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.

5

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

6

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)

7

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

8

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

9

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%

13

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

15

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

17

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

18

Calorimeter Calibration

19

Cerenkov Calibration

20

Trigger Efficiency

✔ High trigger efficiency achieved using combination of

Cerenkov, Calorimeter and Scintillators.

✔ High tracking efficiency for all rates.

21

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

25

Cross Section Ratios σA/σ

D

26

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

27

Rosenbluth Separation Results

28

Rosenbluth Separation Results

29

Rosenbluth Separation Results

30

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.