Measurement of FMeasurement of F22 and and R=R=σσLL//σσTT in Nuclei at Low Q in Nuclei at Low Q22

Phase IPhase I

Ya LiHampton University

January 18, 2008

Outline

• Physics Overview• Physical Motivation

and Description of Experiments E02-109/E04-001 (Jan05)

• Analysis Status• Preliminary Results• Future Plans

e - N scattering

2L

2T Qx, Qx,

dE'd

d

2L

2T Qx, Qx,

dE'd

d

NN

QQ22

e(Ee(E))

e’(E’e’(E’))

θθ

QQ22 - Negative - Negative squared mass squared mass of the virtual of the virtual photonphoton

MMpp - mass of the - mass of the ProtonProton

WW – invariant mass– invariant mass

One-Photon-exchange One-Photon-exchange ApproximationApproximationOne-Photon-exchange One-Photon-exchange ApproximationApproximation

12

'2

22

EMQ

MWE

p

p

12

'2

22

EMQ

MWE

p

p

Transverse Transverse virtual photon virtual photon fluxflux

1

22

2

2tan121

Q

1

22

2

2tan121

Q

Virtual photon Virtual photon polarization polarization

parameterparameter

/EE /EE

σσTT ( (σσLL) is the ) is the TransverseTransverse ((LongitudinalLongitudinal) virtual photon Cross ) virtual photon Cross SectionSection

L/T separations - Rosenbluth Method

),(2),(41

),(2)(

41 21

222

222

122

2

QxxFQxFQ

xMQxxF

MWxEdd

d p

p

),(2),(41

),(2)(

41 21

222

222

122

2

QxxFQxFQ

xMQxxF

MWxEdd

d p

p

At ε =0, F1

Diff. FL {

2L

2T Qx, Qx,

dE'd

d1

2L

2T Qx, Qx,

dE'd

d1

Reduced Reduced Cross-Cross-sectionsection

At ε =1, F2

Fit reduced cross section linearly with ε at fixed W2

and Q2 (or x, Q2) --> Need multiple beam energies.

Linear fit yields:

σσLL = Slope = Slope

σσTT = Intercept = Intercept

),(2),(41

),( 21

222

222 QxxFQxF

Q

xMQxF p

L

),(2),(41

),( 21

222

222 QxxFQxF

Q

xMQxF p

L

),(2),(),( 2

1

22

QxxFQxFQxR L

T

L

),(2),(),( 2

1

22

QxxFQxFQxR L

T

L

Physical Motivation

• 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…

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 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!

Experiment Description

• 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.

Experiment setup and procedure

Jlab Hall C

• HMS for scattered electrons

• SOS for positrons

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

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

HMS

SOS

Kinematics' Coverage Rosenbluth Separation DataRosenbluth Separation Data• Targets: D, C, Al, Fe , and some H Targets: D, C, Al, Fe , and some H

• Final Uncertainties estimated at ~1.6 Final Uncertainties estimated at ~1.6 % pt-pt in e (2% normalization).% pt-pt in e (2% normalization).

Rosenbluth Separation DataRosenbluth Separation Data• Targets: D, C, Al, Fe , and some H Targets: D, C, Al, Fe , and some H

• Final Uncertainties estimated at ~1.6 Final Uncertainties estimated at ~1.6 % pt-pt in e (2% normalization).% pt-pt in e (2% normalization).

Low QLow Q2 2 data for data for modelingmodeling• Targets: H,D, C, Al Targets: H,D, C, Al

• Final Uncertainties estimatedFinal Uncertainties estimated at ~3 - 8% (Much larger RCs at ~3 - 8% (Much larger RCs and rates)and rates)

Low QLow Q2 2 data for data for modelingmodeling• Targets: H,D, C, Al Targets: H,D, C, Al

• Final Uncertainties estimatedFinal Uncertainties estimated at ~3 - 8% (Much larger RCs at ~3 - 8% (Much larger RCs and rates)and rates)Rosenbluth Rosenbluth

separationseparations at multi. s at multi. energiesenergies

Rosenbluth Rosenbluth separationseparations at multi. s at multi. energiesenergies

Analysis Methodology

2.36 GeV2.75 GeV

1.75 GeV2.00 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 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.

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

CompletedCompletedCompletedCompletedCompletedCompletedCompleted for E’ > 1.5 GeVCompleted CompletedCompletedCompletedCompletedPreliminary Sieve SlitCompletedNearly completed inelastic ~5% and Preliminary QE

Beam and Targets Position Offsets

From geometry, we can express this as:

Tan * Z X Y/Cos Tan * Z X Y/Cos

Sin Z Cos X Y Sin Z Cos X Y

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 = 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

MCData Y - Y YMCData Y - Y Y

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. π0

γ

γ

e+

e-

e+

e-Parameterized e+ CS

eTotalCorrected eTotalCorrected

)1()( )(21

EEppe eeE )1()( )(21

EEpp

e eeE

Polynomial Fit across Theta

SOS e+ Cross-section HMS e+ Cross-section

Preliminary Cross Sections

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