement obtained whenthe given additional overall-normalization errors are accounted for: fN ≠ 1 !

PHENIXσnorm=10%

STARσnorm=17%

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EPS08 and forward-rapidity negative hadron RHIC data:

Good agreement obtained for pT>2 GeV

From the EPS08 fitfN=1.02not a big effect

BRAHMSσnorm=5%

here fN=0

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The EPS08 nuclear effects at the initial scale Q=1.3 GeV

Note the strong gluon shadowing! Constrained regionUnconstrainedregion

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Comparison with earlier global analyses

Much more gluon shadowing in EPS08-- correspondingly more antishadowing

EPS08: chi2/N = 0.71

EKPS

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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,…

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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 Au+Au

hope to have D production in d+Au at RHIChope 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