John Arrington Argonne National Lab Nuclear Physics Symposium: Exploring the Heart of Matter Sep. 27, 2014 Large-x Structure of Nucleons and Nuclei

Roy Holt – many things to many people…  Mr. Deuteron  At Jefferson Lab –Early days( ,d):Mr. Radiation –More recently:Mr. Triton –Currently: Mr. “Superheated laughing gas and liter of mercury” And while he’s busy mucking about with SeaQuest now…… Mr. “Oh no, he’s back again” –To me:Mr. Bubba Ho-Tep

Large-x physics in the “Mr. Triton” Era  Low x (x<0.8) –EMC effect in light nuclei –EMC effect in deuteron, free neutron structure function –MARATHON  Moderate x (x=1 (x=2)) –T 20 at Novosibirsk/VEPP-3 –Two-photon exchange at Novosibirsk/VEPP-3  Intermediate x (1 < x < 3) –n(p) for proton/neutron in A=3 –SRCs in 3 H, 3 He  Large x (x=3) – 3 H, 3 He charge radii Ideas initiated/driven by Roy Measurements that wouldn’t have been possible without ‘parastic’ use of novel ideas Roy led/developed Internal gas target, 3 H target,…

Deeply-inelastic scattering (DIS) measures structure function F 2 (x) –x = quark longitudinal momentum fraction –F 2 (x) related to parton momentum distributions (pdfs) Nuclear binding << energy scales of probe, proton/neutron excitations Expected F 2 A (x) ≈ Z F 2 p (x) + N F 2 n (x) i.e. insensitive to details of nuclear structure beyond Fermi motion F 2 (x)   e i 2 q i (x) i=up, down, strange R = F 2 A (x) / F 2 D (x) Quark distributions in nuclei: EMC effect

Nucleon structure is modified in the nuclear medium or Nuclear structure is modified due to hadronic effects Models of the EMC effect Many models, no complete and accepted picture that is consistent with other data (e.g. Drell-Yan)  Nucleon ‘swelling’  Dynamical rescaling  Multiquark clusters (6q, 9q ‘bags’)  More detailed binding calculations - Fermi motion + binding - N-N correlations  Nuclear pions

EMC effect: x dependence A dependence SLAC E139 –Most precise large-x data –Nuclei from A=4 to 197 Conclusions –Universal x-dependence Limited data at large x –A-dependence unclear Scales with ln(A), A 1/3 Scales with density Something else?? J. Gomez, et al., PRD 94, 4348 (1994)

Importance of few-body nuclei 4 He much lighter than 12 C, but has similar average density 9 Be much lower density than 12 C, but similar mass 3 He has low A and low density Light nuclei help test scaling with mass vs. density Constrain 2 H – free nucleon difference

8 JLab E03-103: Light nuclei Consistent shape for all nuclei (curves show shape from SLAC fit) 12 C 9 Be 4 He If shape (x-dependence) is same for all nuclei, the slope (0.35<x<0.7) can be used to study dependence on A 3 He J. Seely, et al., PRL103, (2009)

A-dependence of EMC effect in light nuclei Density determined from ab initio calculation S.C. Pieper and R.B. Wiringa, Ann. Rev. Nucl. Part. Sci. 51, 53 (2001) Data show smooth behavior as density increases… except for 9 Be 9 Be has low average density, but large component of structure is 2  +n Most nucleons in tight,  -like configurations K. Arai, et al., PRC54, 132 (1996) Credit: P. Mueller

A-dependence of EMC effect in light nuclei Density determined from ab initio calculation S.C. Pieper and R.B. Wiringa, Ann. Rev. Nucl. Part. Sci. 51, 53 (2001) Data show smooth behavior as density increases… 9 Be too heavy for Roy, so let’s ignore it – focus on H, He EMC effect very small for 3 He Suggests small nuclear corrections in 2 H, impact on extraction of free neutron as extracted from 2 H

E140 E139 Neutron Structure Function  Attempts to extract F 2n (x) from deuteron and proton data yield large range of results, depending on the model of the deuteron  “Scaled EMC effect”: Use F 2A /F 2D data as measure of nuclear effects; scale to determine effects in the deuteron  Yields larger n/p  Neglects Fermi motion, difference in F 2p and F 2n, Q 2 dependence of smearing

F 2 n / F 2 n, d/u Ratios and A 1 Limits for x→1 F 2 n /F 2 p d/u A1n A1n A1p A1p SU(6) 2/3 1/2 0 5/9 Diquark Model/Feynman 1/ Quark Model/Isgur 1/ Perturbative QCD 3/7 1/5 1 1 QCD Counting Rules 3/7 1/5 1 1 Extensive recent review on the valence/high-x structure of the nucleon: R. J. Holt and C. D. Roberts, Rev. Mod. Phys. 82, 2991 (2010).

