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) ~ S ei2 qi(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
4He is low mass, higher density
9Be is 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, (2009) 5 5

6. A-dependence of EMC effect
J.Seely, et al., PRL103, (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
High momentum tails should yield constant ratio if SRC-dominated QE
N. Fomin, et al., PRL 108 (2012)
n(k) [fm-3]
k [GeV/c]

9. Comparison to the EMC effect
J.Seely, et al., PRL103, (2009)
N. Fomin, et al., PRL108 (2012)

10. EMC-SRC correlation: Importance of nuclear structure
J. Seely, et al., PRL103, (2009)
Not too surprising without 9Be; both effects has always been assumed to roughly scale with density
N. Fomin, et al., PRL 108, (2012)
JA, A. Daniel, D. Day, N. Fomin, D. Gaskell, P. Solvignon, PRC 86, (2012)
O. Hen, et al, PRC 85, (2012)
L. Weinstein, et al., PRL 106, (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, , 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 High Virtuality (HV) of the nucleons [L. Weinstein et al, PRL 106, ,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)

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, (2012); PRL 102, (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, (2012); PRL 102, (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, (2012); PRL 102, (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)

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 E ]
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 GeV1H 2H
3He
4He
6,7Li
9Be
10,11B
12C
40Ca
48Ca Cu Au 3H
3He
SRCs at x>1 at 12 GeV
[E06-105: JA, D. Day, N. Fomin, P. Solvignon]
…help us determine if all pairs, or just np (‘fast’) pairs matter
EMC effect at 12 GeV
[E10-008: JA, A. Daniel, D. Gaskell]
Full 3H, 3He program (4 expts) in 2016 (Hall A)
Initial set of light/medium nuclei in 2017 (Hall C)
3H, 3He DIS: EMC effect and d(x)/u(x)
SRC Isospin dependence: 3H vs 3He
Charge radius difference: 3He - 3H

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

24. A major caveat…
Discussion generally assumes a single origin for EMC effect In 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 energy So it’s not purely an exotic density- or virtuality-driven effect, but appears to be mix of binding corrections and something more exotic The 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 uncertain NOTE: removal energy depends on n vs. p  should have same isospin dependence as “high-virtuality” model
JA et al, PRC 86 (2012)
O. Benhar and I Sick, arXiv: ,
S. Kulagin and R. Petti, Nucl. Phys. A765 (2006) 126

25. JLab E03-103 Results 12C 9Be 3He Consistent shape for all nuclei 4He
(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, (2009) 25 25

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