new measurement of the emc effect for light nuclei and global study of the a-dependence patricia...
DESCRIPTION
3 The EMC ratio Isoscalar correction Ratio of cross sections per nucleon:TRANSCRIPT
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New Measurement of the EMC effect for Light Nuclei and Global Study of the A-Dependence
Patricia SolvignonArgonne National Laboratory
ECT 2008 WorkshopNuclear Medium Effects on the Quark and Gluon Structure of Hadrons
June 3-7, 2008
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Outline
JLab E03-103 preliminary results: Q2-dependence study with Carbon 3He and 4He Heavy nuclei and Coulomb distortion
Nuclear dependence of the EMC effect World data re-analysis New extrapolation to nuclear matter
Resonance data and target mass corrections
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The EMC ratio
€
REMC = σ 2A / A
σ 2D /2
⋅ 1+ F2n /F2
p
Z + NF2n /F2
p
⎛ ⎝ ⎜
⎞ ⎠ ⎟
Isoscalar correction
Ratio of cross sections per nucleon:
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Existing EMC Data SLAC E139 most complete and precise data set for x>0.2
A/D for A=4 to 197 4He, 9Be, 12C, 27Al, 40Ca, 56Fe, 108Ag, and 197Au Size at fixed x varies with A, but shape is nearly constant
E139
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Existing EMC Data SLAC E139 most complete and precise data set for x>0.2
A/D for A=4 to 197 4He, 9Be, 12C, 27Al, 40Ca, 56Fe, 108Ag, and 197Au Size at fixed x varies with A, but shape is nearly constant
E03-103 will improve with Higher precision data for 4He Addition of 3He data Precision data at large x and on heavy nuclei
Lowering Q2 to reach high x region
E139
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JLab Experiment E03-103
A(e,e’) at 5.0 and 5.8 GeV in Hall C
Targets: H, 2H, 3He, 4He, Be, C, Al, Cu, Au
10 angles to measure Q2-dependence
Spokespersons: D. Gaskell and J. ArringtonPost-doc: P. Solvignon
Graduate students: J. Seely and A. Daniel
W=2
.0G
eV
W=1
.4G
eVW
=1.1
GeV
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E03-103: Carbon EMC ratio and Q2-dependence
Small angle, low Q2 clear scaling violations for x>0.7, but surprisingly good agreement at lower
x
Preliminary
at x=0.6
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E03-103: Carbon EMC ratio and Q2-dependence
Preliminary
At larger angles indication of scaling to very large x
at x=0.6
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More detailed look at scaling
E03-103SLAC e139
W>2 GeV
W>1.4 GeV
C/D ratios at fixed x are Q2
independent for:
W>1.4 GeV2 and
Q2>3 GeV2
limits E03-103 coverage to x=0.85
Note: Ratios at larger x will be shown, but should be taken cautiously
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E03-103: Carbon EMC ratio and Q2-dependence
Preliminary
At larger angles indication of scaling to very large x
The combined two highest Q2 are used in the rest of the talk
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E03-103: Carbon EMC ratio
Preliminary
W>2.0 GeVW>1.4 GeV1.1<W<1.4 GeV
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E03-103: 4He
Preliminary
JLab results consistent with SLAC E139Improved statistics and systematic errors
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E03-103: 4He
Preliminary
JLab results consistent with SLAC E139Improved statistics and systematic errors
Large x shape more clearly consistent with heavier nuclei
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E03-103: 4He
JLab results consistent with SLAC E139Improved statistics and systematic errors
Large x shape more clearly consistent with heavier nuclei
Models shown do a reasonable job describing the data
Preliminary
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E03-103: comparison carbon and 4He
Magnitude of the EMC Effect for C and 4He very similar
4He more consistent with SLAC A=12 fit than A=4
Preliminary
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E03-103: comparison carbon and 4He
Magnitude of the EMC Effect for C and 4He very similar
4He more consistent with SLAC A=12 fit than A=4
4He acts like a “real nucleus”
Some hint of difference in shape, but hard to tell with existing errors
Preliminary
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E03-103: Preliminary 3He EMC ratio
Large proton excess correction
Preliminary
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E03-103: Preliminary 3He EMC ratio
Good agreement with HERMES in
overlap regionPreliminary
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E03-103: Preliminary 3He EMC ratio
Preliminary
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E03-103: Preliminary 3He EMC ratio
Melnitchouk = Afnan et.al. PRC68 035201 (2003)Smirnov = Molochkov and Smirnov Phys. Lett. B 466, 1 (1999)Benhar = private communication (Hannover SF, Paris potential)
All calculations shown use convolution formalism at some level
)( 22
2
3
pD
He
FFF
Preliminary
)2( 22
2
3
np
He
FFF
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Initial (scattered) electrons are accelerated (decelerated) in Coulomb field of nucleus with Z protons – Not accounted for in typical radiative corrections– Usually, not a large effect at high energy machines – not true at JLab (6 GeV!)
