measurement of f2 and r on nuclear targets in the nucleon ...4 physics motivation quark-hadron...
TRANSCRIPT
Measurement of F2 and R on Nuclear Targets in the Nucleon Resonance Region
Vahe Mamyan
HALL C, August 16 2013
Carnegie Mellon University
2
Outline
✔ Physics Motivation.
✔ Formalism and Rosenbluth Technique.
✔ The Experimental Details.
✔ Analysis Technique.
✔ RA-RD results.
✔ Summary.
3
What Is New
✔ COSY matrix elements
✔ Rate Correction
✔ Pion contamination subtraction
✔ New RA-RD
4
Physics Motivation
✔ Quark-hadron duality, transition from the perturbative to the
non perturbative region of QCD.
✔ Understand the nuclear dependence of R=σL/σ
T .
✔ New data in Nuclear Resonance region enhances our
knowledge of nuclear structure.
✔ Neutrino oscillations need nuclear structure functions as input
from electron experiments.
✔ Measurements of SF in the resonance region may allow to
determine DIS SF in the high x region which is kinematically
inaccessible.
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Inelastic Electron Scattering
One photon exchange approximation.d2
d dE '=
T
L
Purely transverse Longitudinal
F L
Transverse virtual photons.
Longitudinal virtual photons.
d2
d dE '=
4 2
x W 2−M p2 [2xF1x ,Q2
14MP
2 x2
Q2 F 2x ,Q2−2xF1 x ,Q2
]
=[12 1 2
Q2 tan2
2 ]−1
= E' W 2−M P
2
2Q2 M P E 1−
R=L
T
=F L
2xF1
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The Nuclear Dependence of R
SLAC E140 data, nuclear dependence
of (RA-R
D) in DIS.
World's data of nuclear dependence
of R=σL/σ
T at high Q2 in the DIS region
for nucleon and nuclei.
R
RA-
RD
Q2 (GeV2)Q2 (GeV2)
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Rosenbluth Separation Technique
Rosenbluth separation can be done by making measurements
at two or more values of ε for fixed W2 and Q2.
d2 /=T L R= L
T
=F L
2xF1
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Experimental Hall C
HMS
Electron beam energy – 0.7 – 5.7 GeV
HMS – High Momentum Spectrometer
➢ Maximum central momentum – 7.5 GeV/c
➢ Momentum bite – 15 %
➢ Solid angle – 6 msr
➢ Luminosity > 1038 cm-2 sec-1
Beam line
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Experimental Setup
XeAe +→+ '
Drift Chambers,Horizontal and vertical
Gas Cherenkov
Target Scattering Chamber
e- e´-
Electron Beam
HMS
X
Detector Hut
Calorimeter
Segmented hodoscopes
10
Kinematics Range
New data with Q2 > 3 GeV2
Targets : C, Al, Cu, Fe.
Different epsilon values for same Q2 and W2 allows LT separation.
New data compliments data from experiment E02-109.
➢Measurements for
each energy are done
at least for 3 different
angles.
➢Wide epsilon range
allows Rosenbluth
separation.
11
COSY Matrix Elements
✔ Fitted matrix elements are not well constrained on FP where multiple scattering is a problem (low E')
✔ About ~5% of events are in the not well constrained region (red points in the scatter plot)
✔ COSY matrix elements are used for the ~5% to reconstruct target variables
12
Precision Cross Section Measurement
➢ High statistical (<2%) and good systematic (~2%) precision.
➢ Wide range of counting rate, from a 1 kHz to 0.5 MHz. Keep
trigger efficiency high for all rates.
➢ Linearity of detector response.
➢ Charge measurement.
Corrections Systematic ErrorBackground 0.4%
Acceptance 0.7%
Detector efficiency 0.3%
Tracking efficiency 0.3%
Radiative corrections 1.0%
Model dependence 0.6%
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Particle Identification
➢ Cherenkov detector for pion rejection.
➢ Calorimeter to increase pion rejection power at low energies.
➢ Combined pion rejection power of better then 100:1 for momentum
range 0.4-4.2 GeV.
14
Events Selection and Backgrounds
Pion contamination 0.8%, E’=0.44 GeV, θ=75o
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Pion Contamination Subtraction
✔ Some pions pass all PID cuts
✔ Need to subtract the pion background
✔ Subtracted for both electron and positron runs
16
Wrong Track Rate Correction
➢ Tracking finds tracks but choose the wrong one, needs correction➢ Correction depends on rate ( number of tracks)➢ The total energy deposited in the calorimeter can be used to estimate number of tracks wrongly chosen as the correct one
Wrong track correction for one track and for more than one track
Difference of wrong track correction of one track and more than one trackversus rate
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Cross Section Extraction
Cross section
Where:
➢A(E΄,θ): acceptance correction.
➢ L: integrated luminosity.
➢ Eff: total efficiency of detecting an electron.
A(E΄,θ) acceptance correction is calculated from
Monte Carlo.
d2 , E '
d dE '=
Yield
AE ' ,× ×L×EFF
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Calorimeter Calibration
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Cerenkov Calibration
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Trigger Efficiency
✔ High trigger efficiency achieved using combination of
Cerenkov, Calorimeter and Scintillators.
✔ High tracking efficiency for all rates.
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Charge Symmetric Background
Negative pions corrected after applying CSB.
πo
γ
γ
e++e-
e++e-
22
Radiative and Bin Centering Corrections
Elastic Quasi-elastic Inelastic
IE+ QE rad. corrected CS
Bin correction factor
Bin centered CS
σ IE+QEexp (θ , E ' )=(σ All
exp−σRadElmod )/(σ RadAll
mod −σ RadElmod )×σ IE+QE
mod
BC (θi , E j ')=σBornmod (θo , E j ' )/σBorn
mod (θi , E j ')
σ(θo , E j)=
∑i
n
σ(θi ,E j)BC (θi , E j)/(Δσ (θi , E j)BC (θi ,E j))2
∑i
n
1/(Δσ(θi , E j)BC (θi , E j))2
23
Delta P Correction
Systematic shape in cross section to model ratio versus dp/p is present,probably caused by over fitting of matrix elements
The correction can be implemented as an optic correction
24
Cross Sections
Carbon Aluminum
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Cross Section Ratios σA/σ
D
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Rosenbluth Separation Ratio Method
σ AσD
=σA
T
σDT
1+ϵR A
1+ϵ RD
≈σA
T
σDT [1+ϵ ' (RA−RD)]
ϵ '= ϵ(1+ϵRD)
Nuclear to deuteron cross section ratio
➢ Acceptance error cancel
➢ Charge uncertainty cancel
➢ Beam energy offset independent
➢ Uncertainty of model cross section is minimized
➢ Allows to do Rosenbluth separation at more points
d2σ /Γ=(σT+ϵσL)
Const σA
T
σDT
Slope RA−R D
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Rosenbluth Separation Results
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Rosenbluth Separation Results
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Rosenbluth Separation Results
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Summary
➢ Jlab's Hall C allows high precision measurements of nuclear
structure functions by performing Rosenbluth separation.
➢ Study quark-hadron duality in nuclei.
➢ New data in Nuclear Resonance region enhances our
knowledge of nuclear structure.
➢ RA-RD is extracted for C, Al, Fe and Cu in the nuclear
resonance region.
➢ Reduction of uncertainties of neutrino oscillation parameters
in future neutrino oscillation experiments.