Determination of Determination of nuclear PDFs in the EIC eranuclear PDFs in the EIC era

(Status of NPDFs and our requests to EIC experimentalists)(Status of NPDFs and our requests to EIC experimentalists)

Shunzo KumanoShunzo Kumano

High Energy Accelerator Research Organization (KEK) High Energy Accelerator Research Organization (KEK)

Graduate University for Advanced Studies (GUAS)Graduate University for Advanced Studies (GUAS)

October 20, 2009October 20, 2009

Workshop onWorkshop onPhysics at a High Energy Electron Ion Collider

October 19 - 23, 2009, INT, Seattle, USAOctober 19 - 23, 2009, INT, Seattle, USAhttp://www.int.washington.edu/PROGRAMS/09-43w.html

Our nuclear PDF pageOur nuclear PDF pagehttp://research.kek.jp/people/kumanos/nuclp.htmlhttp://research.kek.jp/people/kumanos/nuclp.html

Requested tasks Requested tasks (try to reply in the end of my talk)(try to reply in the end of my talk)

•• What are the "headline" physics issues that could be addressed by a stage-I machine?

•• In which ways can it add to studies performed at Jlab 12 GeV and at RHIC?

•• What are the key processes, cross sections, kinematical regions, event rates?

•• What is the status of the required theoretical tools?

•• What are the machine and detector parameters required to meet these physics goals and to maximize the benefit for the high energy EIC?

Physics case for a "stage-I" electron-ion collider (EIC): polarized 2-5 GeV electrons 250 GeV polarized protons or 100 GeV/nucleon light and heavy ions.

KinematicsKinematics "stage-I" EIC: 2-5 GeV electron 100 (250) GeV nucleon

x Q2

2 pq

Q2

y2 pk

Q2

ys, y

pqpk

s 4Ee EN 800 ~ 2000 GeV2 , ( s 28.3 ~ 44.7 GeV), Q2 1 GeV2

x 1

y(800 ~ 2000)

1

y(0.0005 ~ 0.0012) ~ 10 3

x

1

10

100

500

0.001 0.01 0.1 1

Q2 (

GeV

2 )

2 )

NMC (F2A /F2

D)

SLAC

EMC

E665

BCDMS

HERMES

NMC (F2A /F2

A')

E772/E886 DY

F2 & Drell-Yan datafor nuclei

Stage-I EIC coverageStage-I EIC coverage

Our requests:Our requests:

• • Accurate measurements ofAccurate measurements of QQ22 dependence of dependence of FF22

AA / / FF22

DD..

• • FFLLAA measurements. measurements.

Accurate gluon distributions Accurate gluon distributions in nuclei!in nuclei!

ContentsContents

1.1. Introduction Introduction

• Motivations• Motivations

• • Typical data for modifications in Typical data for modifications in FF22 and Drell-Yan and Drell-Yan

2. PDFs in the nucleon2. PDFs in the nucleon

• • A recent global analysis A recent global analysis (just a brief explanation)(just a brief explanation)

3. Determination of PDFs in nuclei3. Determination of PDFs in nuclei

• • Recent global analysesRecent global analyses

Comparisons of various analysis resultsComparisons of various analysis results

• • Difficulty in determining gluon modifications Difficulty in determining gluon modifications

4. Summary4. Summary

IntroductionIntroduction

Motivations for studying parton distribution functionsMotivations for studying parton distribution functions

(1)(1) To establish QCDTo establish QCD

Perturbative QCDPerturbative QCD • In principle, theoretically established in many processes. (There are still issues on small-x physics.)

• Experimentally confirmed (unpolarized, polarised ?)

Non-perturbative QCD (PDFs)Non-perturbative QCD (PDFs) • Theoretical models: Bag, Soliton, … (It is important that we have intuitive pictures of the nucleon.)

• Lattice QCD

Theoretical non-pQCD calculations are not accurate enough.

Determination of the PDFs from experimental data. Determination of the PDFs from experimental data.

