Measurements of Nuclear Structure Functions at small Bjorken-x with EIC

--An extension of Jlab 12 GeV proposal PR10-012

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Lingyan Zhu

Jlab proposal PRL10-012: M. E. Christy, C. E. Keppel, L. Y. Zhu

Three related physics measurements at small x:[F2 ] The nuclear dependence of F2 scaling violation

[R=L/T] The Q2 and nuclear dependence of R/FL

[FL ] FL moments at Q2 =3.75 GeV2

4/7/2010 EIC e-A WG: Nuclear Chromo-Dynamics Workshop at Argonne

Gluon Distribution in Proton

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Courtesy of the codes downloaded from http://durpdg.dur.ac.uk/hepdata/cteq.htmlRef:J. Pumplin, D. R.Stump, J. Huston, H.L. Lai, P. Nadolsky, W,K. Tung, JHEP0207,012,2002

Proton structure composes of Proton structure composes of singlet (gluons, sea) and non-singlet (gluons, sea) and non-singlet (valence) distributionssinglet (valence) distributions

At moderate x (~ 0.2), gluon At moderate x (~ 0.2), gluon comparable to up quark comparable to up quark distributions (valence+sea).distributions (valence+sea).

The gluon distributions get The gluon distributions get bigger at smaller Bjorken x.bigger at smaller Bjorken x.

There are currently large There are currently large uncertainties in gluon uncertainties in gluon distributions, worse with distributions, worse with nuclear gluon distributions.nuclear gluon distributions.

A-Dependence of Gluon Distributions

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Q2=3 GeV2

Courtesy of I. Schienbein & T. StavrevaRef:Schienbein et al, PRD80,094004(2009)

Courtesy of the codes downloaded from http://research.kek.jp/people/kumanos/nuclp.htmlRef:Hirai, Kumano and Nagai, PRC76,065207(2007)

Large uncertainties in the nuclear dependence of gluon.

The scaling violation of F2 can constrain the gluon

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Altarelli-Parisi equations in leading order QCD in terms of splitting function Pab(z) which determines the probability for a parton b to change to another parton a with reduced momentum by a factor of z after parton radiation.

At small x, the scaling violation is dominated by the contribution from the gluon density. In the leading-order Prytz method for four flavors,

ZEUS,PLB345,576,1995,Extraction of the gluon density of the proton at small x.

World Data for nPDF Fits

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Global study of nuclear structure functions

[Ref: S. A. Kulagin, R. Petti, NPA765, 126, (2006)]

Most of the x < 0.1 DIS data came from NMC.40% of the NMC data are on Sn/C ratio.

Similar stories for other nuclear PDF fits including

[Ref: I. Schienbein et al, PRD80, 094004, (2009)]

[Ref: Eskola, H. Paukkunen, C.A. Salgado,NPA830,599C,2009]

[Ref:M. Hirai, S. Kumano and T.-H. Nagai, PRC76,065207(2007)

Contribution of NMC Sn/C Data to nPDF

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PDF Nuclear Corrections for charged and neutral current processes

[Ref: I. Schienbein et al, PRD80, 094004, (2009)]

144 Sn/C out of 279 DIS F2A/F2

A’ data, as well as 862 DIS F2A/F2

D data, 92 Drell-Yan----12% of the total data points.

EPS09-Global NLO Analysis of Nuclear PDFs and Their Uncertainties

[Ref: Eskola, H. Paukkunen, C.A. Salgado, NPA830,599C,2009]

NMC Sn/C contributes 144/929=16% of the total data and the data x=0.0125 have weighting factors of 10.

Determination of NLO nuclear PDFs and their uncertainties

[Ref:M. Hirai, S. Kumano and T.-H. Nagai, PRC76,065207(2007)

NMC Sn/C contributes 146/1241=12% of the total data

Scaling Violation of the Nuclear F2 ratio

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Ref:Hirai, Kumano &Nagai, PRC76,065207,2007.NMC Sn/C F2 ratio

HERMES Kr/D F2 ratio

Nuclear F2 Results from NMC

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NMC, NPB441(1995)3 Data from NMC, NPB481(1996)23

NMC, NPB441(1995)12

A1/A2=119/12=10A1/A2=40/2=20

A1/A2=6/2=3

• NMC Sn/C F2 ratio is the ONLY data that clearly show the positive lnQ2 dependence. • Due to precision and size of Sn/C data set, it has a major effect in nuclear PDF fits.• Critical need to study / verify this interesting behavior!

VMD approach to the Sn/C data

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Ref: Piller et al, ZPA,352,427(1995); Melnichouk & Thomas, PRC52,3373(1995); Piller & Weise, Phys. Rept. 330,1(2000).

A combination of vector meson dominance(VMD) at low Q2 and diffractive contribution (Pomeron exchange) at high Q2 can describe the Q2 dependence of NMC Sn/C very well.

