Simona Malace (contact/spokesperson) Jefferson Lab

1. Precision Measurements and Studies of Possible Nuclear Medium Modifications of and of Separated Structure Functions F1, FL, F2 SimonaMalace (contact/spokesperson) Jefferson Lab Spokespeople: D. Gaskell, C. Keppel, E. Christy, P. Solvignon Joint Hall A/C Summer Meeting, June 5-6 2014

2. Outline Electron – proton scattering formalism  The Parton Model and Structure Functions  The QCD Parton Model: Parton Distributions Functions (PDFs)  Nuclear Parton Distribution Functions (nPDFs)  Structure Functions from Experiment: Rosenbluth L/T separations Proposal: Motivation and Proposed Measurements  Experimental Status of Rosenbluth L/Ts in DIS  R and FL on proton  R in nuclei: to what degree is R modified by the nuclear medium?  How large of a nuclear medium modification of R is “significant”?  Proposed measurements and their impact  Beam time request

3. Formalism: Electron-Proton Scattering • Electron-nucleon scattering: we probe the nucleon inner structure of quarks and gluons Lorentz invariant kinematics: Lorentz invariant cross section: Electromagnetic structure function = Pure magnetic structure function: reflects the probability of photoabsorption of transversely (helicity +/- 1) polarized virtual photons Natural basis: F1(T) (transversely polarized virtual photon) and FL (longitudinally polarized virtual photon)

4. Formalism: The Parton Model • Electron-nucleon scattering: zero order approximation = incoherent elastic scattering off spin ½ “quasi-free” quarks inside the proton (Infinite Momentum Frame) Elastic electron-quark scattering cross section: elementary differential cross section reflecting the interaction probability between an electron and a quark carrying a fraction x of the proton momentum Assume there are q(x)dx quarks of type q within a proton with momenta between x and x+dx Electron-proton scattering cross section: Bjorken Scaling FL(x) = 0

5. Formalism: Corrections to the Parton Model • QCD corrections to Quark-Parton Model: Bjorkenscaling violations ln()+… leading twist higher twists splitting functions • Perturbative logarithmic corrections (leading twist) - the struck quark sits in a sea of quark-antiquark pairs and of gluons • Non-perturbative (1/Q2)n corrections (higher twist) - the struck quark communicates with the other valence quarks via gluon exchange (specific to the resonance and elastic regimes); contribution from these corrections is suppressed at high Q2

6. Formalism: The QCD Parton Model • QCD Parton Model: leading twist perturbative calculation via the factorization theorem IR safehard scattering cross sections calculable in pQCD (currently to NNLO in the expansion) Parton Distribution Functions (PDFs): IR singular (contain all collinear and soft singularities) but process independent - universal PDFs scale (m) transformation controlled by the pQCD evolution equation (DGLAP) ()(’,) m

7. Formalism: The QCD Parton Model • QCD Parton Model: leading twist perturbative calculation via the factorization theorem ()(’,) From theory:  the hard scattering cross sections  the evolution kernel to calculate the scale dependence of the PDFs  educated guess for the PDFs x functional form at some scale m = Q0 – f(x,Q0) = A0xA1(1-x)A2P(x) From data:  cross sections (or structure functions) over a wide kinematic phase space:

8. Formalism: The Nucleon Structure in QCD • Global QCD analyses: universal PDFshave been extracted from global QCD analyses and the pQCD Q2 evolution has been verified by experiment to high degree of accuracy We have a theory with predictive power • We can verify QCD sum rules; make precision determinations of as • We can predict cross sections for both SM and New Physics at any energy • PDFs become input for searches of new physics Higgs production at LHC dominated by the “gluon-gluon fusion” pQCD prediction (2013) gluon, as induced uncertainty

9. Formalism: Nuclear PDFs • Nuclear PDFs: the free proton framework is typically used to analyze nuclear data in search of process-independent nuclear PDFs (nPDFs) Assumptions: • Factorization • nPDFs obey the same evolution equations and sum rules as free PDFs • Isospin symmetry: • Some collaborations: neglect nuclear modifications in deuterium • ….

