Short-Range Correlations and the EMC Effect

Short-Range Correlations and the EMC Effect
Two seemingly unrelated phenomena
Linear correlation between SRC and EMC
Hypothesis: both effects are related to highmomentum
(high-virtuality) nucleons
Are high-momentum (virtuality) nucleons modified?
Future studies

Short-Range Correlations (SRC)
E
(q,ω)
E’
Partonic (nucleonic) structure of nuclei
Q 2 = !q µ
q µ = q 2 !! 2
! = E '! E
nucleons
x B
=
Q2
2m N
!
E, E’ ≈ 3-5 GeV
Q 2 ≥ 1.5 GeV 2
0 ≤ B ≤ A
B counts the number of
nucleons involved : B > n
==> at least n+1 nucleons
B determines also the minimum
momentum of struck nucleon in nucleus

At high nucleon momenta,
strength is different but shapes
of distributions are similar
Scaling!
Universality of SRC (Scaling)
A(e,e’)
Predictions by
Frankfurt,
Strikman, and
Sargsian
n
A
( k)
= C ⋅n
( k)
A
D
Adapted from
Ciofi degli Atti
Nucleus
d
% 2N corr.
4.1 ± 0.8
3
He 8.0 ± 1.6
4
He 15.4 ± 3.2
12
C 19.8 ± 4.4
56
Fe 23.9 ± 5.3
N. Fomin et al.,
Phys. Rev. Lett. 108
(2012) 092502
Additional data on
A/d and A/ 3 He
from SLAC, Hall B
a 2
(A / d) = ! (A) / A
! (d) / 2

JLAB Experiment E01-015
HRS
HRS
Use 12 C(e,e’p) as a tag to measure
12
C(e,e’pN)/ 12 C(e,e’p)
Optimized kinematics:
p
q
p
Q 2 ≈ 2.0
x B ≈ 1.2
“Semi anti-parallel” kinematics
e’
n array
n
e
Big Bite
Lead wall

What Did We Measure?
Almost all protons with p i > k F in
12
C(e,e’p) have a paired proton or
neutron with similar momentum in
opposite direction
CM momentum of pair σ CM =136±20
MeV/c {(σ CM (BNL)=143±17; σ CM (Ciofi
degli Atti & Simula)=139 MeV/c}
R. Shneor et al., PRL99, 072501 (2007)
12 C(e,e' pp)
= 9.5 ± 2%
12 C(e,e' p)
Corrected for acceptance
12 C(e,e' pn)
12 C(e,e' p) = 96 +4 !23%
12 C(e,e' pn)
12 C(e,e' pp) = 9.0 ± 2.5
Corrected for det. Efficiency and SCX
R. Subedi et al., Science 320 (5882), 1476 (2008)
np SRC is ~18 times pp (nn) SRC!!!

SRC in Data Mining from CLAS E2
!
!
p miss
12
C(e,e’pp)
from 12 C(e,e’p)
p rec
!
prec
!
prec
!
p miss
! q
!
p miss
!
q
!
p miss
!
q
Similar data from
56
Fe(e,e’pp)
208
Pb(e,e’p)
Or Hen, Tel Aviv University

What do we know about SRC?
Structure of 12 C
R. Subedi et al., Science 320 (2008) 1476
12
C(e,e’pN) and 4 He(e,e’pN)
Tensor NN Force and beyond?
R. Schiavilla, R. B. Wiringa, S. C. Pieper, J.
Carlson, Phys. Rev. Lett. 98 (2007) 132501
A(e,e’pp) data from Hall B is being
analyzed by O. Hen, TAU – “Data Mining”

DIS and the EMC Effect
E
lepton
(q,ω)
nucleon
E’
lepton
F.S.
hadrons
W 2
Q 2 = !q µ
q µ = q 2 !! 2
! = E '! E
0 < x B
= Q2
2m N
! < 1
Scale is several GeV
Nuclear binding energy
scale is several MeV
Expectation: DIS of bound nucleons ≅
DIS of a free nucleons
EMC
DIS off bound N ≠ DIS
off free N
Origin of EMC effect
! 1000
unknown!!
publications

Universality of EMC
Minimal dependence on Q 2
J. Seely et al., Phys. Rev. Lett. 103 (2009) 202301

Universality of EMC
Data from CERN, SLAC, JLAB
Size of effect (“depth” or slope) grows with A

Eureka Moment!
“…effect scales with the
local environment of the
nucleons…”
Local density?
J. Seely et al., PRL 103 (2009) 202301
SRC is a local-density
effect related to highmomentum
nucleons
Effective number of
high-momentum nucleons
in SRC is given by a 2
Is EMC related to
modified SF of highmomentum
nucleons?
|dR EMC /dx B |
a 2 (A/d)-­‐1

