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Nuclear structure and the flavor dependence of the EMC effect

This workshop presentation discusses the EMC effect and quark distributions in nuclei. It explores the universal x-dependence and weak A-dependence of the effect, highlighting the importance of light nuclei and the role of nuclear structure.

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Nuclear structure and the flavor dependence of the EMC effect

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  1. Nuclear structure and the flavor dependence of the EMC effect John Arrington Argonne National Lab GHP Workshop Baltimore, MD April 9, 2015

  2. Quark distributions in nuclei: EMC effect Deeply-inelastic scattering (DIS) measures structure function F2(x) • x = quark longitudinal momentum fraction • F2(x) related to parton momentum distributions (pdfs) Nuclear binding << energy scales of probe, proton/neutron excitations Expected F2A(x) ≈ Z F2p(x) + N F2n(x) F2(x)~ Sei2qi(x) i=up, down, strange R = F2Fe(x) / F2D(x) J. J. Aubert, et al., PLB 123, 275 (1983)

  3. EMC effect:A-dependence SLAC E139 • Most precise large-x data • Nuclei from A=4 to 197 Conclusions • Universal x-dependence • Magnitude varies • Scales with A (~A-1/3) • Scales with density Universal x dependence and weak A dependence make it hard to test models J. Gomez, et al., PRD49, 4349 (1994)

  4. Importance of light nuclei Test mass vs. density dependence 4Heis low mass, higher density 9Beis higher mass, low density 3He is low mass, low density (no data) • New information on A-dependence • Nuclei for which detailed structure calculations exist

  5. JLab E03-103 Results 12C Consistent shape for all nuclei (curves show shape from SLAC fit) Measurements on 3He, 4He, 9Be, 12C JA, D. Gaskell, spokespersons 9Be 4He If shape (x-dependence) is same for all nuclei, the slope (0.35<x<0.7) can be used to study dependence on A J.Seely, et al., PRL103, 202301 (2009) 5

  6. A-dependence of EMC effect J.Seely, et al., PRL103, 202301 (2009) Density determined from ab initio few-body calculation S.C. Pieper and R.B. Wiringa, Ann. Rev. Nucl. Part. Sci 51, 53 (2001) Data show smooth behavior as density increases, as generally expected… except for 9Be 9Be has low average density, but large component of structure is 2a+n - most nucleons in dense a-like configurations Connected to “local density?” – nucleons very close together? Credit: P. Mueller

  7. Short-range correlations; high momentum nucleons n(k) [fm-3] k [GeV/c]

  8. Short-range correlations; high momentum nucleons QE n(k) [fm-3] High momentum tails should yield constant ratio if SRC-dominated k [GeV/c] N. Fomin, et al., PRL 108 (2012) 092052

  9. Comparison to theEMC effect J.Seely, et al., PRL103, 202301 (2009) N. Fomin, et al., PRL108 (2012) 092052

  10. EMC-SRC correlation: Importance of nuclear structure J. Seely, et al., PRL103, 202301 (2009) N. Fomin, et al., PRL 108, 092052 (2012) JA, A. Daniel, D. Day, N. Fomin, D. Gaskell, P. Solvignon, PRC 86, 065204 (2012) O. Hen, et al, PRC 85, 047301 (2012) L. Weinstein, et al., PRL 106, 052301 (2011)

  11. Short-distance behavior and the EMC effect • EMC effect, SRCs driven by average density of the nucleus • [J. Gomez, et al., PRD 94, 4348 (1994), Frankfurt and Strikman, Phys. Rept. 160 (1988) 235] • 2. EMC effect is driven by Local Density (LD) • [J. Seely et al., PRL 103, 202301, 2009] • SRCs generated by interactions in short-distance (high-density) np pairs • EMC effect driven by high-density nucleon configurations (pairs, clusters) • 3. EMC effect driven by HighVirtuality (HV)of the nucleons [L. Weinstein et al, PRL 106, 052301,2011] • SRC measurements directly probe high-momentum nucleons • EMC effect driven by off-shell effects in high-momentum nucleons Dominance of np pairs in SRCs implies slightly different correlation: Small, dense configurations for all NN pairs, high momentum only for np pairs Data favors local density interpretation, but very much an open question… JA, A. Daniel, D. Day, N. Fomin, D. Gaskell, P. Solvignon, PRC 86 (2012) 065204

