E08014 Analysis Update:
Short Range Correlations at x>2
Zhihong Ye
University of Virginia & E08014 Collaboration
Hall-A Meeting, 06/13/2013
Overview of Nuclear Structure
 Mean Field Theory (Independent Particle Shell Model):

Nucleons move independently in an average
potential induced by the surrounding nucleons;

Occupying separated energy shells bellow Fermi sea:
hM     

Predicting nucleons eigen-states and magic numbers.
 Missing Strength:

The Spectroscopy Factor should equal to the number
of states a nucleon is allowed to occupied:
S
 1,
(2 j  1)
j  number of “shells”
 Proton knock-out experiments show 30% -- 40% missing lower than the mean field prediction;
 Can’t be explained by advanced Hartree-Fock calculation including long range interactions.
Short Range Correlations
 Attribute To The Missing Strength:
C. Ciofi degli Atti and S. Simula, Phys. Rev. C 53 (1996).
• Strong repulsive force at short-distance (<1 fm);
• High relative momenta; Zero total momentum.
• Similar shape for High momentum tails (k>kFermi).
Slow decreasing momentum distribution is
responsible for the missing strength.
Short Range Correlations
 Attribute To The Missing Strength:
• Strong repulsive force at short-distance (<1 fm);
C. Ciofi degli Atti and S. Simula, Phys. Rev. C 53 (1996).
• High relative momenta; Zero total momentum.
• Similar shape for High momentum tails (k>kFermi).
2N-SRC
n
p
kfermi
High-momentum
region: SRCs
dominated.
3N-SRC
1.7 fm
n
p p
Mean Field
Region
p
< 1.0 fm
•
2N-SRC dominates at 300 < k < 600 MeV/c  scaled to Deuterium
•
3N-SRC dominates at k – 800 MeV/c  scaled to He3;
•
Non-Nucleonic D.O.F at extremely high momentum (Dense nuclear matter such as Neutron Stars).
Short Range Correlations
 Probing Srcs With A(e,e’):
 At Quasi-Elastic (QE) Region (PWIA):


d
  dk  dE   ep  S (| k |, E ),
ddE '
Q2
xbj  A
, 0  xbj  A, QE , xbj  1
2m p
 Extract momentum distribution:
d 3
   F ( y ),
dE ' d
n( p ) 
 1 dF ( y )
2p dy
 Inclusive Cross Section in SRCs (for xbj >1.3):
A
 A ( x, Q )  
2
j 2
A
A
A
a j ( A) j ( x, Q 2 )  a2 ( A) 2 ( x, Q 2 )  a3 ( A) 3 ( x, Q 2 )  ...
j
2
3
 Scaling (independent of xbj and Q2):
2N-SRC (1.3<xbj <2)
2  A ( x, Q 2 )
a2 ( A, D) 
,
A  D ( x, Q 2 )
3N-SRC (2<xbj <3)
3 A
a3 ( A,3He)  K 
A He
3
E08014 Goals
 3N-SRC Plateau:
K. Egiyan et al, PRL96, 082501 (2006)
N. Fomin et al, PRL 108,092502 (2012)
CLAS & E02-019 results:

Agreement for xbj <2 region

Different onset values for 3N plateau

CLAS: Q2 ≈ 1.6 GeV2,
E02-019: Q2 ≈ 2.7 GeV2

Large error bars at 3N-SRCs for E02-019
E08014: Study the onset of 3N-SRC scaling plateau at x>2, using high precision HRSs and high Statistic.
E08014 Goals
 Isospin Effect in SRCs:
 The abstractive NN interaction is mainly due to
Tensor Force.
 Study in Inclusive measurement:
 E08-014 using Ca48/Ca40
 In 2N-SRC, iso-singlet np pairs (T=0) dominates.
 Hall-A results shows 80% of 2N-SRC in np pairs.
R. Subedi et al, Science, 320 1476 (2008)
Theory of srcs assumes isospin independent;
 Ca 48 / 48 (20 p  28 n ) / 48

