1. Questions about the connection between the EMC effect and Short-Range Correlations
John Arrington Argonne National Lab
ECT* Workshop on Exposing Novel Quark and Gluon Effects in Nuclei
April 16-20, 2018

2. Nucleus as a dilute systems
The nucleus is often described as a dilute system: Nucleon radius much smaller than average nucleon separation in nuclei Nucleus = protons + neutrons + small binding (to very (to a very good approximation) “[The strong] force makes the nucleus a fairly dilute system and allowed calculations that treated the nucleus as a collection of hard objects in a mean field to describe many of the properties of nuclear matter.” - D. Higinbotham, E. Piasetzky and M. Strikman [DNP webpage, adapted from CERN Courier article]

3. Nuclei as dense systems
Picture the proton as a hard sphere: R=1.15 fm (RMS=0.85 fm)  density=0.16 fm-3
Cubic packing of hard spheres  50% empty space
Ideal packing of hard sphere  25% empty space
To obtain densities of nuclei, can’t have ANY empty space
Can internal structure be unchanged??

4. What did JLab do at 6 GeV? New focus for EMC effect: light nuclei
A dependence for A≤12 clearly demonstrate role of nuclear structure
New techniques/observables:
Polarization transfer measurements of ‘In-medium form factors’
Tagged measurements in the deuteron
Low-momentum spectators: free neutron – BoNUS
High-momentum spectators: off-shell effect – D(e,e’ps)
New direction: SRC studies
A dependence
Isospin structure

5. EMC effect at JLab 12C 9Be 3He 4He E03-103 (Hall C)
J.Seely, et al., PRL103, (2009)
3He

6. 1-slide detour: Comparing nuclei (to each other)
Isoscalar corrections typically applied to (largely) remove F2n-F2p difference when trying to isolate “nuclear effects” on F2
Different F2n/F2p values used, AND it can be applied in slightly different ways
Full JLab EMC results (light and heavy nuclei): Applying isoscalar correction to denominator (deuteron) using F2n/F2p in the deuteron - should be better
Still not perfect: even if the PHYSICS of the EMC effect is same for protons&neutrons the impact of smearing, off-shell effects, etc…, will differ because F2n ≠ F2p
Important for precise comparisons of nuclei (e.g. 3H and 3He, 40,48Ca)
Shouldn’t be an issue when comparing to models (if corrections clear/understood)
3He
3He and 3H won’t be identical even with perfect isoscalar correction, because one is seeing mainly proton smearing, the other is seeing more neutron smearing.

7. 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)
Smooth behavior as density increases, except for 9Be
Details of the nuclear structure matter!
9Be has low average density, but large component of structure is 2a+n
Most nucleons in tight, a-like configurations
K. Arai, et al., PRC54, 132 (1996)

8. Short-range correlations
Mean-field region: collective behavior, strongly A-dependent
High-momentum region: short-range interactions, mainly 2-body physics, largely A-independent
Small N-N
separation
Somewhat simplified version of Jerry’s summary slide…
Large
momenta
(SRCs)
High-density
Configurations
(EMC effect?)
Cioffi Degli Atti, et al, PRC53, 1689 (1996)

9. SRC evidence: A/D ratios
JLab E02-019
N. Fomin, et al., PRL108 (2012) QE
Ratio of cross section (per nucleon) shows plateau above x ≈1.4, as expected if high-momentum tails dominated by 2N-SRCs

10. 2-body tensor force leads to dominance of T=0 pairs
Dominance of the tensor force
R. Subedi et al, Science 320, 1476(2008)
Observed ~10:1 ratio of np to pp pairs implies ~20:1 in nuclei
(can detect either proton in experiment)
Previous assumption of isospin independence is totally wrong pp np
20:1 dominance includes impact of having more potential np pairs than pp pairs (observe 10:1)
Newer 4He data: 4np pairs, 1 pp possible. With 2 protons in pp, experiment is twice as sensitive to np pairs for isospin-independent SRC. Isospin-independent SRC predicts pp/np=50%
Observe 10-20% pp/np; so isospin-dependent NN potential gives factor 3-5, not factor 10 or 20
Carbon: 6% pp/p (with factor of 2 for proton), 12% observed. Isospin independent: expect 15/36 to begin with (15/51=30%, 30/66 with weighting=45%), so factor ~4
2-body tensor force leads to dominance of T=0 pairs
R. Schiavilla, R. Wiringa, S. Pieper and J. Carlson, PRL98, (2007)

