12.5°

6°

Chicane Magnets

BPM

Spectrometer

Fast Raster

Slow Raster

BCM

Polarized Target

Spectrometer

Local Beam Dump

Septa Magnets

•  Two ways to measure the charge radius •  Energy splitting of 2S1/2 – 2P1/2 levels •  e-P Scattering experiments

•  Main uncertainties (µH) are related to integrals of the spin structure functions

•  ΔS is largest portion of

theoretical uncertainty

• 

• 

The Jefferson Laboratory accelerator has been used to great effect in the study of the polarized structure of nucleons. Measurements of the spin-dependent structure functions have been proven to be powerful tools in testing the validity of effective theories of Quantum Chromodynamics. While the neutron spin structure functions, g1

n and g2n,

and the longitudinal proton spin structure function, g1p, have been measured over a wide kinematic range, the

second proton spin structure function, g2p, has not. This poster will present the E08-027 (g2p) experiment, which

was an inclusive measurement of g2p in the resonance region at Jefferson Lab's Hall A. This is the first

measurement of g2p covering 0.02 GeV2 < Q2 < 0.2 GeV2. The experiment will allow us to test the Burkhardt-

Cottingham Sum Rule at low Q2 as well as extract the longitudinal-transverse generalized spin polarizability and compare it to predictions made by Chiral Perturbation Theory. In addition, the data will reduce the systematic uncertainty of calculations of the hyperfine splitting of hydrogen and extractions of the proton charge radius.

Abstract

On behalf of the E08-027 Hall A collaboration, Jefferson Lab

 Ryan Zielinski

The Proton Spin-Dependent Structure Function, g2 , at Low Q2

 

Experimental Setup

d

2�

d⌦dE0 (#* + "*) =✓d�

d⌦

◆

Mott

✓2

M

F1(x,Q2) tan2

✓

2+

1

⌫

F2(x,Q2)

◆Unpolarized  

•  Deviation from point-like scattering in inclusive electron scattering is described by four structure functions

•  F1 and F2 are the unpolarized structure functions and g1 and g2 are the spin-polarized structure functions •  g2 is sensitive to quark-gluon interactions (higher twist)       W

e’

*

e

p*

!!

*

Longitudinal  d

2�

d⌦dE

0 (#* � "*) = 4↵

2

M⌫Q

2

E

0

E

[(E + E

0cos ✓)g1(x,Q

2)� Q

2

⌫

g2(x,Q2)]

*

d

2�

d⌦dE0 (#) � ")) =4↵2sin✓

M⌫

2Q

2

E

02

E

[⌫g1(x,Q2)� 2Eg2(x,Q

2)]

Transverse  

** *

What is g2p ?

•  Spectrometer detectors provide trigger, tracking and particle identification •  Achieved record Hall A DAQ rate of 6-7 kHz during the run period

•  Low beam current ( 50 – 100 nA) and fast/slow rasters used to minimize target depolarization •  Two dipole ‘chicane’ magnets correct for beam bending due to field from polarized target •  Septa magnets bend electrons scattered at 6° to spectrometers set at 12.5° •  Local beam dump for kinematic settings where beam won’t reach Hall A dump

•  NH3 target polarized using dynamic nuclear polarization •  Target operated at 5 and 2.5 T •  NMR measured polarization

Polarized Target

High-Resolution Spectrometers

Beamline Diagnostics

Motivation Measure a fundamental spin observable, g2p, in the

region 0.02 GeV2 < Q2 < 0.20 GeV2 for the first time.  

Z 1

xmin

g2(x,Q2)dx

Resonance Contribution

•  Extract longitudinal-transverse generalized spin polarizability (δLT) to test Chiral Perturbation Theory (χPT) calculations

•  Test Burkhardt-Cottingham (BC) Sum Rule

•  Crucial input for hydrogen hyperfine splitting and proton charge radius measurements

Measurement of g2p is useful for …

Burkhardt-Cottingham Sum Rule

Longitudinal-Transverse Spin Polarizability

Z 1

0g2(x,Q

2)dx = 0

•  BC Sum rule will fail if: •  g2

p behaves as a δ-function at x = 0

•  Exhibits non-Regge behavior

Proton

Neutron

Neutron

•  δLT is insensitive to Δ-resonance, so it is a good place to test χPT calculations

•  Deviations from calculations could indicate significant short-range contributions