  12. Isospin dependence of the EMC effect • Always assumed that EMC effect is identical for proton and neutron • Becoming hard to believe, at least for non-isoscalar nuclei • Recent calculations show difference for u-, d-quark, as result of scalar and vector mean-field potentials in asymmetric nuclear matter [I. Cloet, et al, PRL 109, 182301 (2012); PRL 102, 252301 (2009)]

  13. Isospin dependence of the EMC effect • Always assumed that EMC effect is identical for proton and neutron • Becoming hard to believe, at least for non-isoscalar nuclei • Recent calculations show difference for u-, d-quark, as result of scalar and vector mean-field potentials in asymmetric nuclear matter [I. Cloet, et al, PRL 109, 182301 (2012); PRL 102, 252301 (2009)] Analysis by M. Sargsian: EMC effect fit as function of A, with additional correction for neutron excess of nuclei: same sign, similar size to Cloet, et al., calculations

  14. Isospin dependence of the EMC effect • Always assumed that EMC effect is identical for proton and neutron • Becoming hard to believe, at least for non-isoscalar nuclei • Recent calculations show difference for u-, d-quark, as result of scalar and vector mean-field potentials in asymmetric nuclear matter [I. Cloet, et al, PRL 109, 182301 (2012); PRL 102, 252301 (2009)] • 48Ca, 208Pb expected to have significant neutron skin: neutrons preferentially sit near the surface, in low density regions • EMC-SRC correlation + n-p dominance of SRCs suggests enhanced EMC effect in minority nucleons • In 3H, np-dominance suggests single proton generates same high-momentum component as two neutrons –> larger EMC effect in ‘high-virtuality’ picture All of these imply increased EMC effect in minority nucleons

  15. Estimates from Quantum Monte Carlo • Provides ab initio calculations of several important quantities up to A=12 • Momentum distributions: Fraction of high-momentum nucleons • Momentum distributions: Average kinetic energy of nucleons • Density distributions: Average density of nucleus • Two-body densities: Average ‘overlap’ (local density)of nn, pn, pp pairs R. Wiringa, R. Schiavilla, S. Pieper, and J. Carlson, Phys. Rev. C89 (2014) 024305

  16. Estimates from Quantum Monte Carlo • Provides ab initio calculations of several important quantities up to A=12 • Momentum distributions: Fraction of high-momentum nucleons • Momentum distributions: Average kinetic energy of nucleons • Density distributions: Average density of nucleus • Two-body densities: Average ‘overlap’ (local density)of nn, pn, pp pairs • Can calculate each of these for protons and neutron separately • Predict A-dependence of unpolarized EMC effect [JLab E12-10-008] • Cross section weighted average of proton and neutrons • Isospin dependence (EMC effect for proton vs. neutron) as function of fractional neutron excess: (N-Z)/A

  17. A-dependence of unpolarized EMC effect 4 simple models of EMC scaling: Fraction of n(k) above 300 MeV Average Kinetic Energy Average Density Nucleon Overlap (r12 < 1 fm) Fixed normalizations for 2H for 12C Preliminary 3H 3He A-dependence of light nuclei already excludes average density High-momentum tail has small, systematic difference for most nuclei