(2) For discussing any high-energy reactions, accurate PDFs(2) For discussing any high-energy reactions, accurate PDFs are needed.are needed.

origin of nucleon spin:origin of nucleon spin: quark- and gluon-spin quark- and gluon-spin

contributionscontributions

exotic events at large Qexotic events at large Q22:: physics of beyond current physics of beyond current

frameworkframework

heavy-ion reactions:heavy-ion reactions: quark-hadron matter quark-hadron matter

neutrino oscillations: neutrino oscillations: nuclear effects in nuclear effects in + + 1616O O

cosmology: cosmology: ultra-high-energy cosmic raysultra-high-energy cosmic rays

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

x

EMC

NMC

E139

E665

JLab

JLab

(W2 > 3 GeV2)

(W2 < 3 GeV2)

Nuclear binding

(+ Nucleon modification)

Fermi motionof the nucleon

Nuclear modifications of structure function Nuclear modifications of structure function FF22

Shadowing

Anti-shadowing

Drell-Yan and Antiquark DistributionsDrell-Yan and Antiquark Distributions

DYpCa

DYpD

qCa

q D

The Fermilab E772 Drell-Yan data suggested that nuclearmodification of antiquark distributions should be smallin the region, x≈0.1.

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

x

E772

Drell-Yan cross-section ratiois roughly equal to antiquark ratio.

p A X

Recent Global Analysis forRecent Global Analysis for

Parton Distribution FunctionsParton Distribution Functions

in the Nucleonin the Nucleon

J. Blümlein’s talkat this workshop

Recent papers on unpolarized PDFsCTEQ (uncertainties) D. Stump (J. Pumplin) et al., Phys. Rev. D65 (2001) 14012 & 14013. (CTEQ6) D. Pumplin et al., JHEP, 0207 (2002) 012; 0506 (2005) 080; 0602 (2006) 032; 0702 (2007) 053; PRD78 (2008) 013004. (charm) PR D75 (2007) 054029; (strange) PRL 93 (2004) 041802; Eur. Phys. J. C40 (2005) 145; JHEP 0704 (2007) 089.

GRV (GRV98) M. Glück, E. Reya, and A. Vogt, Eur. Phys. J. C5 (1998) 461. (GJR08) M. Glück, P. Jimenez-Delgado, and E. Reya, Eur. Phys. J. C53 (2008) 355.

MRST A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, (MRST2001, 2002, 20033) Eur. Phys. J. C23 (2002) 73; Eur. Phys. J. C28 (2003) 455; (theoretical errors) Eur. Phys. J. C35 (2004) 325; (2004) PL B604 (2004) 61; (QED) Eur. Phys. J. C39 (2005) 155; PL B636 (2006) 259; (2006) PRD73 (2006) 054019; PL B652 (2007) 292. (2009) Eur. Phys. J. C63 (2009) 189.

Alekhin S. I. Alekhin, PRD68 (2003) 014002; D74 (2006) 054033.

BB J. Blümlein and H. Böttcher, Nucl. Phys. B774 (2007) 182-207. S. Alekhin, J. Blumlein, S. Klein, S. Moch, arXiv:0908.2766 [hep-ph].

NNPDF S. Forte et al., JHEP 0205 (2002) 062; 0503 (2005) 080; 0703 (2007) 039.

H1 C. Adloff et al., Eur. Phys. J. C 21 (2001) 33; C30 (2003) 1.

ZEUS S. Chekanov et al., PRD67 (2003) 012007; Eur. Phys. J. C42 (2005) 1.

It is likely that I miss some papers!

Recent activities uncertainties NNLO QED s – s charm for LHC

Recent upgrades.

Parton distribution functions are determined by fitting various experimental data.

electron/muon: p X

neutrino: p X

Drell-Yan: p p X

(1) assume functional form of PDFs at fixed Q2 (Q02 ) :

e.g. fi (x,Q02 ) Aix

i (1 x)i (1 ix),

where i uv , dv , u, d , s , g

(2) calculate observables at their experimental Q2 points.

(3) then, the parameters Ai , i , i , i are determined so as

to minimize 2 in comparison with data.

Recent improvements on data setRecent improvements on data set

A. D. Martin, W. J. Stirling, R. S. Thorne,

and G. Watt, Eur. Phys. J. C63 (2009) 189.

HERAHERA

TevatronTevatron

F2 and F3 for charged-current deep-inelastic processes

e p e X and e p e X

(u, d at large x without nuclear corrections in Fe)

F2cc : Heavy-quark production

(c, g at x ~ 0.001 by g cc )

Inclusive jet (g at 0.01 x 0.1)

FL (some constraint on g)

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ǙDZÇÃÉsÉNÉ`ÉÉǾå©ÇÈǞǽDžÇÕïKóvÇ ÇÅB

NuTeVNuTeVCHORASCHORAS

HERAHERA

TevatronTevatron

NuTeV, CHORASNuTeV, CHORAS Neutrino F2 and F3 by CHORUS (Pb) and NuTeV (Fe)

(Flavor decomposion of quarks at 0.01 x 0.5, s s )

W , Z productions

(q at large x 0.05 with a different weight than DIS,

large Q2 )

Jet production

(g (and q) at 0.01 x 0.1)

MSTW-2008MSTW-2008 A. D. Martin, W. J. Stirling, R. S. Thorne,and G. Watt, Eur. Phys. J. C63 (2009) 189.