11. Question about Final-State Interactions (FSIs)
2N knockout shows nearly all high-Pm events have fast backward spectator
Plane wave indistinguishable from FSI
What about FSI?
For A(e,e’p), expect to measure mainly low-p nucleons rescattered to high Pm in most kinematics
2-nucleon knockout measurements chose kinematics (e.g. x>1) to suppress FSI
A(e,e’p) data is still FSI dominated at high Pm. Observed np dominance suggests FSI occur only within SRC, or that FSI in tensor correlation momentum region generate np dominance.
Calculations suggest that FSI occur between nucleons close together [SRCs??]
We can have two low-p nucleons close together (short-range configuration), meaning that if FSI depends on separation, it should enhance pp and np pairs as well
Do these FSI contributions depend on having high-momentum (highly off-shell) nucleons??

12. Comparing EMC effect and SRCs in light nuclei
J.Seely, et al., PRL103, (2009)
N. Fomin, et al., PRL108 (2012)
JLab E03-103
JA and D. Gaskell, spokespersons
EMC effect in light nuclei
JLab E02-019
JA, D. Day, B. Filippone, A. Lung
Probe high-momentum nucleons
Study short-distance (high-density) structures in nuclei

13. EMC-SRC correlation
SRCs are both short-distance and high-momentum components
Which matters for EMC effect?? (or does neither matter?)
J. Seely, et al., PRL103, (2009)
N. Fomin, et al., PRL 108, (2012)
L. Weinstein, et al., PRL 106, (2011)
O. Hen, et al, PRC 85, (2012)
JA, A. Daniel, D. Day, N. Fomin, D. Gaskell, P. Solvignon, PRC 86, (2012)

14. Short-distance behavior and the EMC effect
EMC effect driven by average density of the nucleons
[J. Gomez, et al., PRD 94, 4348 (1994), Frankfurt and Strikman, Phys. Rept. 160 (1988) 235]
If EMC effect and SRC contributions both scaled with density, it would explain the EMC-SRC correlation
It would not explain the anomalous result for 9Be

15. 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

16. Short distance (“local density”) vs high-momentum (“high-virtuality”) pictures
High-momentum pairs (SRCs) come mainly from isosinglet (np) pairs
More np SRCs than pp+nn by about a factor of 10
[2N-knockout measurements, assuming nn same as pp]
Can (and do) have short-distance configurations with pp, np, and nn
More np than pp+nn pairs a ~1fm, by about a factor of 2
[From Carbon 2-body densities from Wiringa, Pieper, et al.]
High-Virtuality (HV) picture of the EMC effect
Effect strongly dominated by np pairs
Nuclear structure generates SRCs
SRCs cause the EMC effect
Local density (LD) picture
All NN pairs contribute
Contribution from np pairs is larger than pp+nn by factor ~2
Nuclear structure (high density) causes EMC effect and SRCs

17. Isospin structure of short-distance configurations
QMC calculation of 2-body densities for pp and np pairs Dominant effect is trivial pair counting (36 np pairs vs 15 pp) After correction for that, ratio of np/pp pairs is nearly one at large distances, up by factor of ~2 at large distances Only slight np dominance when looking at short-distance

18. Two Hypotheses for EMC-SRC correlation
HV: OK linear correlation (χv2=1.26)
Fair extrapolation to deuteron:
EMC(2H) = ± 0.036
# of nucleons at high momentum (relative to 2H)
High Virtuality o
LD: Good linear correlation (χv2=0.64)
Good extrapolation to deuteron:
EMC(2H) = ± 0.033
Local Density o
# of nucleons in small-sized configurations
JA, A. Daniel, D. Day, N. Fomin, D. Gaskell, P. Solvignon, PRC 86 (2012)
LD picture: Estimate #/NN pairs based on measured np (SRC) pairs.
Better fit, but not conclusive. Want more light nuclei, better precision, larger N/Z range

