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Measurement of F 2 and R= σ L / σ T in Nuclei at Low Q 2 Phase I

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Measurement of F2 and R=σL/σT in Nuclei at Low Q2Phase I

Ya Li

Hampton University

January 18, 2008

- Physics Overview
- Physical Motivation and Description of Experiments E02-109/E04-001 (Jan05)
- Analysis Status
- Preliminary Results
- Future Plans

e(E)

e’(E’)

θ

Q2

N

Transverse virtual photon flux

Virtual photon polarization parameter

One-Photon-exchange Approximation

σT (σL) is the Transverse (Longitudinal) virtual photon Cross Section

Mp- mass of the Proton

W– invariant mass

Q2 - Negative squared mass of the virtual photon

Reduced Cross-section

At ε =1, F2

Diff. FL {

At ε =0, F1

Fit reduced cross section linearly withεat fixed W2 and Q2 (or x, Q2) --> Need multiple beam energies.

- Linear fit yields:
σL = Slope

σT = Intercept

- Sparse data available in Resonance Region on Fundamental Separated Structure Functions in Nuclei (F1,F2,FL, R)
- Low Q2 L/T Structure Function Moments
- Study Quark-Hadron Duality in Deuteron, Neutron, and Nuclei.
- Also, important input for Spin Structure Function extraction from asymmetry measurements, RCs, etc…

- New generation of neutrino experiment are being built to investigate neutrino oscillations and interactions
-i.e. MinervA, mini-Boone, MINOS, , T2K

- Input for neutrino cross section models, needed for new generation of oscillation experiments around the world
- However…Neutrino Cross Sections still poorly understood
- Neutrino Oscillations Dm2 ~ E / L, requires E in few GeV range (same as JLab!)
- Global models needed linking electron and neutrino scattering data

Resonance region is a major contribution!

- E02-109: Meas. of F2 and R on Deuterium.
- E04-001: Meas. of F2 and R on Carbon, Iron, and Aluminum. Also, Hydrogen for crosschecks. (Data from this will also be used by neutrino scattering community).
- Beam Energies used were: 4.6, 3.5, 2.3, and 1.2 GeV.
- Experiments ran for ~2 weeks in Hall C of January 2005 to cover 0.05 < Q2 < 2 (GeV)2 and 0.5 <W2 < 4.25 (GeV)2.

- Jlab Hall C
- HMS for scattered electrons
- SOS for positrons

At fixed Ebeam, θc, scan E’ from elastic to DIS.

Repeat for each Ebeam, θcto reach a range in ε for each W2, Q2.

HMS

SOS

- Rosenbluth Separation Data
- Targets: D, C, Al, Fe , and some H
- Final Uncertainties estimated at ~1.6 % pt-pt in e (2% normalization).

- Low Q2 data for n modeling
- Targets: H,D, C, Al
- Final Uncertainties estimatedat ~3 - 8% (Much larger RCs and rates)

Rosenbluth separations at multi. energies

HMS Momentum

2.75 GeV

2.36 GeV

2.00 GeV

1.75 GeV

- Bin efficiency corrected e- yield in p/p - (∆p/p = +/- 8%, ∆ = +/- 35 mrad)
- Subtract scaled dummy yield bin-by-bin, to remove e- background from cryogenic target Aluminium walls.
- Subtract charge-symmetric background from π0 decay via measuring e+ yields.
- Apply acceptance correction for each - bin.
- Apply radiative corrections bin-by-bin.
- Apply bin-centering correction and average over => for each bin.

Structure Function Extraction

- Rosenbluth separations at each W2 and Q2 where possible (range in ε exist to perform a good linear fit)
- A global fitting of F2 and R over the entire kinematics range.

Completed

Completed

Completed

Completed

Completed

Completed

Completed for E’ > 1.5 GeV

Completed

Completed

Completed

Completed

Completed

Preliminary Sieve Slit

Completed

Nearly completed

inelastic ~5% and Preliminary QE

Detector Calibrations

Calorimeter Efficiency

Cerenkov Efficiency

Tracking Efficiency

Trigger Efficiency

Computer Dead Time

Acceptance Corrections

Beam Position Offsets

Beam Position Stability

Kinematics Offsets

Beam Energy Stability Study

Target Density Corrections

Optics Checks

Radiation Corrections

Charge Symmetric Background

Cross-Sections

Where ∆X is the offset of the beam, ∆Z is the offset of the target relative to the pivot, and θ is the HMS angle.

From geometry, we can express this as:

- Comparing the beam position of the Data to the Monte Carlo for different , we’ve arrived at these offsets (mm)

FeCHD

∆X = 0.8627 1.1837 1.0795 1.1420

Err = 0.2811 0.4530 0.3043 0.3501

∆z = 2.5009 -2.0983 1.7682 1.6016

Err = 0.6245 0.4530 0.4340 0.4058

Data and MC

(before position corrections)

Data and MC

(after position corrections)

Subtract off Charge Symmetric electrons by subtracting off positron Cross-Sections.

e+

γ

e-

π0

e+

γ

e-

Polynomial Fit across Theta

Parameterized e+ CS

SOS e+ Cross-section

HMS e+ Cross-section

- Model only accounts for Inelastic Cross Section
- Results do not account for Quasi-Elastic contribution
- Model does not accurately account for resonances at low Q2

- Extract position cross sections for CSB correction
- Extract QE and Inelastic cross sections
- Improve on Global Fits of Data
- Complete Final Cross Sections
- Rosenbluth Separations
- Extract Structure Functions