Functional form: Q02 1 GeV2

xuv (x) Aux1 (1 x)2 (1 u x ux), xdv (x) Ad x3 (1 x)4 (1 d x d x)

xS(x) ASxS (1 x)S (1 S x Sx), x d (x) u(x) Ax (1 x)S 2 (1x x2 )

xg(x) Agx g (1 x)g (1 g x gx) Agx g (1 x) g

x s(x) s (x) AxS (1 x) (1 S x Sx), x s(x) s (x) A x (1 x) (1 x / x0 )

uv dv

g s s

u d

Gluon distributionsGluon distributions (MSTW)(MSTW)

Large x

Small x

Longitudinal structure function FL

Gluon distributions still have large uncertainties at small- and large-x regions.

Determination of Nuclear Determination of Nuclear

Parton Distribution FunctionsParton Distribution Functions

Recent global analyses on nuclear PDFsRecent global analyses on nuclear PDFs

See also L. Frankfurt, V. Guzey, and M. Strikman, Phys. Rev. D 71 (2005) 054001;L. Frankfurt, V. Guzey, and M. Strikman, Phys. Rev. D 71 (2005) 054001; S. A. Kulagin and R. Petti, Phys. Rev. D 76 (2007) 094023.S. A. Kulagin and R. Petti, Phys. Rev. D 76 (2007) 094023.

– EPS09EPS09 • K. J. Eskola, H. Paukkunen, and C. A. Salgado, JHEP 04 (2009) 065. K. J. Eskola, H. Paukkunen, and C. A. Salgado, JHEP 04 (2009) 065. • Charged-lepton DIS, DY, Charged-lepton DIS, DY, 00 production in production in dAu.dAu.

– SYKMOO08SYKMOO08• I. Schienbein, J. Y. Yu, C. Keppel, J. G. Morfin, F. I. Olness, I. Schienbein, J. Y. Yu, C. Keppel, J. G. Morfin, F. I. Olness, and J. F. Owens, Phys. Rev. D 77 (2008) 044013.and J. F. Owens, Phys. Rev. D 77 (2008) 044013.• Neutrino DIS (only NuTeV data).Neutrino DIS (only NuTeV data).

– HKN07HKN07• M. Hirai, S. Kumano, and T. -H. Nagai, Phys. Rev. C 76 (2007) 065207.M. Hirai, S. Kumano, and T. -H. Nagai, Phys. Rev. C 76 (2007) 065207.• Charged-lepton DIS, DY.Charged-lepton DIS, DY.

– DS04DS04• D. de Florian and R. Sassot, Phys. Rev. D 69 (2004) 074028.D. de Florian and R. Sassot, Phys. Rev. D 69 (2004) 074028.• Charged-lepton DIS, DY.Charged-lepton DIS, DY.

It is likely that I miss some papers!

Q2 evolution by the DGLAP equation

Supply the initial nuclear PDFs fi (x) at the initial scale Q02 .

No unique functional form.

The nuclear PDFs should satisfy the following conservations.

Baryon number: A uvA(x) dv

A(x) dx 3A

Charge: A2

3uv

A(x) 1

3dv

A(x)

dx Z

Momentum: A xfiA(x)dx A

iq,q , g (Note: NPDFs are defined the ones per nucleon.)

Three parameters are fiex by these conditions.

The distributions are neglected in the region 1 x A.

No DIS data.

Small contributions from this region.

Uncertainty estimation by the Hessian method

HKN07, SYKMOO08, EPS09

Global nuclear PDF analysisGlobal nuclear PDF analysis

0xA Q2

2MA1.

xA Q2

2MA

MN

MA

Q2

2MN;

1

Ax 1

0x% A for a nucleus

• Charged-lepton DIS, DY 0.005 < x < 0.8, 1 < Q2 < 113 GeV2

• 0 production from d-Au collision

• Neutrino DIS (NuTeV/CCFR): 0.015 < x < 0.75

Analysis results: total 2 / d.o.f. (# of parameter)– EPS09: 0.80 (17)– HKN07: 1.21 (12)– DS06: 0.80 (18)– SYKMOO08-A: 1.37 [data]

Data set for nuclear PDF analysesData set for nuclear PDF analyses

HKN07, PRC 76 HKN07, PRC 76 (2007) 065207.(2007) 065207.