Hydrogen Hyperfine Splitting

Δ2 is dominated by low Q2 g2p

Proton Charge Radius

Analysis Optics and Simulation

Sieve Slit After Optics Matrix Calibration

Simulated Electron Trajectories

Detector Calibration

central momentum (GeV/c)0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

/e R

atio

π

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

central momentum (GeV/c)0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

/e R

atio

π

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

Pion Suppression for RHRS

central momentum (GeV/c)0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

/e R

atio

π

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01Legend

2.2 GeV, 2.5T, 90deg1.7 GeV, 2.5T, 90deg1.2 GeV, 2.5T, 90deg1.2 GeV, 2.5T, 90deg (short cell)2.2 GeV, 5.0T, 90deg2.2 GeV, 5.0T, 0deg3.3 GeV, 5.0T, 90deg

Mp π Δ 900 1000 1100 1200 1300W (MeV)

Δ - Resonance

Nitrogen Elastic

Proton Elastic/Nitrogen Quasi-Elastic

VeeVeeVeeeeeeVereVereererVererererererererererereererereeeeererererererererererererereererereeee

Yield

Online Results

�  

Figure 13: Harp scan data combined with DAQ data, the as-terisk is the harp scan data, while the dot is the DAQ data.

and c00, c01, c

02 are the calibration constant. The value of c1 is

close to 1 and c2 is close to 0, the value of c0 can be adjusted to0 if carefully adjust the value g

x

. From equation (14), at leastthree points are needed.

For the BPM calibration, the following steps is used:1.Do the linear fit for a group of runs which have same posi-

tion but different current. The calibration run should be takenfor several currents for each position, so just choice one to getthe parameter b for each raw signal and g

x/y

.2.Calculate the x and y by using equation (10)3.Combine with the harp data, doing the fit for the equation

(14)An example of the BPM calibration picture is shown in fig-

ure 13 . The asterisk in picture is the absolute beam positioncalculated from the harp scan data, and the dot at the centerof the asterisk is the DAQ data from ADC after calibration.

22

•  Optics calibration for the LHRS mostly complete (with and without target field)

•  Monte-Carlo simulates the effect of the target and septum fields in combination with HRS

•  Used for optics calibration with target field and also acceptance study

SNAKE Transport Model

•  Cuts to suppress pion contamination are

chosen to keep electron detection efficiency above 99%

Particle ID

•  Multi-track events are carefully examined and

resolved bringing the systematic uncertainty below 1% for all settings

VDC Track Efficiency

99.2

99.4

99.6

99.8

100

3000 3500 4000 4500 5000 5500 6000 6500

Tri

gger

Eff

icie

ncy(

%)

Run Number

•  Efficiency is

above 99% on each HRS

Trigger Efficiency

LHRS Trigger Efficiency Dilution Study

BPM Calibration

Slow raster shape at BPM Inner Circle: Carbon ‘Hole’ for

raster size calibration

Asterisk: Harp Signal Points: Calibrated BPM

signal

Nu (MeV)300 400 500 600 700 800

0.1

0.15

0.2

0.25

0.3

0.35 P.Bosted 2009

Nucleon Ratio

P.Bosted 2009

Nucleon Ratio

P.Bosted 2009

Nucleon Ratio

P.Bosted 2009

Nucleon Ratio

P.Bosted 2009

Nucleon Ratio

P.Bosted 2009

Nucleon Ratio

3.350GeV Dilution

Preliminary

Yields for E = 2.2 GeV (LHRS)

Asymmetry for E = 2.2 GeV

Acknowledgements: Spokespeople: A. Camsonne, J.P. Chen, D.Crabb, K.Slifer, Post-Docs: K. Allada, J.Maxwell, V. Sulkosky, J.Zhang, Graduate Students: T. Badman, M. Cummings, C. Gu, M. Huang, J. Liu, P.Zhu

Top-View of Hall A

rp (fm) Unc. (fm) � Method0.84184 0.00067 0.0 µH Lamb Shift0.897 0.018 3.1 e-P scattering0.8768 0.0069 5.0 eH Lamb Shift

Kinematic Coverage

•  BPM calibration

is completed

•  Position and angle uncertainty at target center are approx. 1mm and 1mrad, respectively

•  Dilution factor accounts for scattering from unpolarized material in the ammonia target

 

�E = (1 + �)EF

� = �QED + �R + �small +�S

�

LT

(Q2) =16↵M2

Q

6

Zx0

0x

2[g1 + g2]dx