Or Hen, Tel-Aviv University Short Range Correlations The EMC Effect and nucleon modification The EMC – SRC correlation Implications of the EMC-SRC correlation 12 GeV Measurement of nucleon modification
Photonuclear Reactions, Holderness Scholl, NH, August 2012
Short Range Correlations and the EMC Effect
Can not be explained only by simple Fermi motion and binding effects
The EMC EffectDIS cross section per nucleon in nuclei ≠ DIS off a free nucleon
EMC Effect: Universal
J. Gomez, PRD 49, 4348 (1994)J. Seely, PRL 103, 202301 (2009)Linear for 0.3 < xB < 0.7
(the lines shown are not fits)
4He/d
12C/d
9Be/d
4He/d
Au/d
SLAC
JLab - Hall C
x x x
Size of effect (“depth” or slope) grows with A
DIS scale: several tens of GeV
Nucleons
Nucleon in nuclei are bound by ~MeV
Naive expectation :
(Except some small Fermi momentum correction)
DIS off a bound nucleon = DIS off a free nucleon
Why was the EMC Effect a Surprise ?
DIS scale: several tens of GeV
Nucleons
Nucleon in nuclei are bound by ~MeV
Naive expectation :
(Except some small Fermi momentum correction)
Naive expectation :
Deuteron: binding energy ~2 MeV
Nucleons
Average nucleons separation ~2 fm
DIS off a deuteron = DIS off a free proton neutron pair
DIS off a bound nucleon = DIS off a free nucleon
Why was the EMC Effect a Surprise ?
F2
n unknown → Normalize using deuterium:
Kulagin and Petty, PRC 82, 054614 (2010)
Nuclear Effects only
Full calculation
• Nuclear Effects:• Fermi motion• Binding energy
• Full Calculation• Nucleon modification• Nuclear pions• shadowing
Nucleon modification: Phenomenological change to bound nucleon structure functions, change proportional to virtuality v = (p2-M2)/M2
12C
9Be
4He
EMC Theory
Kulagin and Petty, PRC 82, 054614 (2010)
Nuclear Effects only
Full calculation
• Nuclear Effects:• Fermi motion• Binding energy
• Full Calculation• Nucleon modification• Nuclear pions• shadowing
Nucleon modification: Phenomenological change to bound nucleon structure functions, change proportional to virtuality v = (p2-M2)/M2
12C
9Be
4He
Nucleon modificationneeded to describe data
EMC Theory
Q2=−qμqμ=q2−ω2
ω=E'−E
xB= Q2
2mω
Deep InelasticScattering (DIS)
E E`
(ω ,q)
nucleon
Final state Hadrons
W2
Incident lepton
scattered lepton
Nucleons
E E`
nucleus
Incident lepton
scattered lepton
xB counts the minimum number of nucleons involved
Inclusive electron scattering A(e,e’)
0≤x B≤1 0≤x B≤A
(ω ,q)
xB gives the fraction of
nucleon momentum carried by the struck parton
Study the partonic structure of the
nucleon
Study the nucleonicStructure of the
nucleus
3He 1.93±0.10
4He 3.02±0.17
9Be 3.37±0.17
12C 4.00±0.24
63Cu 4.33±0.28
197Au 4.26±0.29
a2(A/d)
K. Sh. Egiyan et al. Phys. Rev. Lett 96, 082501 (2006)K. Sh. Egiyan et al. Phys. Rev. C 68, 014313 (2003)D. Day et al. Phys. Rev. Lett 59, 427 (1987)
Interpretation: L. L. Frankfurt et al. Phys. Rev. C 48, 2415-2461 (1993)
JLab Inclusive A(e,e') Data
3He 1.93±0.10
4He 3.02±0.17
9Be 3.37±0.17
12C 4.00±0.24
63Cu 4.33±0.28
197Au 4.26±0.29
a2(A/d)
K. Sh. Egiyan et al. Phys. Rev. Lett 96, 082501 (2006)K. Sh. Egiyan et al. Phys. Rev. C 68, 014313 (2003)D. Day et al. Phys. Rev. Lett 59, 427 (1987)
Interpretation: L. L. Frankfurt et al. Phys. Rev. C 48, 2415-2461 (1993)
JLab Inclusive A(e,e') Data
Predicted by Frankfurt, Strikman,
and Sargsian
See talk byC. Degli Atti
Almost all protons with pmiss
> 300 MeV/c in 12C(e,e’p) have a
correlated nucleon with similar momentum in opposite direction
R. Subedi et al., Science 320 (5882), 1476 (2008)R. Shneor et al., PRL 99, 072501 (2007)
Ratios corrected for acceptance, det. Efficiency, transparency and SCX
Missing momentum (GeV/c)0.3 0.5
SR
C P
air
Fra
ctio
n
1
0.1
np SRC is ~18 times pp or nn SRC
12C(e,e ' pn)12C(e,e ' p)
= 96−23+4 %
12C(e,e ' pp)12C(e,e ' p)
= 9.5 ± 2%
Decomposing the High-Momentum Tail
The probability for a nucleon to have momentum ≥ 300 MeV / c in medium nuclei is ~25%
More than ~90% of all nucleons with momentum ≥ 300 MeV / c belong to 2N-SRC.