Functional form of initial distributions at Functional form of initial distributions at QQ0022

Initial nuclear PDFs at

fiA(x)

1

AZ fi

p / A(x) (A Z) fin / A(x) fi

N / A(x) : PDF of bound nucleon in the nucleus

Isospin symmetry is assumed: u d n u p , d un d p

Functional forms EPS09 (Q0

2 = 1.69 GeV2 )

fiN / A(x) Ri

A(x) fiCTEQ6.1M (x,Q0

2 ), RiA(x)

a0 (a1 a2x)[exp( x) exp( xa )] (x xa : shadowing)

b0 b1x b2x2 b3x3 (xa x xe : antishadowing)

c0 (c1 c2x)(1 x) (xe x 1 : EMC&Fermi)

SYKMOO08 (Q02

= 1.69 GeV2 )

xfiN / A(x)

A0x A1 (1 x)A2 eA3 x (1 eA4 x)A5 : i uv , dv , g,u d ,s, s

A0x A1 (1 x)A2 (1 A3x)(1 x)A4 : i d / u

DS04 (Q02

= 0.4 GeV2 )

fi

N / A

(xN

) dy

yW

i( y, A, Z) f

i

Nx

N

y, Q

0

2

x

A

,

Wv( y, A, Z) a

v (1 Ú

v y) (1 a

v) (1 Ú

v ' y) n

v

y

A v

1 y

A v

ns

y

A s

1 y

A s

Ws , g

( y, A, Z) A (1 y) a

s , g

Ns , g

y

A s , g

1 y

A s , g

HKN07 (Q02

= 1 GeV2 )

fiA(x) wi (x, A, Z)

1

AZ fa

p (x) (A Z) fan (x) , wi (x, A, Z) 1 1

1

A1/ 3

ai bix cix2 dix

3

(1 x)0.1

0.7

0.8

0.9

1

1.1

1.2

0.03 0.1 1

x

E772

Q2= 50 GeV

2

LO

NLO

H H

H

HHHH

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

F2C

a/F

2D

x

EMC

NMC

H E136

E665

Q2= 10 GeV

2

Comparison with FComparison with F22CaCa/F/F22

DD & & DYDYpCapCa/ / DYDY

pDpD data data

(R(Rexpexp-R-Rtheotheo)/R)/Rtheo theo at the same Qat the same Q22 points points R= FR= F22CaCa/F/F22

DD, , DYDYpCapCa/ / DYDY

pDpD

H H H H HHHF FF

FF

-0.2

0

0.2

0.001 0.01 0.1 1

x

EMC

NMC

H E139

F E665

-0.2

0

0.2

x

E772

NLO analysisNLO analysisLO analysisLO analysis

QQ22 dependence dependence

0.75

0.8

0.85

0.9

0.95

0.8

0.85

0.9

0.95

1x = 0.01

0.95

1

1.05

1.1

1.15

1 10 1000.8

0.85

0.9

0.95

1

1 10 100

x = 0.1 x = 0.7

Q2 (GeV2) Q2 (GeV2)

LO

x = 0.001

NLO

Only NLO uncertainty bands are shown.Only NLO uncertainty bands are shown.

0.8

1

1.2

x=0.035 x=0.045

HERMES

x=0.055

0.8

1

1.2x=0.07

x=0.09 x=0.125

0.8

1

1.2

1 10

x=0.175

1 10

x=0.25

1 10

x=0.35

Q2 ( GeV2 )

The differences between LO and NLO The differences between LO and NLO become obvious only at small become obvious only at small xx..

• Experimental data are not accurate enough to find the differences.

Determination of gluon distributions (NLO terms) is not possible.

• The uncertainties become smaller in NLO at small x.

Nuclear PDFsNuclear PDFs

0.6

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1x

0.6

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1x

D

4He

Li

Be

C

N

Al

Ca

Fe

Cu

Kr

Ag

Sn

Xe

W

Au

Pb

0.6

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1x

0.6

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1x

Wdv

Q2 = 1 GeV2

Wuv

Q2 = 1 GeV2

Q2 = 1 GeV2 Q2 = 1 GeV2

WgW q

HKN07 results HKN07 results and future experimentsand future experiments

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1

x

LO

NLO

uv

Q 2 = 1 GeV

2

JLab

FactoryMINARA

0.4

0.6

0.8

1

1.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1

x

q

gluon

FermilabJ-PARC

RHICLHC

RHICLHC

FermilabJ-PARCGSI

EIC

HKN07, PRC 76 (2007) 065207.HKN07, PRC 76 (2007) 065207.EIC

EPS09 (K. J. Eskola et al.), JHEP 04 (2009) 065

Comparison of nuclear PDFsComparison of nuclear PDFs

Different analysis results are consistent with each otherbecause they are roughly within uncertainty bands.