10. Formalism: Nuclear PDFs • Nuclear PDFs: the free proton framework is typically used to analyze nuclear data in search of process-independent nuclear PDFs (nPDFs) Example: EPS09 nPDF obeying standard DGLAP Factorization: usual hard scattering cross section free proton PDFs nPDF: Nuclear modifications to the free proton PDFs Data: most constraints from charged lepton scattering DIS (F2A/F2D) but few also from Drell-Yan dilepton production on p+A and from neutral pion production on dAu and pp

11. Nuclear PDFs: EPS09 • Not enough data to allow for an independent extraction of each parton flavor; only 3 distributions: valence, sea, gluons open circles: data on s2A/A/s2D/2 from SLAC

12. Nuclear PDFs: Importance • The collinear factorization framework has been used to extract universal nPDFs by several groups • Most nPDFs extractions rely on experimental constraints from: •  DIS charged lepton scattering e+A/e+D •  Drell-Yan dileptons in p+A/p+d and RHIC d+Au/p+p •  very few use neutrino-nucleus DIS • Whether this framework is applicable to a wider class of processes remains to be verified • Important application of nPDFs: study of the properties of the quark-gluon plasma

13. DIS Structure Functions from Experiment • Technically the separated L and T contributionsto the total cross section are needed to extract F1, FL, F2 transversely longitudinally polarized virtual photon cross sections AND = Example: When transitioning from cross sections to F2 at low Q2 and moderate x, a small change (0.08) in R (~0.2) leads to few % (up to 4) change in F2 [1-] 1-] • RA-RD needed to transition from cross sections to structure functions ratios

14. Formalism: Rosenbluth L/T Separations • The L & T contributions are separated by performing a fit of the reduced cross section dependence with eat fixed x and Q2 slope intercept Requirements for precise L/T extractions: • As many epoints as possible spanning a large interval from 0 to 1 •  as many (E, E’, q) settings as possible • Very good control of point-to-point systematics  1-2 % on the reduced cross section translates into 10-15 % on FL • Most precise, model-independent extractions come from dedicated experiments where all e points have been measured in a short time interval

15. Formalism: RA – RD Extraction • RA – RDandsAT/sDTare extracted by performing a fit of the cross section ratio dependence with e’at fixed x and Q2 Example: extraction from SLAC E140 • R: small quantity (< 1) Even a small RA – RDin absolute value could imply non-negligible nuclear medium modifications of R R = 0.2 x = 0.175, Q2 = 4 GeV2 DR = 0.04  20% effect Phys. Rev. D 86 054009 (2012)

16. DIS Measurements of Rp: HERA • R and FLstructure function are determined in a model independent way from cross section measurements at the same x and Q2 using 3 energies (Ep= 460, 575 and 920 GeV) x = 10-4 – 10-3 At HERA low to intermediate Q2 corresponds to very low x • HERA provided constraints for the gluon PDF: gluon PDF related uncertainty of the pQCD prediction for the Higgs production cross section was ~25% before HERA, after ~5%

17. DIS Measurements of Rp: SLAC and JLab • E140x and E99-118 (L/T dedicated experiments): R is determined in a model independent way from cross section measurements at the same x and Q2 using multiple beam energies

18. Nuclear Dependence of R: Experimental Status • Model-dependent extractions of RA-RD: NMC (DR extracted using Q2 dependent fit at fixed x), HERMES (one beam energy only, assumed RA/RD scales with Q2) • NMC:Phys. Lett. B 294, 120 (1992) Conclusion: DR consistent with zero • NMC:Nucl. Phys. B 481, 23 (1996) DR: positive shift? • HERMES: Phys. Lett. B 567, 339 (2003)