 Ca 40 / 40 (20 p  20 n ) / 40
 3
p


n  0.92
For 2n-src, n-p (t=0) pairs dominate.
 Ca 48 / 48 (20  28) / 48

 Ca 40 / 40 (20  20) / 40

1.17
25% difference
 New Hall-A experiment using He3/H3 :
E12-11-112, P. Solvignon, J. Arrington,
D. Day, D. Higinbotham
E08-014 Experiment in Hall-A@JLab
 Configurations:
Un-polarized Electron Beam at 3.356 GeV; Two HRSs taking data Simultaneously;
Standard Detector Packages; One DAQ system.
 Modified Triggers:
T1&T3: S1 + S2m + GC, main production triggers.
T6&T7: S1 + S2m, for efficiencies and PID study.
T3&T4: Efficiencies Study
 Mis-Match RQ3
HRS-R Q3 was scaled down to 87.72% due to a
power supply problem.
Kin6.5
Kin5.2
Kin5.05 Kin5.1
Kin5.0
Kin4.1 Kin4.2
Kin3.1
Kin3.2
E0 = 3.356GeV
 Targets:
Cry-Targets: LH2, He3, He4  Non-uniform density (“bump”)!
Solid Targets : C12, Ca40, Ca48, and other calibration targets.
First time used in Hall-A
E08014 Analysis Status
 In General:
 Instruments have all been calibrated, i.e., Detectors, Optics, Beam charge, Target
Boiling …
 Efficiencies, Dead Time, and Statistical Errors (and partial Systematic Errors) are
evaluated.
 Cross Section Model (XEMC) and Monte Carlo Simulation (SAMC) work well.
 Prelim. Cross Section Results and SRC Ratio are available.
On Progress:
 Additional Corrections on DeltaP on HRS-R (reported in this talk)
 Cryo-Target Density Distribution (Simulation by Silviu Crovig, reported in this talk)
 Iteration Cross Section and Check Radiation Correction
E08-014 Data Analysis - Optics
 Optics Calibration – HRS-R:
Scaled down Q3 field by 87.72% for each HRS-R central momentum setting.
Y-Terms, T-Terms, and P-Terms were able to calibrate using new optics data.
Reconstructed with original optics!
Sieve Slit Pattern
Target Vertex
E08-014 Data Analysis - Optics
 Optics Calibration – HRS-R:
Scaled down Q3 field by 87.72% for each HRS-R central momentum setting.
Y-Terms, T-Terms, and P-Terms were able to calibrate using new optics data.
Reconstructed with NEW optics!
Target Vertex
Sieve Slit Pattern
E08-014 Data Analysis -DeltaP
 DeltaP Correction for HRS-R Data with SAMC:
 HRS Optics  Polynomials functions  Transportation functions in SNAKE
Forward transportation Functions:
Target Plane  Focal Plane
Backward transportation Functions: Focal Plane  Target Plane
 Asked John LeRose to generate new transportation functions for HRS-R, with Q3 field
scaled down by 87.72% compared to Dipole field.
 Two sets of RQ3 “DeltaP-Optics” in SAMC:
“Old” -> DeltaP functions with Q3 field equal to Dipole field;
“New” -> DeltaP functions with Q3 field equal to 87.72% of Dipole field.
 In SAMC, generating two sets of data with the same seeds:
but wrong!
1, New Forward + Old Backward  Simulate the REAL DeltaP reconstruction on HRS-R (δpwrong);
2, New Forward + New Backward  Simulate the CORRECTED DeltaP reconstruction (δpright).
12
E08-014 Data Analysis -DeltaP
 DeltaP Correction for HRS-R Data:
 Correcting Data by defining the polynomial correction function:
f ( x fp , y fp ,  fp ,  fp )  pright  pwrong
higher order
residuals
4