Valence quark: Well determined except at small x.

Antiquark: Determined at small x, Large uncertainties at medium and large x.

Gluon: Large uncertainties in the whole-x region.

Valence Sea Gluon

Q2 1.69 GeV2

Q2 100 GeV2

EPS09

HKN07

DS04

Why is it so difficultWhy is it so difficultto determine to determine

nuclear gluon distributions?nuclear gluon distributions?

Current nuclear data areCurrent nuclear data arekinematically limited.kinematically limited.

x

Q2

2pq;Q2

ys

fixed target: min(x) Q2

2M NElepton

1

2Elepton (GeV)

if Q2 1 GeV2

for Elepton (NMC) 200 GeV, min(x) 1

22000.003

(from H1 and ZEUS, hep-ex/0502008)

F2 datafor the proton

x

1

10

100

500

0.001 0.01 0.1 1

Q2 (

GeV

2 )

2 )

NMC (F2A /F2

D)

SLAC

EMC

E665

BCDMS

HERMES

NMC (F2A /F2

A')

E772/E886 DY

F2 & Drell-Yan datafor nuclei

region of nuclear data

x 0.65

x0.013

x0.0005

Scaling violation and Gluon distributionsScaling violation and Gluon distributions

at small x

F2

lnQ2 20 s

27xg

0.811.20.811.20.811.2110110HERMES110x=0.035x=0.045x=0.055x=0.07x=0.09x=0.125x=0.175x=0.25x=0.35Q2 ( GeV2 )

0.8

1

1.2

1 10 100 1 10 100

x=0.035 x=0.045

Q2 ( GeV2 )

HERMES

x=0.055

0.8

1

1.2

0.8

1

1.2

NMC

x=0.0125 x=0.0175 x=0.025

x=0.035 x=0.045 x=0.055

No experimental consensus ofQ2 dependence! gA(x) determination is difficult.

logQ2

qi(x,Q2 )

s

2dy

y

x

1

Pqiq j (x / y) q j(y,Q2 )

j Pqg (x / y) g(y,Q2 )

dominant term at small xqi qi qi

Q2 dependence of F2 is proportionalto the gluon distribution.

K. Prytz, PLB 311 (1993) 286.

Summary ISummary I

Nuclear PDFsNuclear PDFs

Valence quark:Valence quark: Well determined except at small Well determined except at small x.x.

Antiquark:Antiquark: Determined at small Determined at small xx, Large uncertainties at medium and large , Large uncertainties at medium and large xx..

Gluon:Gluon: Large uncertainties in the whole- Large uncertainties in the whole-xx region region

The antiquark modifications at medium x should be clarified by Fermilab-P906The antiquark modifications at medium x should be clarified by Fermilab-P906

and other hadron-beam projects (J-PARC?).and other hadron-beam projects (J-PARC?).

EIC can contribute to determination of gluon shadowing at x~10EIC can contribute to determination of gluon shadowing at x~10––33..

Summary II: Summary II: Short reply to the requestsShort reply to the requests

•• What are the "headline" physics issues that could be addressed by a stage-I machine? Determination of gluon shadowing.Determination of gluon shadowing.

•• In which ways can it add to studies performed at Jlab 12 GeV and at RHIC? ggAA((xx ~~ 1010–3–3) cannot be determined at both facilities. ) cannot be determined at both facilities. (RHIC forward?)(RHIC forward?)

•• What are the key processes, cross sections, kinematical regions, event rates? Accurate Accurate QQ22 dependence measurements of dependence measurements of FF22

AA / / FF22DD..

FFLLA A measurements, …measurements, …

•• What is the status of the required theoretical tools? Theoretical tools (pQCD) are well established at NLO (even NNLO).Theoretical tools (pQCD) are well established at NLO (even NNLO). There may be an issue of standard DGLAP evolution at small There may be an issue of standard DGLAP evolution at small xx..

•• What are the machine and detector parameters required to meet these physics goals and to maximize the benefit for the high energy EIC? ? ?

"stage-I" EIC: 2-5 GeV electrons 250 GeV protons or 100 GeV/nucleon ions

The EndThe End

The EndThe End