Correlations Between EMC and SRC!
SLAC data
L. Frankfurt, M. Strikman, D. Day, M. Sargsian,
Phys. Rev. C48, 4251 (1993)
Q 2 =2.3 GeV/c 2
J. Gomez et al., Phys. Rev. D49, 4348 (1983)
Q 2 =2,5,10, 15, GeV/c 2 (averaged)
SRC
High local density
High nucleons momenta
EMC
Is EMC related to highmomentum
nucleons?
Slopes 0.35 ≤ X B ≤ 0.7
EMC
EMC data
SLAC (Gomez et al.)
JLab Hall C (Seely et al.)
Free p+n?
SRC
SRC data
SLAC (Day et al.)
JLab Hall B (Egiyan et al.)
JLab Hall C (Fomin et al.)
Scaling factors X B ≥ 1.4
O. Hen et al., arXiv:1202.3452 [nucl-ex

Robustness of SRC-EMC Correlations
O. Hen et al., arXiv:1202.3452 [nucl-ex]
Insensitive to:
Isoscalar corrections
Radiative corrections
Coulomb corrections
Inelastic contributions
Pair C.M. moaon correcaon for A > 2:
Reduces x-­‐secaons by ~20%
Reduces intercept by ~20%
Does not make a qualitative change
to conclusions

Suggested Explanation of Correlation
between SRC and EMC
EMC effect does not occur (or is very small) for meanfield
nucleons
Both SRC and EMC are related to high-momentum (high
virtuality) nucleons in nuclei
High momentum (high virtuality) nucleons in the medium
are modified
&Hmm..
We can measure the in-medium modified structure
function F 2 in DIS
We can also measure the EMC effect for highmomentum
nucleons

Dependence of Nucleons SF on Momenta
Dependence on:
Models
Nucleon’s momentum and x B
Melnitchouk, Screiber, Thomas, Phys. Lett. B 335, 11 (1994)
Nucleon’s momentum, not x B
Gross, Liuti, Phys. Lett. B 356, 157 (1995)
Melnitchouk, Sargsian, Strikman,
Z. Phys. A 359, 99 (1997)
Binding/
off shell
Rescaling
PLC
suppression
! S
= (E S
" p Z S
) / m S

Nucleons Modified at High Momentum
M. Paolone et al. PRL 105,072001 (2010)
This is in quasi-elastic
scattering, not DIS!
Our experiment will cover the
range of virtuality 0.2 – 0.5

Explore Connection between EMC and SRC
If we are right, we should
measure a large EMC
effect by selecting highmomentum
nucleons!?
Deuteron
Is there an “EMC” effect in
the deuteron?
Is there a large “EMC”
effect in the highmomentum
tail of the
deuteron?
Does the structure function
F 2 depend on nucleon
momentum (virtuality)?
Consequences for F 2n
-­‐0.082±0.004
! d DIS " ! p DIS + ! n
DIS
! d
! p
+ ! n
= 1! (0.082 ± 0.004)(0.6 ! 0.31± 0.04) " 0.976
! d
! p
+ ! n
(x B
= 0.6) ! 0.976
! p
*
! ! *
n
! 2.4%
! p
! n
5% ! 0.5

Experimental Program at JLAB
Compare F 2 in DIS off high-momentum nucleons to F 2 of free nucleons
E12-11-107 – TAU, ODU, MIT JLAB
Experimental method
Use deuteron as a target in DIS
Tag high-momentum nucleons with high-momentum backwardrecoiling
(“spectator”) partner nucleon as in SRC using the
reaction d(e,e’N S )

Experimental Method
Utilize factorization of the d(e,e’N S ) cross section to SF and
distorted momentum distribution.
Keeping the recoil kinematics fixed and measuring x-section ratios
at 2 different χ’, the ratio is:
d 4 !
d" 1
dQ 2 d p ! d 4 !
S
d" 2
dQ 2 d p ! = ( K 1
K 2 )"# F ! 2
(! 1
'," S
, p T
,Q 2 1
) F ! 2
(! 2
'," S
, p T
,Q 2 1
) $ %
S
For χ 1 ’≈0.45 – 0.6 and χ 2 ’≈0.3 we shall measure:
" d 4 #
F ! 2
(! 1
'," S
, p T
,Q 2 1
) F ! 2
(! 2
'," S
, p T
,Q 2 1
) =
d! 1
dQ 2 d p ! %
/ K 1
#
$
S &
'
" d 4 !
d" 2
dQ 2 d p ! %
/ K 2
#
$
S &
'
Integraang over θ pq > 107° (small FSI), we’ll compare the measured raao f(α S ) to
the BONUS results for free neutron, and to the free proton SF in d(e,e’n S )

Experimental Method (cont.)
Minimize experimental and theoretical uncertainties
by measuring cross-section ratios
'
! DIS
(x high
,Q 2 1
, p ! s
)
'
! DIS
(x low
,Q 2 2
, p ! s
) ! " free DIS
(x low
,Q 2 2
)
free (x high
,Q 2 1
) ! R FSI = F bound '
2
(x high
,Q 2 1
, p ! s
)
F free 2
(x high
,Q 2 1
)
" DIS
'
x high
! 0.45
FSI correction factor
'
0.25 ! x low
! 0.35 No EMC is expected
x B
'
(For
2p µ
q = d) Q 2
µ 2[(M d
! E S
)! + p ! S
" q]
!
= Q2
x B
=
Q2
2m N
!

x B
'
= Q2
x B ’ vs. x B (Why x’?)
D(e,e’N) no FSI
2 p µ
q µ x B
= Q2
x’ B – Nucleon rest frame
x B – Lab frame
2m N
!