2N-SRC dominated by np pairs
PRL 162504(2006); Science 320, 1476 (2008)
1
2
3
1
2
3
~80% of kinetic energy of nucleon in nuclei is carried by nucleons in 2N-SRC.
1
2
PRL 108 (2012) 092502
What do we Know About SRC
Where is the EMC effect ?
High local nuclear matter density, large momentum, large off shell, large virtuality ( )
Mean field
SRC
OR
ν=p2−m2
80% nucleons(20% kinetic energy)
20% nucleons(80% kinetic energy)
np
ppnn
Largest attractive force
Where is the EMC Effect ?
Where is the EMC effect ?
Mean field
SRC
OR High local nuclear matter density, large momentum, large off shell, large virtuality ( )ν=p2−m2
80% nucleons(20% kinetic energy)
20% nucleons(80% kinetic energy)
np
ppnn
Largest attractive force
Where is the EMC Effect ?
J. Seely et al., PRL 103 (2009) 202301
dREMC
/dXB
a2(12C/d)
EMC SRC
J. Seely et al., PRL 103 (2009) 202301 N. Fomin et al., Phys. Rev. Lett. 108, 092502 (2012)
Looking at the Full Picture
EM
C S
lope
s0
.35
≤ X
B ≤
0.7
SRC Scaling factors XB ≥ 1.4
Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
SRC data: Fomin et al.EMC data: Gomez et al,. and Seely et al.
EMC Effect and 2N-Correlations
EM
C S
lope
s0
.35
≤ X
B ≤
0.7
SRC Scaling factors XB ≥ 1.4
Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
SRC data: Fomin et al.EMC data: Gomez et al,. and Seely et al.
EMC and SRC are probably both dominated by high momentum (high virtuality) nucleons in nuclei• EMC Effect not due to binding \ Fermi Motion alone• Probably due to nucleon medium modification
EMC Effect and 2N-Correlations
O. Hen et al, PRC 85, 047301 (2012)
Correction Stuck:• Isoscalar corrections (Egiyan only) – most important for 3He• Coulomb (up to 6% for Fe) and Inelastic corrections (1-3%) (Fomin only)• Pair center-of-mass motion corrections (Fomin only)
Robustness of the EMC-SRC Correlation
Isoscalar Isoscalar CoulombInelasticCM motion
CoulombInelastic
O. Hen et al, PRC 85, 047301 (2012)
Isoscalar Isoscalar CoulombInelasticCM motion
CoulombInelastic
Correction Stuck:• Isoscalar corrections (Egiyan only) – most important for 3He• Coulomb (up to 6% for Fe) and Inelastic corrections (1-3%) (Fomin only)• Pair center-of-mass motion corrections (Fomin only)
Robustness of the EMC-SRC Correlation
Fomin-Egiyan Consistency
O. Hen et al, PRC 85, 047301 (2012)
Correction Stuck:• Isoscalar corrections (Egiyan only) – most important for 3He• Coulomb (up to 6% for Fe) and Inelastic corrections (1-3%) (Fomin only)• Pair center-of-mass motion corrections (Fomin only)
Robustness of the EMC-SRC Correlation
Isoscalar Isoscalar CoulombInelasticCM motion
CoulombInelastic
O. Hen et al, PRC 85, 047301 (2012)
Correction Stuck:• Isoscalar corrections (Egiyan only) – most important for 3He• Coulomb (up to 6% for Fe) and Inelastic corrections (1-3%) (Fomin only)• Pair center-of-mass motion corrections (Fomin only)
Robustness of the EMC-SRC Correlation
EMC-SRC Slope
EMC-SRC χ2Isoscalar Isoscalar Coulomb
InelasticCM motion
CoulombInelastic
SRC Correction Factors:• Inelastic corrections:
• Small (1-3% for Fomin et al), • Very model dependent (100% uncertainty in Fomin et al)
• Coulomb Corrections: small (6% for Fe)• Isoscalar Correction:
• Largest for 3He• Not appropriate if SRC are dominated by pn pairs
• Pair Center-of-Mass motion correction• No correction:
a2(A/d) is the ratio of the number of high-momentum nucleons
Related to overall nucleon virtuality• With correction:
R2(A/d) is the ratio of the number of 2N-SRC pairs
Related to the number of nucleons at short distances• Very model dependent• Little guidance from data which to prefer• EMC-SRC slope � 2/ndf = 4.1/5 with CM correction• EMC-SRC slope � 2/ndf = 4.9/5 without CM correction
So...Which Corrections to Apply ?