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]
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
Proton/neutron n(k) from 3H/3He(e,e’p)
Charge radius difference: 3He - 3H
Hall A 3H, 3He program: 4 (5?) experiments currently taking data

20. Flavor dependence: going beyond 40Ca – 48Ca
We have added 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. A major caveat…
Discussions of the EMC-SRC correlation frequently assume a single origin of the EMC effect, e.g. local density or high virtuality as THE source. But other explanations (or combinations) can still yield a correlation between EMC and SRCs. Used to assume that EMC effect and SRCs scaled with average density. The observed correlation was expected, until 9Be data showed different results for EMC and SRC. In the rest frame convolution formalism, the ‘binding’ contribution to the EMC effect scales with average removal energy, which is dominated by the high-momentum contribution associated with SRCs. In Kulagin & Petti calculations, binding explains half of the EMC effect, but the effect is correlated with the presence of SRCs. Will yield EMC-SRC correlation if the remaining portion has similar nuclear dependence as SRCs. In calculations by Cloet/Bentz/Thomas the EMC effect arises from the scalar, vector, and isovector-vector mean-fields. No connection to SRCs, but EMC effect generally increases with mean-field density, and denser nuclei will generate more SRCs.
JA, et al, PRC 86 (2012)
O. Benhar and I Sick, arXiv:
S. Kulagin and R. Petti, Nucl. Phys. A765 (2006) 126
I.C.Cloet, W.Bentz, and A.W.Thomas, PRL 102 (2009)
I.C.Cloet, W.Bentz, and A.W.Thomas, PRL 109 (2012)

22. Spin-dependent EMC effect and SRCs
Proton spin up and down nearly identical at low momentum; neutron very different. So at low-k (and on average) the neutron carries the spin
At high momentum, much smaller differences between spin up for neutron (and larger differences for the proton)
If the EMC effect came entirely from high-virtuality nucleons, one would expect a small spin EMC effect, as the region of large modification has almost no polarization. Not trivially obvious what this would predict for the measure ratio
A ‘tagged’ spin EMC effect would show a large difference compared to a free polarized neutron, coming from the k-dependent polarization of the proton, neutron. Not clear that one could learn more. IF unpolarized measurements showed large effect at k>2 fm-1, then spin could, potentially, add important information

23. Flavor/Isospin dependence of the EMC effect?
Generally 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)]
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 proton EMC effect in ‘high-virtuality’ picture
48Ca, 208Pb expected to have significant neutron skin: neutrons preferentially sit near the surface, in low density regions
All of these imply increased EMC effect in minority nucleons

24. Estimates from Quantum Monte Carlo
R. Wiringa, R. Schiavilla, S. Pieper, and
J. Carlson, Phys. Rev. C89 (2014)
Provides ab initio calculations of several important quantities up to A=12
n(k): Fraction of high-momentum nucleons, ave. kinetic energy of nucleons
Density distributions: Average density of nucleus
Two-body densities: Average ‘overlap’ (local density) of nn, pn, pp pairs
Predict A-dependence of unpolarized EMC effect [JLab E ]
Cross section weighted average of proton and neutrons
Can calculate each of these for protons and neutron separately
Isospin/flavor dependence as function of fractional neutron excess: (N-Z)/A

25. 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

26. 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 (9Be, 48Ca): scaled from nuclear matter
48Ca
9Be
Cloet, et al.
Preliminary
Can be probed directly in parity-violating electron scattering
48Ca measurements proposed at JLab
- Need detailed structure calculations for 48Ca
Light nuclei (e.g. 9Be) may also have good sensitivity; help disentangle effects

