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Global reanalysis of nuclear PDFs

Kari J. Eskola,Department of Physics, University of Jyväskylä

Helsinki Institute of Physics

hep-ph/0703104, in collaboration withVesa Kolhinen, Hannu Paukkunen, Carlos Salgado

High-pT Physics at LHC, Jyväskylä, 24 March, 2007

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URHIC Theory group at Jyväskylä (JYFL & HIP)

Seniors Vesa Ruuskanen, prof. emer

Kari J. Eskola, prof (1.4.07 – ) Kimmo Tuominen, doc.

Postdocs T. Renk, V. Kolhinen

Graduate studentsT. Kähärä H. Niemi H. Paukkunen

Undergraduate studentsJ. Auvinen M. Heikinheimo T. Karavirta P. Mäkinen

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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 inpendent

DGLAP

Comparison with data at various x & Q

noVary {aj}

{ fi(x) } at Q>Q0

Min(chi2) ?Impose sum rules

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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) [hep-ph/0103208,hep-ph/0404093]

- automated chi2 minimization- uncertainty estimates

3. nDS (de Florian, Sassot) [hep-ph/0311227]

- first NLO global analysis for nPDFs

Global analyses for…

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Goals of our reanalysis, hep-ph/0703104

• Improve the old EKS98 global analysis by

- Automating chi2 minimization (in EKS98 fits done by eye only) - Improve chi2 over EKS98 (difficult...)? - Obtain uncertainty estimates on the EKS98-type nuclear modifications of PDFs

• Study whether DIS&DY data support stronger gluon shadowing -- BRAHMS data would seem to suggest stronger shadowing than in EKS98, HKN, nDS

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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

• As in EKS98, parametrize initial distributions at Q0=1.3 GeV in terms of three different initial modifications Ri(x,Q0) for valence, sea & gluons

• piecewise construction; functional forms simpler than in EKS98

• Sum rules imposed baryon # conservation constrain valence

momentum conservation constrain gluons

The framework = EKS98

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xa

yo

ya

xe

ye

β

xs

A-dependence is in the parameters, e.g. ya=ya(C) (A/12)pya

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No constraints for large-x sea&gluons modifications fix their modifications to that of valence

Lots of manual labour to figure out which parameters are important!

Minimize chi2 for 16 free fit parameters

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The data used

DIS: l+ASLAC-E-139NMC 95, 95re, 96E665

Drell-Yan in p+AE772E866

#datapoints = 514

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DIS; A/C

A-systematics

11DIS; A/D

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Drell Yan in p+A; A/DDY in p+A; A/Be

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

Small-x Q2-dependence nicely reproduced if RG

A(x,Q0) ~1at x~0.03-0.04.

If gluon shadowing at x ~ 0.01is clearly stronger than sea quark shadowing, then log Q-slope of F2(Sn)/F2(C) becomes small or even negative…

Based on the chi2s obtained inglobal analysis, we do not find support for strong gluon shadowing from DIS&DY data.

However… stronger gluon shadowingdoes not lead to much worse overall chi2 – the gluon constraint from current DIS & DY data is not very stringent…

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Comparison with other global analyses: chi2

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Comparison with other global analyses

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Estimated uncertainties on initial modifications (Hessian method, from Minuit):

• analyzed small-x and large-x errors separately• EKS98 works very well new parametrization not needed!• gluon and sea quark shadowings function-form dependent, the uncertainties shown are lower limits stronger gluon shadowing at x<0.03 ?? ( since still Chi2/N<1)

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Support for stronger gluon shadowing from BRAHMS d+Au data?

Next steps for us - include these data in global analysis- NLO analysis

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Extra slides….

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Comparison with other global analyses: log Q2 slopes of F2(Sn)/F2(C)

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