coulomb distortion in the inelastic regime patricia solvignon argonne national laboratory work done...
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Coulomb distortion in the inelastic regime
Patricia SolvignonArgonne National Laboratory
Work done in collaboration with Dave Gaskell (JLab) and John Arrington (ANL)
International Workshop on Positrons at Jefferson LabJPOS09
March 25-27 2009
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Coulomb distortion and two-photon exchange
Incident (scattered) electrons are accelerated (decelerated) in the Coulomb well of the nucleus. e
e’
Exchange of 2 (hard) photons with a single nucleon
TPE
Coulomb distortion
Opposite effect with positrons
pn
Exchange of one or more (soft) photons with the nucleus, in addition to the one hard photon exchanged with a nucleon
OPE
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3
Effective Momentum Approximation (EMA)
E → E + V Ep→ Ep + V }
3
How to correct for Coulomb distortion ?
__
⇔
Aste and Trautmann, Eur, Phys. J. A26, 167-178(2005)
1st method 2nd method
- Focusing of the electron wave function- Change of the electron momentum
DWBA
➫
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- Focusing of the electron wave function- Change of the electron momentum
➫
Effective Momentum Approximation (EMA)
E → E + V Ep→ Ep + V }
4
How to correct for Coulomb distortion ?
__
⇔
Aste and Trautmann, Eur, Phys. J. A26, 167-178(2005)
1st method 2nd method
DWBA
One-parameter model depending only on the effective potential seen by the electron on
average.
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Coulomb distortion measurements in quasi-elastic scattering
Aste and Trautmann, Eur, Phys. J. A26, 167-178(2005)
Gueye et al., PRC60, 044308 (1999)
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Coulomb distortion measurements in quasi-elastic scattering
Aste and Trautmann, Eur, Phys. J. A26, 167-178(2005)
Gueye et al., PRC60, 044308 (1999)
Coulomb potential established in Quasi-elastic scattering regime !
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Physics sensitive to Coulomb distortion
x>1 experiments
L/T experiments
EMC effect
Color transparency
In-medium modification on the nucleon FF
x>1 experiments
L/T experiments
EMC effect
Color transparency
In-medium modification on the nucleon FF
About every experiments that used nuclei with A>12
Coulomb distortion:➡ Not accounted for in typical radiative
corrections➡ Usually, not a large effect at high energy
machines➡ Important for Ep<<E
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Physics sensitive to Coulomb distortion
x>1 experiments
L/T experiments
EMC effect
Color transparency
In-medium modification on the nucleon FF
x>1 experiments
L/T experiments
EMC effect
Color transparency
In-medium modification on the nucleon FF
About every experiments that used nuclei with A>12
Coulomb distortion:➡ Not accounted for in typical radiative
corrections➡ Usually, not a large effect at high energy
machines➡ Important for Ep<<E
in this talk
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The EMC effect
€
θ
p n
γ∗
Nucleus at rest(A nucleons = Z protons + N neutrons)
e-
e-
≠ γ∗ γ∗Z + N
EMC (Cu) BCDMS (Fe) E139 (Fe)
σ A
/σD
Effects found in several experiments at CERN, SLAC,
DESY
x
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SLAC E139 results on the EMC effect
SLAC E139:
Most complete data set: A=4 to 197
Most precise at large x
→ Q2-independent→ universal shape→ magnitude dependent on A
E139
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1111
Effect of Coulomb distortion on JLab E03-103 results
50o
40o
JLab is at lower energy than SLAC but the luminosity is much higher.
We obtain similar or larger Q2 values in many cases by going to larger angles such that Ep is smaller.
So Coulomb distortion effects are 'doubly' amplified: lower beam energy and lower fractional Ep.
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E03-103 heavy target results
Preliminary
no Coulomb corrections applied
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E03-103 heavy target results
Preliminary
Coulomb corrections applied
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Extrapolation to nuclear matter
NM
Exact calculations of the EMC effect exist for light nuclei and for nuclear matter.
SLAC E139&E140
CERN EMC
CERN BCDMSCERN NMC
No Coulomb corrections applied
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Extrapolation to nuclear matter
NMSLAC E139&E140
CERN EMC
CERN BCDMSCERN NMC
Coulomb corrections applied
Exact calculations of the EMC effect exist for light nuclei and for nuclear matter.
Non-negligible effects on SLAC data
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Extrapolation to nuclear matter
NMSLAC E139&E140
CERN EMC
CERN BCDMSCERN NMC
JLab E03-103 prel.
Coulomb corrections applied
Exact calculations of the EMC effect exist for light nuclei and for nuclear matter.
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R(x,Q2)
Dasu et al., PRD49, 5641(1994)
TPE can affect theεdependence (talk of E. Christy on Thursday)
Coulomb Distortion could have the same kind of impact as TPE, but gives also a correction that is A-dependent.