E03-103 uses modified Effective Momentum Approximation (EMA) Aste and Trautmann, Eur, Phys. J. A26, 167-178(2005)
E E+ E’ E’+
with = -¾ V0
V0 = 3(Z-1)/(2rc)
Coulomb distortions on heavy nuclei
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Initial (scattered) electrons are accelerated (decelerated) in Coulomb field of nucleus with Z protons – Not accounted for in typical radiative corrections– Usually, not a large effect at high energy machines – not true at JLab (6 GeV!)
E03-103 uses modified Effective Momentum Approximation (EMA) Aste and Trautmann, Eur, Phys. J. A26, 167-178(2005)
E E+ E’ E’+ = -¾ V0, V0 = 3(Z-1)/(2rc)
Coulomb distortions on heavy nuclei
EMA tested against DWBA calculation for QE scattering
application to inelastic scattering ?
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Effect of the coulomb distortion on E03-103 data
Gold
Before coulomb corrections
prelimin
ary
E03-103
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Gold
After coulomb corrections
prelimin
ary
Effect of the coulomb distortion on E03-103 data
E03-103
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E03-013 heavy target results and world data
prelimin
ary
prelimin
ary
Before coulomb corrections
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E03-013 heavy target results and world data
prelimin
ary
prelimin
ary
After coulomb corrections on all data
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E03-103: EMC effect in heavy nuclei
E03-103 data corrected for coulomb distortion
Preliminary
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E03-103: EMC effect in heavy nuclei
E03-103 data corrected for coulomb distortion
Cross overs independent of A
Preliminary
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Nuclear dependence of the EMC effect
Main difference due to E139 data sets used: - Sick & Day used E139 Q2-avg tables- we used E139 constant Q2 to be able to apply CC
NM
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Nuclear dependence of the EMC effect
After coulomb corrections
NM
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Nuclear dependence of the EMC effect
Good agreement between E03-103 and SLAC E139 data after Coulomb corrections.
Preliminary E03-103 results confirm A-dependence of the EMC effect.
prelimin
ary
NM
After coulomb corrections
Note: n/p correction is also A-dependent !
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Nuclear matter
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Nuclear matter
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prelimin
ary
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Target Mass Correction on the EMC ratio
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€
F2(x,Q2) = F2(x,Q2;M = 0) + M 2
Q2 F2(1)TMC (x,Q2) + h(x,Q2)
Q2 + O(1/Q4 )
from pQCDfrom experiments
Purely kinematic effects: finite value of 4M2x2/Q2
Need to be applied before calculating higher twist effects
TMCs are expressed by higher moments of F2(x,Q2;M=0)
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Target Mass Correction on the EMC ratio
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Target Mass Correction on the EMC ratio
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At first order, the TM correction on the EMC ratio is equivalent to express them versus and plot versus x
A-independent mostly cancel in the ratio
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prelimin
ary
E03-103 data on Carbon
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E03-103 data on Carbon with TMC
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prelimin
ary
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A-dependence
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NM
prelimin
ary
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A-dependence with TMC
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NM
prelimin
ary
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Nuclear matter
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prelimin
ary
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Nuclear matter and TMC
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prelimin
ary
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Summary JLab E03-103 provides:
Precision nuclear structure ratios for light nuclei Access to large x EMC region for 3He 197Au
Preliminary observations: Scaling of the structure function ratios for W<2GeV down to low Q2
Carbon and 4He have the same EMC effect Large EMC effect in 3He Similar large x shape of the structure function ratios for A>3
In progress: Absolute cross sections for 1H, 2H, 3He and 4He: test models of n/p and nuclear effects in few-body nuclei Quantitative studies of the Q2-dependence in structure functions and their ratios Coulomb distortion Nuclear density calculations Target mass correction