EMC Correction Factors:Arrington et al, ArXiv 1206:6343
• (A-1)/A correction: nuclear density seen by struck nucleon.• Only appropriate if comparing to average nuclear properties, • Not appropriate for comparing to SRC (pairs of nucleons)
● Ntot
/ Niso
= A(A-1) / 2NZ: “The EMC effect should scale with the number of
possible NN pairs in the nucleus, Ntot
=A(A-1)/2, while the SRC contribution
is sensitive to only the possible np pairs, NISO
=NZ.”
• We Disagree. The EMC effect is either due to mean-field nucleons (and therefore will not scale with SRC pairs) or to short range nucleon pairs. It cannot be due to all possible NN pairs.
So...Which Corrections to Apply ?
20 40 60
EM
C S
lope
Separation Energy (MeV)
Benhar and Sick, ArXiv 1207:4595
• Average kinetic energy calculated using GFMC wave functions is much larger than previous calculations and\or (e,e'p) measurements.
• Not bad, but since the average separation energy is just proportional to the average nucleon virtuality.
• This is just another way to connect the EMC effect to Short Range Correlations!
How do we know the EMC slope for nuclear matter?
EMC and Separation Energy
E=T A−2A−1
−2E0
A
EMC and Separation Energy
∞
This is just another way to connect the EMC effect to Short Range Correlations!
∞Use E(A→∞) to predict a
2(∞/d)
Excellent correlation between the strength of the EMC effect and the relative amount of 2N-SRC pairs.
This correlation is robust. In dependent of SRC corrections.
EMC Corrections are inappropriate
The Correlation between the EMC effect and the average nucleon separation energy is just another aspect of this EMC-SRC correlation
EMC effect does not occur (or is very small) for mean-field nucleons
Both SRC and EMC are related to high-momentum (high virtuality) nucleons in nuclei
High momentum (high virtuality) nucleons in the nuclear medium are modified (?)
Conclusions
Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
Deuteron EMC Effect
SRC=0 free nucleons
SRC
0.084±0.004
σdDIS=σ p
DIS+σnDIS
Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
Deuteron EMC Effect
SRC=0 free nucleons
SRC
0.084±0.004
b=0.31±0.04 EMC ratio=1
d
n p
=1−a X B−b
σdDIS=σ p
DIS+σnDIS
b=0.31±0.04 EMC ratio=1Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
Deuteron EMC Effect
SRC=0 free nucleons
SRC
σ p+σnσd
(x=0.7)= 1.034
0.084±0.004
d
n p
=1−a X B−b
σdDIS=σ p
DIS+σnDIS
Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
Deuteron EMC Effect
SRC=0 free nucleons
SRC
σ p+σnσd
(x=0.7)= 1.034
0.084±0.004
b=0.31±0.04 EMC ratio=1
d
n p
=1−a X B−b
Get the free neutron out !Corrected for the In Medium
Correction (IMC) Effect
σdDIS=σ p
DIS+σnDIS
Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
Deuteron EMC Effect
SRC=0 free nucleons
SRC
σ p+σnσd
(x=0.7)= 1.034
0.084±0.004
σdDIS=σ p
DIS+σnDIS
Weinstein et al, PRL 106, 052301 (2011)Hen et al, PRC 85, 047301 (2012)
Deuteron EMC Effect
SRC=0 free nucleons
SRC
σ p+σnσd
(x=0.7)= 1.034
0.084±0.004
Robust !
