Measurement of F 2 and R=σ L /σ T in Nuclei at Low Q 2 Phase I Ya Li Hampton University January 18, 2008

Outline Physics Overview Physical Motivation and Description of Experiments E /E (Jan05) Analysis Status Preliminary Results Future Plans

e - N scattering N Q2Q2Q2Q2e(E)e’(E’)θ Q 2 - Negative squared mass of the virtual photon M p - mass of the Proton W – invariant mass One-Photon-exchange Approximation Transverse virtual photon flux Virtual photon polarization parameter σ T (σ L ) is the Transverse (Longitudinal) virtual photon Cross Section

L/T separations - Rosenbluth Method At ε =0,  F 1 Diff.  F L { Reduced Cross-section At ε =1,  F 2 Fit reduced cross section linearly with ε at fixed W 2 and Q 2 (or x, Q 2 ) --> Need multiple beam energies. Linear fit yields: σ L = Slope σ L = Slope σ T = Intercept σ T = Intercept

Physical Motivation Sparse data available in Resonance Region on Fundamental Separated Structure Functions in Nuclei (F 1,F 2,F L, R) Low Q 2 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…

Motivation from Neutrino Experiments 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 Dm 2 ~ 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!

Experiment Description E02-109: Meas. of F 2 and R on Deuterium. E04-001: Meas. of F 2 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 < Q 2 < 2 (GeV) 2 and 0.5 <W 2 < 4.25 (GeV) 2.

Experiment setup and procedure Jlab Hall C HMS for scattered electrons SOS for positrons At fixed E beam, θ c, scan E’ from elastic to DIS. Repeat for each E beam, θ c to reach a range in ε for each W 2, Q 2. HMS SOS

Kinematics' Coverage Rosenbluth Separation Data Rosenbluth Separation Data Targets: D, C, Al, Fe, and some H Targets: D, C, Al, Fe, and some H Final Uncertainties estimated at ~1.6 % pt- pt in e (2% normalization). Final Uncertainties estimated at ~1.6 % pt- pt in e (2% normalization). Low Q 2 data for  modeling Low Q 2 data for  modeling Targets: H,D, C, Al Targets: H,D, C, Al Final Uncertainties estimatedat ~3 - 8% (Much larger RCs and rates) Final Uncertainties estimated at ~3 - 8% (Much larger RCs and rates) Rosenbluth separations at multi. energies

Analysis Methodology 2.36 GeV 2.75 GeV 1.75 GeV 2.00 GeV HMS Momentum 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 π 0 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 W 2 and Q 2 where possible (range in ε exist to perform a good linear fit) A global fitting of F 2 and R over the entire kinematics range.

Analysis Status 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 Completed Completed for E’ > 1.5 GeV Completed Preliminary Sieve Slit Completed Nearly completed inelastic ~5% and Preliminary QE

Beam and Targets Position Offsets From geometry, we can express this as: 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.

Beam and Targets Position Offsets Comparing the beam position of the Data to the Monte Carlo for different , we’ve arrived at these offsets (mm) Fe C H D ∆X = Err = ∆z = Err =

Data and MC (before position corrections) Data and MC (after position corrections) Beam and Targets Position Offsets

Charge Symmetric Backgrounds Subtract off Charge Symmetric electrons by subtracting off positron Cross-Sections. π0π0 γ γ e+e+ e-e- e+e+ e-e- Parameterized e+ CS Polynomial Fit across Theta SOS e+ Cross-sectionHMS e+ Cross-section

Preliminary Cross Sections

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

Plans in the Future 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