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Lingyan Zhu

Lingyan Zhu. Measurements of Nuclear Structure Functions at small Bjorken-x with EIC --An extension of Jlab 12 GeV proposal PR10-012. Jlab proposal PRL10-012: M. E. Christy, C. E. Keppel, L. Y. Zhu Three related physics measurements at small x:

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Lingyan Zhu

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  1. Lingyan Zhu Measurements of Nuclear Structure Functions at small Bjorken-x with EIC--An extension of Jlab 12 GeV proposal PR10-012 • 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=sL/sT] The Q2 and nuclear dependence of R/FL • [FL ] FL moments at Q2 =3.75 GeV2 EIC e-A WG: Nuclear Chromo-Dynamics Workshop at Argonne

  2. Gluon Distribution in Proton 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 Q2=3 GeV2 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 F2 can constrain the gluon • 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.

  5. World Data for nPDF Fits • 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 • 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/F2A’ data, as well as 862 DIS F2A/F2D 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 F2 ratio Ref:Hirai, Kumano &Nagai, PRC76,065207,2007. NMC Sn/C F2 ratio HERMES Kr/D F2 ratio

  8. Nuclear F2 Results from NMC NMC, NPB441(1995)3 Data from NMC, NPB481(1996)23 A1/A2=40/2=20 A1/A2=119/12=10 NMC, NPB441(1995)12 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!

  9. VMD approach to the Sn/C data 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.

  10. EIC Kinematic Coverage eA mEIC: 3+30/11+30 (0.04<y<0.6) eA eLIC: 11+120 (y=0.6) ep mEIC: 11+60 EIC connects JLab and HERA kinematic region.

  11. Projection on F2 ratio at small x 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 F2 ratio at small x It is important to compare the Q2 dependence between Sn/C and Ca/D data.

  13. FL can constrain the gluon distributions Ref:R. G. Roberts, The structure of the proton, Cambridge University Press,1990 • 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

  14. Rosenbluth (L/T) Separation Rosenbluth(L/T) Separation Technique: sT sL(slope) Another to fit, used in H1 and ZEUS 1-e At Q/E<<0, e only depends on y~Q2/(xs).

  15. The Rosenbluth (L/T) Separation • Rosenbluth separation works from elastic scatting (form factors ) to DIS (structure functions) . It is also used in semi-inclusive (e,e’p) 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.

  16. The Q2 dependence of R • R=0 at Q2infinity (Bjorken limit) • R=0 at Q20 (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. RH

  17. New H1 data on FL vs Q2 Summary of DIS09, arXiv:0908.2194v2 x:0.00005~0.04 Q2:2.5~800 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 Q2infinity?

  18. Existing Data on RA-RD and RD-RH NMC, NPB481(1996)23 E99-118, PRL98(2007)142301 Q2 ~4 Q2 =35.1 Q2 =3.3 Q2 =9.9 Nontrivial RD-RH at small Q2<1.5 GeV2. At a mean Q2=10 GeV2, RSn-RC =0.040+-0.021+-0.026

  19. Epsilon Span of EIC With constraint of y~Q2/(xs) <0.6, the maximum epsilon span is 0.3

  20. Projection for RA-RD y=0.6 for E=3+30 ys was fixed. EIC 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.

  21. World data on FL for different Q2 bins

  22. Projection of FL Measurements at Q2=3.75 • 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 e points and expanding the e 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)+EIC(E=11+30) EIC(E=3+30)+JLab 11 GeV EIC(E=3+30)+EIC(E=3+5)

  23. Summary • Valuable and precise inclusive data in three sets of measurements: • [F2 ] The nuclear dependence of F2 scaling violation at the kinematics similar to NMC • Measurement of F2 at small x to measure lnQ2 dependence of Sn/C F2 , and its consistency with other nuclear ratios includng Ca/D. • [R=sL/sT] 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 R0 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

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