Updated F 2n Extraction  Similar to previous extractions – emphasis on improved treatment of the data, evaluation of systematics –Interpolate R dp = F 2d /F 2p data to fixed Q 0 2 = 12 GeV 2 Fit Q 2 dependence using full Q 2 range (3-230 GeV 2 ) Average R dp from GeV 2 –Average Q 2 for each bin always within factor of two of Q 0 2 –Interpolation to fixed Q 2 typically 0.5% –Use fit to F 2p (from M.E.Christy)  Deuteron evaluated in a light cone impulse approximation, without “DIS” approximations (e.g. doesn’t assume scaling, doesn’t neglect k ┴ )

Newer CTEQ6x analysis (model similar to Melnitchouk and Thomas) yields consistent results (A. Accardi, et al., PRD 81 (2010) )  Ave. Q 2 values for the D/p ratios have a strong dependence on x We interpolate data to fixed Q 2 Previous extractions treated data as if it were at fixed Q 2 Significant Q 2 dependence in S p at large x, F 2n ~ R dp - S p  Much of the “model-dependence” due to evaluating S p, S n at fixed Q 2 Neutron Structure Function JA, F.Coester, R.J.Holt, T.S.-H.Lee, J.Phys.G36, (2009)

Detailed investigations of model-dependence N3L0 Av18 CDBonn WJC2 WJC1 Melnitchouk&Thomas WBA [CTEQ6X] Kulagin&Petti Arrington, et al Rinat, et al Solid: On-shell Dashed: Off-shell [MST or KP] REF: Arrington, MST offshell Extract F 2n /F 2p with a variety of microscopic deuteron calculations Vary N-N potential – top plot Vary deuteron model – bottom

Extracted n/p ratio including estimates of experimental and model-dependent uncertainties Detailed investigations of model-dependence

Conclusions  Significantly reduced sensitivity to deuteron model –F 2n /F 2p relatively well known, barring significant extra nuclear effects (e.g. large “EMC effect” in 2 H) –Calculations for 3 He, 4 He allow comparison to EMC ratios [T.-S. H. Lee]  Model-independent extractions of F 2n /F 2p at large x still critical: 3 H/ 3 He –Significant cancellation between nuclear effects in 3 H and 3 He –Improved precision, reduced model dependence, in extraction of F 2n –Combined with extraction from d/p ratio, sensitive to nuclear effects beyond convolution, standard off-shell prescriptions, in the deuteron

MARATHON: DIS from A=3 Mirror symmetry of A=3 nuclei –Extract F 2 n /F 2 p from ratio of measured 3 He/ 3 H structure functions R = Ratio of ”EMC ratios” for 3 He and 3 H Relies only on difference in nuclear effects Calculated to within 1% Most systematic, theory uncertainties cancel

Triton ( 3 He & 3 H) Measurements E : Marathon u/d ratios from 3He(e,e’)/3H(e,e’) DIS measurements [A]* E : elastic: 3 H – 3 He charge radius difference [ 3 H “neutron skin”] [A] E : x>1 measurements of correlations [A-]* E : (e,e’p) momentum distribution measurements[B+] Relatively small amount of tritium (~1kC) in a cell machined from single block of Al. 19

Triton ( 3 He & 3 H) Measurements E : Marathon u/d ratios from 3He(e,e’)/3H(e,e’) DIS measurements [A]* E : elastic: 3 H – 3 He charge radius difference [ 3 H “neutron skin”] [A] E : x>1 measurements of correlations [A-]* E : (e,e’p) momentum distribution measurements[B+] Relatively small amount of tritium (~1kC) in a cell machined from single block of Al. 20

Hard interaction at short range N-N interaction Mean field part n(k) [fm -3 ] k [GeV/c] Short-Range Correlations Nucleon momentum distribution in 12 C