  18. Isospin dependence vs fractional neutron excess 4 simple models of EMC scaling: Fraction of n(k) above 300 MeV Average Kinetic Energy Average Density Nucleon Overlap (r12 < 1 fm) EMC effect isospin asymmetry: (neutron-proton)/average Cloet estimates: scaled from NM Preliminary 48Ca 9Be Cloet, et al. • Can be probed directly in parity-violating electron scattering • 48Ca measurements proposed at JLab • Light nuclei (e.g. 9Be) may also have good sensitivity; help disentangle effects

  19. Unpolarized EMC measurements: JLab@12 GeV 1H 2H 3He 4He 40Ca 48Ca Cu Au 6,7Li 9Be 10,11B 12C 3H 3He SRCs at x>1 at 12 GeV [E06-105: JA, D. Day, N. Fomin, P. Solvignon] EMC effect at 12 GeV [E10-008: JA, A. Daniel, D. Gaskell] 3H, 3He DIS: EMC effect and d(x)/u(x) SRC Isospin dependence: 3H vs 3He Charge radius difference: 3He - 3H Full 3H, 3He program (4 expts) in 2016 (Hall A) Initial set of light/medium nuclei in 2017 (Hall C)

  20. EMC and SRC: Additional Nuclei We are planning to add additional heavier nuclei • Vary N/Z for approximately fixed mass • Vary mass for approximately fixed N/Z Start trying to disentangle A dependence and N/Z dependence

  21. Parity-Violating EMC effect (PV-EMC) Knowing d(x)/u(x) for the proton and assuming flavor-independent EMC effect, can calculate e-A PV-DIS response PV asymmetry is independent of overall size of EMC effect; only sensitive to difference in EMC effect for u and d quarks Cloet, et al. calculations predicts 5% deviation at large x Other structure effects considered could modify this SoLID spectrometer planned for Hall A at Jefferson Lab can make ~1% measurements of PVDIS on non-isoscalar nuclei

  22. Summary Measurements of the EMC effect in light nuclei show importance of detailed nuclear structure, connection with short-range correlations This, along with recent calculations, suggest that there must be a flavor dependence to the EMC effect in neutron rich nuclei • Important to separate A dependence from isospin dependence • Provides information on underlying causes Some information can be gained by trying to separate dependence on nuclear mass and neutron excess in unpolarized EMC effect data with varying N/Z Direct measurements can be made with Parity-violating scattering from nuclei using SoLID detector • 2H PVDIS: search for beyond standard model physics • 1H PVDIS: clean separation of u(x)/d(x) at large x in the proton • 48Ca: flavor dependence of EMC effect • Light nucleus (9Be) may also be important to disentangle effects

  23. A major caveat… Discussion generally assumes a single origin for EMC effectIn the rest frame convolution formalism, the average removal energy, not just the overall binding energy, is relevant. The EMC effect scales with average removal energy, as does the contribution of SRCs which contribute a large part of the removal energySo it’s not purely an exotic density- or virtuality-driven effect, but appears to be mix of binding corrections and something more exoticThe binding calculations of Kulagin & Petti explain half of the EMC effect, and the effect is correlated with the presence of SRCs. This suggests that the remaining half is also correlated with SRCs, although the evaluation of the removal energy is model dependent and uncertainNOTE: removal energy depends on n vs. p  should have same isospin dependence as “high-virtuality” model JA et al, PRC 86 (2012) 065204 O. Benhar and I Sick, arXiv:1207.4595, S. Kulagin and R. Petti, Nucl. Phys. A765 (2006) 126

  24. JLab E03-103 Results 12C 9Be 3He Consistent shape for all nuclei (curves show shape from SLAC fit) 4He If shape (x-dependence) is same for all nuclei, the slope (0.35<x<0.7) can be used to study dependence on A J.Seely, et al., PRL103, 202301 (2009) 25

  25. SRC evidence: A/D ratios QE Ratio of cross sections shows a (Q2-independent) plateau above x ≈ 1.5, as expected in SRC picture High momentum tails should yield constant ratio if SRC-dominated N. Fomin, et al., PRL 108 (2012) 092052

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