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Meaning of R
In a model with:• spin-1/2 partons: R should be small and decreasing rapidly with Q2
• spin-0 partons: R should be large and increasing with Q2
Dasu et al., PRD49, 5641(1994)
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Access to nuclear dependence of R
Dasu et al., PRD49, 5641(1994)
slopes ⇒ RA-RD
Nuclear higher twist effects and spin-0
constituents in nuclei: same as in free nucleons
⇐ RA-RD=0
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Access to nuclear dependence of R
A non-trivial effect in RA-RD arises after applying Coulomb corrections
Dasu et al., PRD49, 5641(1994)
➫re-analysized
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Access to nuclear dependence of R
Preliminary
Preliminary
New data from JLab E03-103: access to lowerε
Coulomb corrections appliedNo Coulomb corrections applied
Iron-Copper
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Access to nuclear dependence of R
PreliminaryPreliminary
Coulomb corrections appliedNo Coulomb corrections applied
Gold
New data from JLab E03-103: access to lowerε
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Access to nuclear dependence of R
Preliminary
After taking into account the normalization uncertainties from each experiment
Hint of an A-dependence in R in Copper-Iron
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ε dependence of the Coulomb distortion
E=11 GeV
E=8.8 GeV
E=6.6 GeV
Theε-dependence of the Coulomb distortion has effect on the extraction of R in nuclei
Iron-Copper
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Summary
At present, corrections for Coulomb distortion in inelastic regime are done using a prescription for quasi-elastic scattering regime
➡ need a measurement of the amplitude of the effect in the inelastic regime➡ need a prescription in the inelastic regime
Coulomb distortion affects the extrapolation to nuclear matter which is key for comparison with theoretical calculations
Coulomb distortion has a real impact on the A-dependence of R: clearε-dependence
➡ hint of an A-dependence of R: could impact many experiments which used Rp or RD for RA
➡ could change our conclusion on the spin-0 constituent contents and higher twist effect in nuclei versus free nucleons.
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Back-ups
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Nucleon only model
€
F2A (xA )
A= dy ⋅ fN (y)F2
N (xA / y)xA
A
∫
€
fN (y)
€
y ≈1
€
F2A
A≈ F2
N no EMC effect
Smith & Miller,PRC 65, 015211 and 055206 (2002)
“… some effect not contained within the conventional framework is responsible for the EMC effect.” Smith & Miller, PRC 65, 015211 (2002)
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2828
Nucleons and pions model
Pion cloud is enhanced and pions carry an access of plus momentum:
and using is enough to reproduce the EMC effect
But excess of nuclear pions enhancement of the nuclear sea €
P+ = PN+ + Pπ
+ = MA
€
Pπ+ / MA = 0.04
But this enhancement was not seen in nuclear Drell-Yan reaction
E906 projectedE772 Drell-Yan
Fig from P. Reimer, Eur.Phys. J A31, 593 (2007)
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Another class of models
Interaction between nucleons
Model assumption: nucleon wavefunction is changed by the
strong external fields created by the other nucleons
Cloet, Bentz, and Thomas, PLB 642, 210 (2006)
Model requirements:• Momentum sum rule• Baryon number conservation• Vanishing of the structure
function at x<0 and x>A• Should describe the DIS and DY
data
Smith & Miller, PRL 91, 212301 (2003)
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EMC effect in nuclear matter
No Coulomb corrections applied
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3131
EMC effect in nuclear matter
Coulomb corrections applied
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EMC effect in nuclear matter
preliminary
Coulomb corrections applied
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World data re-analysis
Experiments E (GeV) A x-range Pub. 1st author
CERN-EMC 280 56 0.050-0.650 Aubert
12,63,119 0.031-0.443 Ashman
CERN-BCDMS 280 15 0.20-0.70 Bari
56 0.07-0.65 Benvenuti
CERN-NMC 200 4,12,40 0.0035-0.65 Amaudruz
200 6,12 0.00014-0.65 Arneodo
SLAC-E61 4-20 9,27,65,197 0.014-0.228 Stein
SLAC-E87 4-20 56 0.075-0.813 Bodek
SLAC-E49 4-20 27 0.25-0.90 Bodek
SLAC-E139 8-24 4,9,12,27,40,56,108,197 0.089-0.8 Gomez
SLAC-E140 3.7-20 56,197 0.2-0.5 Dasu
DESY-HERMES 27.5 3,14,84 0.013-0.35 Airapetian
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Figs from J. Gomez, PRC49, 4348 (1994))
A or density dependence ?
Density calculated assuming a uniform sphere of radius: Re (r=3A/4pRe
3)
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The structure of the nucleon
€
θ
γ∗
e-
e-
Deep inelastic scattering: probe the constituents of the nucleon, i.e. the quarks and the gluons
€
Q2 = −q2 = 4 EE 'sin2 θ2
4-momentum transfer squared
€
W 2 = M 2 + 2Mν − Q2Invariant mass squared
€
x =Q2
2Mν
Bjorken variable
€
(E,r k )
€
(E ',r k ')
€
(ν ,r q )
€
(M,r 0 )
€
W
€
d2σ
dΩdE '= σ Mott
1
νF2(x,Q2) +
2
MF1(x,Q2)tan2 θ
2
⎡ ⎣ ⎢
⎤ ⎦ ⎥