19. Nuclear Dependence of R: Experimental Status • Model-independentextractions of RA-RD: SLAC E140 (DIS) – no Coulomb corrections applied E04-001/E06-109 (Res Region) • Hint from JLab L/T separations on D and Al, C, Cu, Fe in the resonance region: R appears to be modified by the nuclear medium E04-001/E06-109 (Hall C): paper to be submitted for publication within the next month

20. Nuclear Dependence of R in DIS: Experimental Status • Coulomb effects have not been accounted for in the SLAC E140 analysis (correction is non-negligibleat SLAC and JLab kinematics) • Re-analysis of combined data sets from E140 (Fe), E139 (Fe) and Hall C (Cu) at x = 0.5 and Q2 = 4 - 5 GeV2 arXiv:0906:0512 • Coulomb corrections calculated within the Effective Momentum Approximation framework • the e’ dependence of the cross section ratios sA/sD has been fitted to extract RA - RD DR 2s from zero No Coulomb Corrections With Coulomb Corrections

21. Implications of V. Guzey et al., PRC 86 045201 (2012) • The impact of a non-zero DR for the antishadowing regionhas been analyzed “Since the nuclear dependence of R has not as yet been systematically measured, we shall test two assumptions for ∆R…” 1) (Absolute) RA – RD = 0.04 2) (Relative) (RA – RD)/RN = 30% Both assumptions based on NMC RSn – RC Two data sets have been analyzed: • EMC, BCDMS, NMC:e~ 1 • SLAC:e< 1

22. Implications of V. Guzey et al., PRC 86 045201 (2012) • The impact of a non-zero DR for the antishadowing region F2A/F2D F1A/F1D • Antishadowing disappears for F1 ratio, remains for F2 • Antishadowing from longitudinal photons?

23. Implications of EMC effect: A very well measured behaviour like the EMC effect still offers surprises – the tension between low eJLab and high e SLAC data on heavy targets EMC slope – SRC correlation: • The SRC and EMC effect: a common (as yet unknown) origin • SRC: measure of some quantity like local density experienced by a nucleon in a correlated pair which gives rise to the EMC effect However: • If R is A-dependent this interpretation needs revision • Does the correlation between -dREMC/dx and SRC apply the same to F2, F1, FL?

24. Proposal: Central Kinematics • We propose to extract Rp, RD- Rp, RA – RD, forC, Cu, Au, F1, FL, F2in a model independent fashionin a x range from 0.1 to 0.6 and Q2 from 1 to 5 GeV2 • to cover the antishadowing and most of • the EMC effect regions • For each L/T extraction (black stars) we would use: •  both Hall C spectrometers, SHMS and HMS •  up to 6 beam energies: 4 standard (4.4, 6.6, 8.8, 11 GeV) and 2 non-standard (5.5 and 7.7 GeV) •  D, Cu targets for all kinematics shown; H, C, Au at select kinematics • Statistical goal: 0.2 – 0.5% (depending on the target) in a W2 bin of 0.1 GeV2 (E, E’, q)

25. Proposal: Kinematics • SHMS has a large momentum “bite”: we will collect a wealth of data within the spectrometers acceptance • Besides the model-independent L/T separations at the central kinematics, we can perform minimally model-dependent L/Ts within the spectrometers acceptance

26. Proposal: Backgrounds and Corrections Charge-Symmetric Background • Largest contribution 20% (less at most kinematics); the background will be measured with same spectrometer as the signal Pion Background • Upper limits on p/e ratio: < 2% contamination Much smaller at most settings Radiative Corrections • Elastic/quasielstic radiative effects: < 20%; total radiative effects within 40% • To test our understanding of external radiative corrections we will take measurements on a 6% r.l. Cu target at x = 0.25, 0.275 and 0.4 Coulomb Corrections • We will take additional measurementsto constrain/verify Coulomb corrections procedure At fixed ewe expect sAu/sD to scale with Q2, any measured variation would be mostly due to Coulomb corrections

