Post on 17-Oct-2021
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