22 SRC evidence at JLab Experimental observations:  Clear evidence for 2N-SRC at x >1.5  Suggestion of 3N-SRC plateau  Isospin dependence ? Simple SRC Model: - 1N, 2N, 3N contributions dominate at x≤1,2,3 - 2N, 3N configurations “at rest” (total p pair = 0) - Isospin independent N. Fomin, et al, arXiv: (2011) K. Egiyan et al, PRL96, (2006) CLAS -  1.5 GeV 2 E Q 2 =2.7 GeV 2 N. Fomin, et al., PRL 108 (2012)

Density dependence? Credit: P. Mueller J.Seely, et al., PRL103, (2009) N. Fomin, et al., PRL108 (2012)

Correlation between SRCs and EMC effect Importance of two-body effects? L. Weinstein, et al., PRL 106, (2011) O. Hen, et al, PRC 85, (2012) J. Seely, et al., PRL103, (2009) N. Fomin, et al., PRL 108, (2012) JA, A. Daniel, D. Day, N. Fomin, D. Gaskell, P. Solvignon, PRC 86 (2012)

25 Tensor force dominance R. Schiavilla, R. Wiringa, S. Pieper and J. Carlson, PRL98, (2007) nppp Scaled deuteron momentum distribution R. Subedi et al, Science 320, 1476(2008) From A(p,p’pn) and 12 C(e,e’pN): 90% of observed pN pairs are pn; tensor force  isosinglet dominance R(pp/pn) =  R(T=1/T=0) = 20  8% Simple SRC Model: - 1N, 2N, 3N contributions dominate at x≤1,2,3 - 2N, 3N configurations “at rest” (total p pair = 0) - Isospin independent

26 Isospin structure of 2N-SRCs 3 He/ 3 H is simple/straightforward case: Simple estimates for 2N-SRC Isospin independentFull n-p dominance (no T=1) 40% difference between full isosinglet dominance and isospin independent Few body calculations [M. Sargisan, Wiringa/Peiper (GFMC)] predict n-p dominance, but with sizeable contribution from T=1 pairs Goal is to measure 3He/3H ratio in 2N-SRC region with 1.5% precision  Extract R(T=1/T=0) with uncertainty of 3.8% Extract R(T=1/T=0) with factor of two improvement over previous triple-coincidence, smaller FSI

27 Momentum-isospin correlations p 3 = p 1 + p 2 p 1 = p 2 = p 3 extremely large momentum “Star configuration” (a) yields R( 3 He/ 3 H) ≈ 3.0 if nucleon #3 is always the doubly-occurring nucleon (a) yields R( 3 He/ 3 H) ≈ 0.3 if nucleon #3 is always the singly-occurring nucleon (a) yields R( 3 He/ 3 H) ≈ 1.4 if configuration is isospin-independent, as does (b) “Linear configuration” R≠1.4 implies isospin dependence AND non-symmetric momentum sharing

3 He(e,e’p)/ 3 H(e,e’p) arXiv: E : Proton and Neutron Momentum Distributions in A = 3 Asymmetric Nuclei 28 3 He/ 3 H ratio for proton knockout yields n/p ratio in 3 H np-dominance at high-P m implies n/p ratio  1 n/p at low P m enhanced

29 Charge radii: 3 He and 3 H(e,e’p)  R RMS = 0.20(10) With new tritium target and JLab Luminosity, we aim to improve precision on  R RMS by factor 3-5 over SACLAY results One-time opportunity for 3 H at JLab Precise theoretical calculations of 3H, 3He Experimental results: large uncertainties, discrepancies 3H 3He GFMC1.77(1)1.97(1)  EFT 1.756(6)1.962(4) SACLAY1.76(9)1.96(3) BATES1.68(3)1.97(3) Atomic (4)  R RMS = 0.29(04)

Large-x physics in the “Mr. Triton” Era  Very-low x (x<0.8) –EMC effect in light nuclei –EMC effect in deuteron, free neutron structure function –MARATHON  Low x (x=1 (x=2)) –T 20 at Novosibirsk/VEPP-3 –Two-photon exchange at Novosibirsk/VEPP-3  Intermediate x (1 < x < 3) –n(p) for proton/neutron in A=3 –SRCs in 3 H, 3 He  Large x (x=3) – 3 H, 3 He charge radii Ideas initiated/driven by Roy Measurements that wouldn’t have been possible without ‘parastic’ use of novel ideas Roy led/developed Internal gas target, 3 H target,…