How to Deal with FSI?
D(e,e’p S )
We know that FSI:
Decrease with Q 2
Increase with W’
Not sensitive to x’ B
Small for pq > 107°
We shall:
Involve theoretical colleagues
Take data at large recoil angles
A. V. Klimenko et al., PRC 73, 035212 (2006)
Take data at 90°
Take data at two x’
Use low x’ data to study FSI dependence on Q 2 , W’ 2 , pq

Experimental Setup – Hall C
HMS and SHMS detect electrons
LAD detect recoiling nucleon
Central values of kinematics
10 cm LD 2 target
Low x’
High x’
LAD

Large acceptance Detector (LAD)

Kinematic Coverage
Scavered electrons
E’ [GeV]
Recoiling nucleons
θ e’
Recoil nucleon
virtuality
P S [GeV]

Expected Results
G eff /G n
G eff /G p
! S
= (E S
" p S Z ) / m S
! S
= (E S
" p S Z ) / m S
SHMS and HMS efficiency and
acceptances (1-2%)
LAD efficiency (3% protons, 5%
neutrons)
Al walls subtraction (1%)
Systematic uncertainty (4-7% total)
FSI ratio (4%)
Free nucleons structure
functions ratio (1% protons,
4% neutrons)

Summary – Nucleons Medium Modification
SRC and EMC are linearly correlated
We suggest that this correlation is because both phenomena
are related to high-momentum nucleons
We assume that highly virtual nucleons are modified
E12-11-107 is approved to measure at JLAB the ratio of F 2 for
highly virtual nucleons to F 2 of free nucleons in the deuteron
Use spectator tagging to select highly virtual nucleons in DIS
Minimize systematic uncertainties by measuring ratios
This is not (yet) an EMC measurement

Second Stage of Program - EMC
Measuring EMC with Tagged High-Momentum Recoil Nucleons
LOI-11-104 - TAU, ODU, MIT, JLAB
Basic idea of measurement
Perform DIS (Q 2 > 2; W > 2) on high-momentum (vituality) nucleons
by tagging the high-momentum recoiling nucleons
Remember, almost all high-momentum nucleons have a SRC partner!!
Measure per-nucleon x-sections (p S > 275 MeV/c; θ pq > 110°) ratio of
4
He to deuteron, σ[ 4 He(e,e’p S )]/σ[d(e,e’p S )], f(0.3 < X B < 0.6)
Signal
If EMC depend on virtuality, σ[ 4 He(e,e’p S )]/σ[d(e,e’p S )] should not
depend on x B
Magnitude of ratio should be a 2N ( 4 He/d) ≈ 4

Basic Idea of Measurement (cont.)
Second Measurement
Ratio of per-nucleon cross section, σ[ 4 He(e,e’p S )]/σ[d(e,e’)], at
the same kinematic range
Only σ[ 4 He(e,e’p S )] is tagged by p S > 275 MeV/c while σ[d(e,e’)]
is not!
Signal
Ratio depends on x B
Shape similar to universal EMC
shape BUT signal is larger
Experimental setup of both
measurements will be similar
to that of E12-11-107
CLAS data, very preliminary!
Or Hen, TAU
Remember a 2N ( 12 C/d) = 4.8 ± 0.4

Summary - EMC
LOI-11-104 plans to measure the doubly-tagged per-nucleon
cross-sections ratio σ[ 4 He(e,e’p S )]/σ[d(e,e’p S )] for p S > 275 MeV/c,
θ pq > 110°, and as f(0.3 < X B < 0.6)
LOI-11-104 also plans to measure the singly-tagged per-nucleon
cross-sections ratio σ[ 4 He(e,e’p S )]/σ[d(e,e’)] in the same conditions
If the EMC effect is related to highly virtual nucleons, then both
measurements will have a very unique signatures
A full proposal will be submitted to the next JLAB PAC
This IS an EMC measurement
Experimental
setup for both
measurements

Who Needs Short-Range Correlations?
A(e,e’p) A-1 measurements:
Shape of momentum distributions
described very well by IPM
X-section is only 65-70% of IPM
Extra high momentum strength
Short-range correlations
A
L. Lapikas, Nucl. Phys. A553, 297c (1993)
Benhar et al., Phys. Lett. B 177, 135 (1986)