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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)


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



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

More Correlations....

More Correlations....

Mexican Lemonade Saves Lives!Mexican Lemonade Saves Lives!

EM

C S

lope

s0

.35

≤ X

B ≤

0.7

SRC Scaling factors XB ≥ 1.4


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)


CoulombInelastic



Fomin-Egiyan Consistency

O. Hen et al, PRC 85, 047301 (2012)




CoulombInelastic

O. Hen et al, PRC 85, 047301 (2012)



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


Deuteron EMC Effect

SRC=0 free nucleons

SRC

0.084±0.004

σdDIS=σ p

DIS+σnDIS


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


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


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


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).



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)

12C/d for 4 < Q2 < 6 [GeV/c]2

J. Seely et al. PRL 103, 202301 (2009)

Q2 independence

J. Gomez et al., Phys. Rev. D 49, 4348 (1994)

EMC slope vs. average of XB=0.4-0.6

Based on data from J. Gomez et al., Phys. Rev. D 49, 4348 (1994)

b Parameter Fits

b Parameter from SLAC Measurements

J. Gomez et al., Phys. Rev. D 49, 4348 (1994)

b Parameter from JLab Measurements

J. Seely et al. PRL 103, 202301 (2009)

A Dependence of R=σ

L/σ

T

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



γp

n

pf

pf = p

1 + p

2 - p

0





Results II: (SRC Threshold?)Recoil neutrons above ~275 Mev/c have back to back angular correlation with the 12C(p,2p) missing momentum vector



γp

n

pf

pf = p

1 + p

2 - p

0





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 kinematicsx

B Distribution

(e,e'p)

(e,e'pp)

Q2≈1.8

Hall-A E01-015 kinematicsQ2 Distribution

Hall-A E01-015 kinematics12C(e,e'p) P

miss Distribution

K1

K2

K3

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

Hall-A E01-015 Delta Contaminationθ

Pmiss Cut

K1

K2

K3

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 %

LAD Drawings

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