27. New directions for JLab@12 GeV
Slide and list of related talks from
“Next generation nuclear physics with JLab12 and EIC”
Deuteron as a variable-density nucleus
Nucleon pdfs as function of initial momentum in deuteron [S. Kuhn, D. Higinbotham]
Measure spectator proton to tag initial neutron momentum or vice-versa [“Deeps”, “BoNUS”]
Nucleon form factors as function of initial momentum in deuteron
Reconstruct initial momentum in d(e,e’p)
Inclusive: quark structure of SRCs [D. Day, A. Freese]
Kinematics (x>1) isolates SRC, high-Q2 probes pdfs
Spin dependence of EMC [I. Cloet]
Further EMC, SRC studies [E. Piasetzky, E. Cohen, N. Fomin, D. Higinbotham,…]
Additional light nuclei, 3H and 3He, etc…
Flavor/isospin dependence of EMC effect
EIC….
Further measurements with tagging [K. Park]
Push Q2 for high-x studies [A. Freese]
Nuclear effects in glue (the dominant low-x, large-distance component)

28. In-Medium Nucleon Form Factors [E12-11-002: E. Brash, G. M. Huber, R
In-Medium Nucleon Form Factors [E : E. Brash, G. M. Huber, R. Ransom, S. Strauch]
Compare proton knock-out from dense and thin nuclei: 4He(e,e′p)3H and 2H(e,e′p)n
Modern, rigorous 2H(e,e’p)n calculations show reaction-dynamics effects and FSI will change the ratio at most 8%
QMC model predicts 30% deviation from free nucleon at large virtuality ?
S. Jeschonnek and J.W. Van Orden, Phys. Rev. C 81, (2010) and Phys. Rev. C 78, (2008); M.M. Sargsian, Phys. Rev. C82, (2010)

29. In-Medium Nucleon Structure Functions [E12-11-107: O. Hen, L. B
In-Medium Nucleon Structure Functions [E : O. Hen, L.B. Weinstein, S. Gilad, S.A. Wood]
DIS scattering from nucleon in deuterium
Tag high-momentum struck nucleons by detecting backward “spectator” nucleon in Large-Angle Detector
d(e,e’n) with reduced (~50%) statistics
R ~ F2tagged/F2untagged
Projected uncertainties

30. In Medium Proton Structure Functions, SRC, and the EMC effect: E12-11-003A
Tagged structure functions in CLAS. Main measurement very similar to Hall C experiment, with similar precision but lower Q2.
CLAS kinematic reach allows additional studies in region of large FSI

31. ALERT: Tagged EMC effect

32. Final digression… Small N-N separation Large High-density momenta
These four ‘tagged’ measurements often present results in terms of the struck nucleon momentum or virtuality, and compare to models based on virtuality/off-shell effects. Correlation between large momenta and short distances means that a momentum-independent effect (e.g. driven by nucleon overlap) could show a virtuality dependence A mean field effect (which could still be correlated with SRCs) might give results that are independent of momentum/virtuality
High-momentum nucleons related to short-range interactions
Small N-N
separation
Large
momenta
(SRCs)
High-density
Configurations
(EMC effect?)

33. Conclusions
EMC-SRC has inspired new ideas and models for explaining EMC effect, but the data are limited
N/Z and A correlated in heavy nuclei; can’t separate mass and isospin dependence
Measurement of the correlation isn’t terribly precise
“The linearity of the EMC-SRC correlation, regardless of the exact corrections considered, is a clear indication of the robustness of the EMC-SRC correlation.” – O.Hen, et al., 2012 PRC
Discussion dominated by “single explanation”
“High Virtuality” pictures often compare only to virtuality-based models
Connection between short-distances and high-momentum mean it’s not so clean to test virtuality vs density pictures
We *know* that a full explanation requires more than one
New nuclei, tagged EMC measurements, spin- and flavor-dependent measurements, etc… will provide important tests/constraints
“Easy” to motivate new experiments based on simple pictures/questions about the origin of the EMC effect
Need more detailed/complete calculations to take full advantage of the new data