σdDIS=σ p
DIS+σnDIS
SLAC Data,
Preliminary calculation by: H. l. Lai, P. Nadolsky, J. Pumplin, .P.Yuan
JPG36(2009) 205005
Comparing to CTEQ Calculations
CT10W -
Constraining d/u at large xB
O. Hen, A. Accardi, W. Melnitchouk, and E. Piasetzky, Phys. Rev. D 84, 117501 (2011)
Swelling Level
Average Nucleon Virtuality
See talk byA. Accardi,
A poor man's BoNuS
O. Hen, A. Accardi, W. Melnitchouk, and E. Piasetzky, Phys. Rev. D 84, 117501 (2011).
Constraining d/u at large xB
Constraining d/u at large xB
d/u(xB→1) = 0.23±0.09
Deuteron IMC constraints
O. Hen, A. Accardi, W. Melnitchouk, and E. Piasetzky, Phys. Rev. D 84, 117501 (2011).
This is all within the theoretical model and the assumptions made to extract the free neutron structure function
d/u robustness
Medium Modification of High-Momentum Nucleons
SRC=0 free nucleons
SRC
1−σ p+σn
σd= 2-3%
σ p*
σ p≈
σn*
σn≈2-3%5%
≈50%
EMC-SRC correlation suggest thathigh momentum (SRC) nucleons are modified in the nuclear medium
Medium Modification of High-Momentum Nucleons
SRC=0 free nucleons
SRC
1−σ p+σn
σd= 2-3%
σ p*
σ p≈
σn*
σn≈2-3%5%
≈50%
Can be studied by performing DIS on high momentum nucleons in deuterium, tagged by high momentum recoils
EMC-SRC correlation suggest thathigh momentum (SRC) nucleons are modified in the nuclear medium
Melnitchouk, Screiber, Thomas, Phys. Lett. B 335, 11 (1994)
Melnitchouk, Sargsian, Strikman, Z. Phys. A 359, 99 (1997)
Dependence on: Models Nucleon’s momentum and x
B
Nucleon’s momentum, not xB
Gross, Liuti, Phys. Lett. B 356, 157 (1995)
Binding/off shell
PLC suppression
Rescaling
p (MeV/c) 400
400
R =
F2’
/F2
R =
F2’
/F2
R =
F2’
/F2
α S = (ES − pSZ ) /mS
Models for Modified Structure Functions
p (MeV/c)
E12-11-107 – TAU, ODU, MIT JLABExperimental method: Use deuteron as a target in DIS
Tag high-momentum nucleons with high-momentum backward-recoiling (“spectator”) partner nucleon as in SRC using the reaction d(e,e’NS)
In Medium Structure Functions, SRC, and the EMC Effect
Projected Uncertainties:
Rescaling Model
Binding/Off-Shell
PLC Suppression
1
1
0.30.2
0.40.50.60.70.80.9
1.1 1.2 1.3 1.4 1.5 1.6
F2
bound/F2
free(xB=0.6)
d(e,e’ps)
LAD Detector:
Conclusions
EMC strength and 2N-SRC abundance in nuclei are correlated
This correlation is robust!
Possible explanation is that both relate to high momentum (high virtuality) nucleons in the nucleus
Correlation was used to extract the free neutron structure function and constrain the d/u ratio at large x
B
Medium modification of high momentum nucleons will be tested in an approved experiment at JLab 12GeV
Thank You !
Medium modification of form factor ratios
Medium modification of the proton's form factor ratio (G
e/G
m) observed
in polarization transfer measurements
The observed modification grows as a function of nucleon virtuality
PR11-107 will cover a much larger virtuality range of ~ 0.2-0.5 (GeV/c2)2
M. Paolone, et al., Phys. Rev. Lett. 105, 072001 (2010)
EMC slope vs. average of XB=0.4-0.6
Based on data from J. Gomez et al., Phys. Rev. D 49, 4348 (1994)
A Dependence of R = σL/σ
T
D.F. Geesaman, K. Saito, and A.W. Thomas, Annu. Rev. Nucl. Part. Sci. 45:337, 1995.
