1. Measurements of Nuclear Structure Functions at small Bjorken-x with EIC --An extension of Jlab 12 GeV proposal PR10-012 1 Lingyan Zhu Jlab proposal PRL10-012: M. E. Christy, C. E. Keppel, L. Y. Zhu Three related physics measurements at small x: [F 2 ] The nuclear dependence of F 2 scaling violation [R=  L /  T ] The Q 2 and nuclear dependence of R/F L [F L ] F L moments at Q 2 =3.75 GeV 2 4/7/2010EIC e-A WG: Nuclear Chromo- Dynamics Workshop at Argonne

2. Gluon Distribution in Proton 2 Courtesy of the codes downloaded from http://durpdg.dur.ac.uk/hepdata/cteq.html Ref:J. Pumplin, D. R.Stump, J. Huston, H.L. Lai, P. Nadolsky, W,K. Tung, JHEP0207,012,2002 Proton structure composes of singlet (gluons, sea) and non- singlet (valence) distributions At moderate x (~ 0.2), gluon comparable to up quark distributions (valence+sea). The gluon distributions get bigger at smaller Bjorken x. There are currently large uncertainties in gluon distributions, worse with nuclear gluon distributions.

3. A-Dependence of Gluon Distributions 3 Q 2 =3 GeV 2 Courtesy of I. Schienbein & T. Stavreva Ref:Schienbein et al, PRD80,094004(2009) Courtesy of the codes downloaded from http://research.kek.jp/people/kumanos/nuclp.html Ref:Hirai, Kumano and Nagai, PRC76,065207(2007) Large uncertainties in the nuclear dependence of gluon.

4. The scaling violation of F 2 can constrain the gluon 4 Altarelli-Parisi equations in leading order QCD in terms of splitting function P ab (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.

5. World Data for nPDF Fits 5 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)

6. Contribution of NMC Sn/C Data to nPDF 6 PDF Nuclear Corrections for charged and neutral current processes [Ref: I. Schienbein et al, PRD80, 094004, (2009)] 144 Sn/C out of 279 DIS F 2 A /F 2 A’ data, as well as 862 DIS F 2 A /F 2 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

7. Scaling Violation of the Nuclear F 2 ratio 7 Ref:Hirai, Kumano &Nagai, PRC76,065207,2007. NMC Sn/C F 2 ratio HERMES Kr/D F 2 ratio

8. Nuclear F 2 Results from NMC 8 NMC, NPB441(1995)3Data from NMC, NPB481(1996)23 NMC, NPB441(1995)12 A1/A2=119/12=10 A1/A2=40/2=20 A1/A2=6/2=3 NMC Sn/C F 2 ratio is the ONLY data that clearly show the positive lnQ 2 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!

9. VMD approach to the Sn/C data 9 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 Q 2 and diffractive contribution (Pomeron exchange) at high Q 2 can describe the Q 2 dependence of NMC Sn/C very well.

10. EIC Kinematic Coverage 10 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.

11. Projection on F 2 ratio at small x 11 EIC enables us to cover NMC kinematics and connect to Jlab 12 GeV kinematics at y=0.75. Precision of 2% is assumed in cross section ratios.

12. Projection on F 2 ratio at small x 12 It is important to compare the Q 2 dependence between Sn/C and Ca/D data.

13. F L can constrain the gluon distributions 13 Longitudianl structure function F L (x,Q 2 ), which implies R~ At small x, the first integral in the above equation equals to F 2 (2x,Q 2 )/2, the second integral can be approxminated by x/0.4*G(x/0.4)/5.85 for x<0.1. Then for N f =3, 2c=2/3, we have Over the whole x region, F L Moments For n=2 and N f =3 Ref:R. G. Roberts, The structure of the proton, Cambridge University Press,1990

14. Rosenbluth (L/T) Separation 14 Rosenbluth(L/T) Separation Technique: TT  L (slope) Another to fit, used in H1 and ZEUS 1-  At Q/E<<0,  only depends on y~Q 2 /(xs).

15. The Rosenbluth (L/T) Separation 15 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 F 2 extraction at the kinematics where R or F L 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 F L. CERN BCDMS/EMC/NMC: some Rosenbluth data in addition to a lot of precise nuclear ratio data including Sn/C F 2 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.

16. The Q 2 dependence of R 16 RHRH R=0 at Q 2  infinity (Bjorken limit) R=0 at Q 2  0 (Real photon limit) The current measurements of R A - R D difference are at higher Q 2 where R itself is relatively small. PR10-012 propose to measure R with hydrogen and nuclear targets at 0.4<Q 2 <3 GeV 2, where R is not small and the Q 2 dependence is not well-constrained.

17. New H1 data on F L vs Q2 17 Summary of DIS09, arXiv:0908.2194v2 x:0.00005~0.04 Q2:2.5~800 Average R=0.25 or F l =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/F L has the expected Q 2 dependence, i.e. R/F L =0 at Q 2  infinity ?

18. Existing Data on R A -R D and R D -R H 18 Nontrivial R D -R H at small Q 2 <1.5 GeV 2. At a mean Q 2 =10 GeV 2, R Sn -R C =0.040+-0.021+-0.026 NMC, NPB481(1996)23 Q 2 =3.3Q 2 =9.9Q 2 =35.1 Q 2 ~4 E99-118, PRL98(2007)142301

19. Epsilon Span of EIC 19 With constraint of y~Q 2 /(xs) <0.6, the maximum epsilon span is 0.3

20. Projection for R A -R D 20 EIC enables us to measure Q 2 dependence of R A -R D 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.

21. World data on F L for different Q 2 bins 21

22. Projection of F L Measurements at Q 2 =3.75 22 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)

23. Summary 23 Valuable and precise inclusive data in three sets of measurements: [F 2 ] The nuclear dependence of F 2 scaling violation at the kinematics similar to NMC Measurement of F 2 at small x to measure lnQ 2 dependence of Sn/C F 2, and its consistency with other nuclear ratios includng Ca/D. [R=  L /  T ] The Q 2 and nuclear dependence of R/F L Model-independent extraction of R, F L,F 2,F 1 at small Q 2 to see whether R A =R D at Q 2 <1.5 GeV 2 and see any indication of R  0 at small Q 2 [F L ] F L moments at Q 2 =3.75 GeV 2. Model-independent extraction of of R, F L,F 2,F 1 at Q 2 =3.75 GeV 2 to improve the nucleon and nuclear F L and F 2 moments