The proton structure function FThe proton structure function FThe proton structure function F222in the resonance regionin the resonance regionin the resonance region

GDH 2002, Genova, Italy, July 2002.Presented by M. Osipenko

OutlineOutlineOutline

IntroductionPhysics backgroundData analysisObtained resultsSummary

IntroductionIntroductionIntroductionTo measure the spin structure functions g1 and g2 one needs:

2 2 22 2

0 1 220

4 ( cos ) ( , ) 2 ( , )d d E E E g x Q xMg x Qd dE d dE Q E M

σ σ α θν

↓⇑ ↑⇑ ′′ − = + − ′ ′Ω Ω

for the longitudinally polarized target and2 2 2

2 201 22

0

24 sin ( , ) ( , )Ed d E g x Q g x Qd dE d dE Q E M

σ σ α θν ν

↓⇐ ↑⇐ ′ − = + ′ ′Ω Ω for the transversely polarized target.

A σ σσ σ

↓⇑ ↑⇑

↓⇑ ↑⇑

−=

+A σ σ

σ σ

↓⇐ ↑⇐

⊥ ↓⇐ ↑⇐

−=

+

But, usually, only asymmetries can be measured

and

Physics BackgroundPhysics BackgroundPhysics Background

To extract the spin structure function g1 it is essential to have a direct measurement of F2 and R in the same kinematical region

22 2

1 2

( , )( , )( , )

F x Qg x Q AD x Q

= where2

22

2 (1 )(2 )(1 ( , ))( , )1 ( , )

x y R x QD x QR x Q

εε

− − +=

+

n=1, GDH, Bjorken and Ellis-Jaffe sum rules1

21

0

( , )n dxx g x Qx∫

n≥1, Wilson twist expansion of the moments41( 2) 22 22

2 2 42 2 2

2 1

( )( , ) ( ) ( ) ...( )

n

sn n n n

k s

QE Q O Q AQ Q

γτ

τ ττ

αµ µµ µ ηα µ

−∞

= +

+ +

∑

Experimental OpportunitiesExperimental OpportunitiesExperimental Opportunities

Hall BHall C

The evaluation of the High Moments requires the structure function to be measured at large x→1 at fixed Q2.

Jefferson LaboratoryJefferson LaboratoryJefferson Laboratory

Detector CLASDetector CLASDetector CLAS4π detector operating at luminosity 1034 cm-2s-1, designed for detecting many particles in the final state, necessary for exploring exclusive channels of the photo- and electro-production;due to large acceptance, well suited for measuring integrated characteristics, in particularly – moments.

Data AnalysisData AnalysisData Analysis

1. Selection of Good Data Sample (Electron Rate Stability, Fiducial Cuts)2. Momentum Correction3. Particle Identification (Good Reconstructed Events, Calorimeter and

Cherenkov Responses)4. e+e- Pair Production Correction (Inclusive π0 Production Fit)5. Empty Target Subtraction6. Efficiency Evaluation (Monte-Carlo Simulations, Elastic ep Cross Section)7. Radiative Corrections

Electron Rate StabilityElectron Rate StabilityElectron Rate Stability

The number of event candidates taken each 10 seconds, normalized to the live-gated FC charge, have to be within ±2σG interval from the average electron rate.

Num

ber

of e

vent

s/FC

Time (10sec) Number of events/FC

Fiducial CutsFiducial CutsFiducial Cuts

θ P

φφ

“Fiducial Cuts” define the most uniform and properly operating volume of the detector. They were obtained by studying φ-distribution of the electron yield for each kinematical bin.

Momentum CorrectionMomentum CorrectionMomentum Correction

Elastic peak

Before

After

The Momentum Correction was based on the study of measured positions of the elastic peak and second resonance peak. They resulted in the significant improvement of the elastic peak width.

Particle IdentificationParticle IdentificationParticle IdentificationFor the sake of confidence in the proper particle identification, only those event candidates were selected for the analysis, whose signals matched all systems of the detector CLAS (DC, EC, CC, TOF).

Deposited Energy in EC

Before cut

After cut

Calorimeter ResponseCalorimeter ResponseCalorimeter Response

The fraction of energy released in the calorimeter has been studied, in order to reduce the background of MIP particles (mostly negative pions).

Cherenkov ResponseCherenkov ResponseCherenkov Response

In order to remove remaining pion background photo-electron distributions in PMTs of the Cherenkov Counter were studied and the separation was performed by a combined fit, using two Poisson distributions convoluted with the Gaussian, accounted for the PMT resolution.

Efficiency EvaluationEfficiency EvaluationEfficiency EvaluationThe Efficiency has been extracted using Monte Carlo simulations of the detector CLAS. Careful test of the simulations results was performed by the comparison of the measured elastic cross section with simulated one. Two cross sections showed good agreement. Extracted efficiency is very smooth function of kinematics and it is very close to 100%.

Structure Function FStructure Function FStructure Function F222

The extracted Structure Function F2 is in agreement with World data and cover whole resonance region in Q2 range from 0.3 to 4 GeV2, giving access to high moments in this region.

Q2=0.625 GeV2 Q2=2.375 GeV2

CLASWORLDWORLD

CLAS

Extracted MomentsExtracted MomentsExtracted Moments

Experimental momentsof the structure function F2 were extracted for n=2-8 with percentage of experimental points in the integral greater than 70% at Q2<5 GeV2.

Higher twist contribution was evaluated with ~10% precision from the fit of the data.

M2

M8

BloomBloomBloom---Gilman DualityGilman DualityGilman Duality

The cross section averaged over each separate resonance peak exhibits the Q2 evolution quite similar to that obtained in DIS.

Correlations and ResonancesCorrelations and ResonancesCorrelations and Resonances

Q2=0.675 Q2=1.725

A combined fit of the cross sections, based on the available information on resonance couplings, gives some indications about the nature of background and nucleon resonances.

SummarySummarySummary

Proton structure function F2 was measured with high precision in a wide two-dimensional range in x from 0.1 to 0.9 and Q2 from 0.3 up to 5 GeV2.

The higher twist contribution was extracted from the data with ~10% precision and it was interpreted in terms of the phenomenological approach.

The phenomenon of Bloom-Gilman duality was studied and showed interesting properties of the resonance-background separation.