27. Proposal: Impact for Rp • We plan to map the x and Q2 dependence of Rpindependently • Without our proposed measurements very few model-independent, true Rosenbluth L/Ts at low to moderate x and Q2

28. Proposal: Impact for RD-Rp • We plan to map the x and Q2 dependence of RD-Rpindependently • Without our proposed measurements very few model-independent, true Rosenbluth L/Ts at low to moderate x and Q2

29. Impact for Rp and RD-Rp: Summary • We will pin down in detail the x and Q2 dependence of Rp in a kinematic region where the contribution to the structure functions coming from R is not negligible • We will extend the RD – Rp measurements to higher Q2 and verify whether the difference between RD and Rp previously observed at Q2 < 1.5 GeV2 disappears at higher Q2 as the very few points from SLAC indicate

30. Proposal: Impact for FL • The FL structure function has strong sensitivity to the nonperturbative initial state distribution of gluons • First few orders of the Nachtmann proton FL moments calculated from data to test pQCD calculations • Phys. Rev. Lett. 110, 152002 (2013) • Our proposed measurements (not shown here) would provide constraints for the integrals at low to intermediate x between Q2 of 1 and 5 GeV2 with very similar precision as E94110 (black circles)

31. Proposal: Impact for RA-RD • We plan to map the x and Q2 dependence of RA-RDindependently by measuring on a Copper target • We will use C and Au to measure RA-RD at select kinematics to check primarily the A-dependence of possible medium modifications of R

32. Proposal: Impact for RA-RD • Existing data have shown that there is not a huge effect on R induced by the nuclear medium • Recent analyses have shown that a huge effect is NOT needed to change the way we think about the origin of the antishadowing or about the EMC effect (a 30% change would be sufficient, for example) • The quality and quantity of existing data is not sufficient to pin down nuclear effects with a high level of precision • We propose to measure via true, model-independent Rosenbluth L/Ts RA-RD in one dedicated experiment and set the most precise constraints to date on possible nuclear medium modifications of R • we would map the x and Q2 dependence separately • we would map a possible A dependence

33. Proposal: Impact for sA/sD • Our data can be used to constrain/verify the universality of the nuclear modification as seen in sA/sD in charged lepton scattering and could be included in nPDF fits Our proposed measurements are shown only at central kinematics; due to the large acceptance of SHMS/HMS constraints from our data would extend to lower and higher x than shown

34. Proposal: Beam Time Request – 22 PAC days Production time per target • We use H and D to extract Rp, • RD-Rp and structure functions • We use D and Cu to measure medium modifications of R and their possible dependence with x and Q2 • We use D, C, Au to measure medium modifications of R and their A dependence Beam time request for all activities We allocated time for:  systematic checks  background measurements  measurements to constrain Coulomb corrections  configuration changes We need a total of 22 PAC days

35. Summary • Theoretical and experimental efforts over the past decades have produced a robust framework for studying the free nucleon structure and its dynamics in terms of quark and gluon distributions and their fundamental interactions • The predictive power of the pQCD Parton Model allows for studies of unexplored physics (within SM) or new physics, beyond the SM • Work is being done to apply a similar framework to the study of the nucleon structure when bound in nuclei • DIS Charged lepton scattering measurements of cross sections and structure functions played/plays a major role in this endeavor • Accessing F1,2,L or F2A/F2D requires the knowledge of R and the current status of experimental determinations of this quantity shows that more model-independent Rosenbluth L/T separations are needed for free and bound nucleons • Recent analyses have shown that even modest medium modifications of R allowed by the existing low-precision data could change the way we think about the origin of the antishadowing region or the EMC effect • We propose to extract Rp, RD- Rp, RA – RD, forC, Cu, Au, F1, FL, F2in a model independent fashionin a x range from 0.1 to 0.6 and Q2 from 1 to 5 GeV2 to cover the antishadowing and most of the EMC effect regions