EIC Kinematic Coverage

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ep mEIC: 11+60 eA mEIC: 3+30/11+30 (0.04<y<0.6)eA eLIC: 11+120 (y=0.6)

EIC connects JLab and HERA kinematic region.

Projection on F2 ratio at small x

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EIC enables us to cover NMC kinematics and connect toJlab 12 GeV kinematics at y=0.75.

Precision of 2% is assumed in cross section ratios.

Projection on F2 ratio at small x

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It is important to compare the Q2 dependence between Sn/C and Ca/D data.

FL can constrain the gluon distributions

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Longitudianl structure function FL (x,Q2) , which implies R~

At small x, the first integral in the above equation equals to F2(2x,Q2)/2, the second integral can be approxminated by x/0.4*G(x/0.4)/5.85 for x<0.1. Then for Nf=3, 2c=2/3, we have

Over the whole x region, FL Moments

For n=2 and Nf=3

Ref:R. G. Roberts, The structure of the proton, Cambridge University Press,1990

Rosenbluth (L/T) Separation

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Rosenbluth(L/T) Separation Technique:

T

L(slope)

Another to fit, used in H1 and ZEUS

1-

At Q/E<<0, only depends on y~Q2/(xs).

The Rosenbluth (L/T) Separation

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Rosenbluth separation works from elastic scatting (form factors ) to DIS (structure functions) . It is also used in semi-inclusive (e,e’) for pion form factor and color transparency measurements.Rosenbluth separation allows a model independent way to measure structure functions. It affects the F2 extraction at the kinematics where R or FL is not negeligible .

Rosenbluth separation requires a wide range of beam energies and spectrometer angles – SLAC, CERN BCDMS/EMC/NMC, JLab, HERA ZEUS/H1,…

SLAC: Except E140X, a re-analysis of different experiments; precise ep and ed data, basis for the world parameterization of R and FL.

CERN BCDMS/EMC/NMC: some Rosenbluth data in addition to a lot of precise nuclear ratio data including Sn/C F2 ratio

Jlab: A lot of data in the resonance region with 6 GeV beam; can be extended with Jlab upgrade.HERA ZEUS/H1 (not HERMES): Variable hadron energy at a few hundred GeV; x is very small.

The Q2 dependence of R

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RHR=0 at Q2infinity (Bjorken limit)R=0 at Q20 (Real photon limit)The current measurements of RA-RD difference are at higher Q2 where R itself is relatively small.

PR10-012 propose to measure R with hydrogen and nuclear targets at 0.4<Q2 <3 GeV2, where R is not small and the Q2 dependence is not well-constrained.

New H1 data on FL vs Q2

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Summary of DIS09, arXiv:0908.2194v2

x:0.00005~0.04Q2:2.5~800

Average R=0.25 or Fl=0.2*F2 from H1; R=0.18(+0.07-0.05) from ZEUS.

Data agree cteq6.6 better than MSTW

Data agree with dipole model

Does R/FL has the expected Q2 dependence, i.e. R/FL=0 at Q2infinity ?

Existing Data on RA-RD and RD-RH

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Nontrivial RD-RH at small Q2<1.5 GeV2.At a mean Q2=10 GeV2,RSn-RC =0.040+-0.021+-0.026

NMC, NPB481(1996)23Q

2 =

3.3

Q2

=9

.9

Q2

=3

5.1

Q2

~4

E99-118, PRL98(2007)142301

Epsilon Span of EIC

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With constraint of y~Q2/(xs) <0.6, the maximum epsilon span is 0.3

Projection for RA-RD

20EIC enables us to measure Q2 dependence of RA-RD at x<0.01, where the x dependence seems to be small based on R1990 fit.

y=0.6 for E=3+30

ys was fixed.

World data on FL for different Q2 bins

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Projection of FL Measurements at Q2=3.75

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The SLAC data excluding e140x did not come from a single optimized experiment.PR10-012 can significantly reduce the uncertainty of the E94-110 data by adding two high points and expanding the coverage.EIC can probe lower x region, which is especially important for the low order moments. However, it requires a wide range of electron and hadron energies.

EIC(E=3+30)+JLab 11 GeV

EIC(E=3+30)+EIC(E=3+5)

EIC(E=3+30)+EIC(E=11+30)

Summary

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Valuable and precise inclusive data in three sets of measurements:[F2 ] The nuclear dependence of F2 scaling violation at the kinematics similar to NMCMeasurement of F2 at small x to measure lnQ2 dependence of Sn/C F2 , and its consistency with other nuclear ratios includng Ca/D. [R=L/T] The Q2 and nuclear dependence of R/FL

Model-independent extraction of R, FL,F2,F1 at small Q2 to see whether RA =RD at Q2 <1.5 GeV2 and see any indication of R0 at small Q2 [FL ] FL moments at Q2 =3.75 GeV2 .

Model-independent extraction of of R, FL,F2,F1 at Q2=3.75 GeV2

to improve the nucleon and nuclear FL and F2 moments