A Dependence of R = σL/σ
T
High Q2
0.3 < XB < 0.7
D.F. Geesaman, K. Saito, and A.W. Thomas, Annu. Rev. Nucl. Part. Sci. 45:337, 1995.
BNL Measurements[SRC Dominance at High Momentum]
A. Tang et al., Phys. Rev. Lett. 90, 042301 (2003)
γp
n
pf
pf = p
1 + p
2 - p
0
p0 = incident proton
p1 and p2 are detected
E. Piasetzky et al., Phys. Rev. Lett. 97, 162504 (2006)
Study the 12C(p,2p+n) reaction in parallel kinematics
Results: SRC Dominance92±18% of high momentum (275<P
miss<550 MeV/c)
proton knockout events were accompanied by single neutron emission
BNL Measurements[SRC Dominance at High Momentum]
A. Tang et al., Phys. Rev. Lett. 90, 042301 (2003)
γp
n
pf
pf = p
1 + p
2 - p
0
p0 = incident proton
p1 and p2 are detected
E. Piasetzky et al., Phys. Rev. Lett. 97, 162504 (2006)
Study the 12C(p,2p+n) reaction in parallel kinematics
Results II: (SRC Threshold?)Recoil neutrons above ~275 Mev/c have back to back angular correlation with the 12C(p,2p) missing momentum vector
BNL Measurements[SRC Dominance at High Momentum]
A. Tang et al., Phys. Rev. Lett. 90, 042301 (2003)
γp
n
pf
pf = p
1 + p
2 - p
0
p0 = incident proton
p1 and p2 are detected
E. Piasetzky et al., Phys. Rev. Lett. 97, 162504 (2006)
Study the 12C(p,2p+n) reaction in parallel kinematics
Results III: (c.m. Momentum)The c.m. momentum distribution was measured to be Gaussian with σ = 143 ± 17 MeV/c
12C(e,e'pp)S:BG ≈ 2:1
Jlab Hall-A E01-015[Triple Coincidence (e,e'pp) and (e,e'pn) TOF Spectra]
12C(e,e'pn)S:BG ≈ 1:3
Jlab Hall-A E01-015[QE Events Selection]
12C(e,e'p)11
B
Quasi Elastic Resonanc
e
12C(e,e'p)
Missing energy spectrum from 12C(e,e'p) at Pmiss
=300
MeV/c kinematics
R. Shneor et al., Phys. Rev. Lett. 99, 072501 (2007)
Hall-A E01-015 Delta Contamination12C(e,e'p) E
miss Distribution
K1
K2
K3 Delta events are killed by cutting on: θ
Pmiss>77-88o
(left) or xB>1 (right)
Large Emiss
is associated with Delta production
Scaling of Inclusive A(e,e') Cross Section Ratios
First observed in SLAC by D. Day et al.
Validates the expected momentum scaling
Interpreted using the 2N-SRC model
Extract the relative number of 2N(3N) SRC pairs in nuclei
K. Sh. Egiyan et al. Phys. Rev. Lett 96, 082501 (2006)K. Sh. Egiyan et al. Phys. Rev. C 68, 014313 (2003)
4He/3He
12C/3He
56Fe/3He
Scaling
3N-SRC2N-SRC
D. Day et al. Phys. Rev. Lett 59, 427 (1987)Theoretical Interpretation: L. L. Frankfurt et al. Phys. Rev. C 48, 2415-2461 (1993)
a2(Fe/d) Q2 independence
From J. Arrington talk in “High Energy Nuclear Physics and QCD” meeting, FIU, Miami, 2010
Q2=2.5 [GeV/c]2
Scaling Onset
nA(k) = a
2(A/d)·n
d(k)
3He 1.93±0.104He 3.02±0.179Be 3.37±0.1712C 4.00±0.2463Cu 4.33±0.28197Au
4.26±0.29
a2(A/d)
High Precision Results from Hall-C
N. Fomin et al., Phys. Rev. Lett. 108, 092502 (2012)
Short Range Correlations From Inclusive Measurements
Scaling onset corresponds to Pmin
≈ 275 MeV/c
In nuclei with A > 12, 2N-SRC account for:● ~20% of the nucleons in the nuclei● ~80% of the kinetic energy carried by the
nucleons
3N-SRC are an order of magnitude less abundant then 2N-SRC
∫0
∞
nd (k )k2dk=100 % ==> ∫
Pmin
∞
nd (k )k2dk=4 %
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