(A x
i , j , k ,l  0
i
i
fp

 B j y fpj  Ck fpk  Dl lfp )   K pwrong
,
 0
 Using MC (Data#1 & Data #2); Fitting the correction
function by correlating with focal plane variables:
δpright - δpwrong
2-D
Profile-Y
Residual
.vs. xfp
δpright - δpwrong
4
2-D
Profile-Y
Residual
.vs. yfp
.vs. ϕfp
.vs. δpold
.vs. θfp
 From MC data, the correction function can recover
DeltaP reconstruction as good as near 0.03%.
13
E08-014 Data Analysis -DeltaP
 DeltaP Correction for HRS-R Data:
 Apply the correction function on experimental data
 To improve:
For uncorrected high-order terms,
using D-Terms from SNAKE as
Starting Point in replay (with the help
from John LeRose)
 Conclusion:
1, HRS optics with distorted Q3 field still can be extracted (need a good optics run plan);
2, Gain additional Yields due to Q3 enlarging the acceptances (Q3 -13%  +5% Yield);
3, Pay attention to the acceptance effect.
14
E08-014 Data Analysis - Target
 Cryo-target Density Uniformity
Bumps are due to the special design of target flow
and coolant system.
He4 Flow in the cell
Cryo-Taget Simulation (Courtesy to Silviu Covrig)
E08-014 Data Analysis - Target
 Extract The Density Distribution From Simulation:
• Cryogenic target density is important for absolute cross sections and ratio.
• Big systematic errors to extract target density using real data and MC data.
He4 density in the cell
Cryo-Taget Simulation (Courtesy to Silviu Covrig)
E08-014 Data Analysis - Target
 Extract The Density Distribution From Simulation:
• Cryogenic target density is important for absolute cross sections and ratio.
• Big systematic errors to extract target density using data and mc.
Simulated upto 10 uA.
Extremely unstable at 45 uA!
LD2 density in the cell
Cryo-Taget Simulation (Courtesy to Silviu Covrig)
E08-014 Data Analysis - Target
 Put the Distribution in SAMC:
LD2 Density in SAMC:
Black  Generated at the target
Blue  See from HRS
(pass the acceptance cut)
He4
Compare MC data and Real data:
Red  Real Data
Blue  MC data weighted by cross sections.
Conclusion: We still need to learn more from the
Cryo-Target system.
LD2
Extracting Cross Sections
 Experimental differential cross section:
EX
i
d born
YEX
MC
( E0 , E 'i ,  0 )  i   born
( E0 , E 'i ,  0 ),
dE ' d
YMC
 Experimental Yield:
i
EX
Y
i
N EX
-- Total events in ith bin;
 Monte Carlo Yield:
i
N EX

N e   eff
N e -- Total electron charge;  eff -- Total Detectors’ efficiencies.
i
MC
YMC
 N tg    rad
( E ' j , j ) 
ji
N tg -- Total target luminosity;
(binning in E’, then calculating xbj)
 MC E 'MC
gen
N MC
 MC , E'MC - Entire phase space in MC (slight larger than HRS)
gen
N MC
-- Total generated MC events;   rad ( E ' j , j ) - Radiated Cross Section Sum of all events in each bin
MC
ji
 Advantage of Yield Ratio:
 Study the acceptance effect;
 Check the difference between data from two HRSs before combining them;
 Experimental Yield remain untouched, but only apply correction on MC Yield and
iterate the XEMC model until the ratio close to one; Reduce model dependence.
Extracting Cross Sections
 Preliminary Cross Section Results: (H2)
 Preliminary Cross Section Results: (He3)
Extracting Cross Sections
 Preliminary Cross Section Results: (He4)
 Preliminary Cross Section Results: (C12)
Extracting Cross Sections
 Preliminary Cross Section Results: (Ca40)
 Preliminary Cross Section Results: (Ca48)
Preliminary Ratio
 Ca48/Ca40 Ratio:
Ratio Results could be shifted after fixing the Ca40 thickness as well as Cross
Section Models
Preliminary Ratio
 C12/He3 Ratio (Comparing with E02-019 ):
E08-014 agrees with E02-019.
Preliminary Ratio
 He4/He3 Ratio (Comparing with CLAS E02-019 ):
No 3N-SRC Plateau?  Can’t conclude yet!
Summary
 SRCs attribute to the 30% - 40% missing strength in nuclei predicted by Mean Field
Theory
 Inclusive QE electron scattering provide a clean tool to probe 2N-SRC, 3N-SRC.
 E08014 aims to verify the onset of 3N-SRC at x>2 and study Isospin dependence using
Ca40 and Ca48.
 Data analysis is nearly completed. Final results will be available soon.