Low Q2 Measurement of g2 and the ?LT Spin Polarizability

1
Low Q2 Measurement of g2and the?LT Spin
Polarizability
p
Resubmission of E07-001 to Jefferson Lab
PAC-33 Jan. 14, 2008

• A. Camsonne, J. P. Chen
• Thomas Jefferson National Accelerator Facility
• Karl J. Slifer
• University of Virginia

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E07-001 Collaboration
72 Physicists
Spin Experts from all three halls
20 Institutions
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Overview

• The inclusive nucleon SSF g1 and g2 are
  measured over wide range,
• but
• remains unmeasured below Q21.3 GeV2.
• The missing piece of the JLab Spin Physics
  Program.
• Motivations
• g2p is central to our understanding of nucleon
  structure.
• BC Sum Rule violation suggested at large Q2.
• State of the Art ?PT calculations fail for
  neutron spin polarizability ?LT.
• Knowledge of is a leading uncertainty in
  Hydrogen Hyperfine calculations.
• Resonance Structure, in particular the (1232).
• Also a leading uncertainty in longitudinal
  measurements of (Hall B EG1, EG4).

This Experiment Measure in the resonance
region for 0.02 lt Q2 lt 0.4 using the Hall A septa
and the polarized ammonia target.
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PAC33 Theory Comments
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E07-001 Conditional Status
PAC31 Report No particular technical obstacles
were identified Called for further
justification of high Q2 points

• Specific PAC31 Issues
• Impact on the purely longitudinal measurements of
  in JLab Hall B.
• Impact on ongoing calculations of the Hydrogen
  Hyperfine Splitting.
• Projected results for BC Sum Rule, d2(Q2), etc.

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Impact on Longitudinal Measurements of g1
Longitudinal cross section difference
Q20.01
Q20.05
E01.1
E02.4
Model Prediction for g2 contribution
E01.6
E03.2
E02.4
reproduced from EG4 proposal
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EG4 Systematic
PBPT 1-2
15N Background 1-2
L and Filling Factor 3.0
Electron Efficiency lt5
Radiative Corrections 5.0
Modeling of g2 1-10
(Q2 Dependent)
Our measurement of g2p will reduce this error to
less than 1 for all Q2
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Hydrogen Hyperfine Structure
NCG PRL 96 163001 (2006)
Structure Dependent
Inelastic
Elastic Scattering
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Hydrogen Hyperfine Structure
This experiment
NCG 2006 Used CLAS model assuming 100 error
Integrand of 2
Assuming this uncertainty is realistic we will
improve this by order of magnitude
But, unknown in this region
Dominated by this region due to Q2 weighting
MAID Model
Simula Model
So 100 error probably too optimistic We will
provide first real constraint on 2
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Generalized Sum Rules
Ji and Osborne, J. Phys. G27, 127 (2001)
Unsubtracted Dispersion Relation Optical
Theorem
Extended GDH Sum
BC Sum Rule
GDH Sum Rule at Q20 Bjorken Sum Rule at Q21
Superconvergence relation valid at any Q2
BC, Annals Phys. 56, 453 (1970).
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Generalized Forward Spin Polarizabilities
Drechsel, Pasquini and Vanderhaehen, Phys. Rep.
378, 99 (2003).
LEX of gTT and gLT lead to the Generalized
Forward Spin Polarizabilities
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Existing Data
These integral relations allow us to test the
underlying theory over a wide kinematic range
Existing Data
Ongoing/Future Analyses
Hall A SAGDH Hall B EG1 EG4
Hall B transverse large Q2 proposal to this
PAC
Hall C SANE large Q2
There are no existing analyses or 6 GeV proposals
for low Q2 g2p
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Existing Resonance g2 Data
3He g2 0.10 lt Q2 lt 0.9 GeV2
Q2
3He g2 (Jlab Hall A)
g2ww
Large deviation from leading twist behaviour g2WW
not good description of data
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Existing Resonance g2 Data
Q21.3
Q2
3He g2 (Jlab Hall A)
g2ww
Lowest Q2 Existing Proton Data
(Jlab Hall C RSS)
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Chiral Perturbation Theory
Though quantum chromodynamics (QCD) is generally
accepted as the underlying theory of the strong
interactions, a numerical check of the theory in
the confinement region is difficult due to the
strong coupling constant. A plethora of models
have been inspired by QCD, but none of these
models can be quantitatively derived from QCD.
Only two descriptions are, in principle,
exact realizations of QCD, namely chiral
perturbation theory and lattice gauge theory.
D. Drechsel (GDH 2000), Mainz Germany, June 2000
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?PT Calculations
The implementation of ?PT utilizes approximations
which must be tested
For example The order to which expansion is
performed. Heavy Baryon approximation. How to
address short distance effects.
?PT now being used to extrapolate Lattice QCD to
the physical region. Quark mass From few
hundred MeV to physical quark mass. Volume
From finite to infinite Lattice spacing
From discrete to continuous.
Example QCDSF Lattice group utilizes Meissner et
al. ÂPT calc
Crucial to establish the reliability of
calculations and to determine how high in Q2
(energy) we can go
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Generalized Polarizabilities
Fundamental observables that characterize nucleon
structure.
Guichon et al. Nucl. Phys. A 591, 606 (1995).
VCS observables are sensitive to the GPs
Need additional out of plane measurements to get
0 which is related to the VCS GPs at Q20.
at Q20
No simple relation between LT and the VCS GPS
Measurement of LT complementary to the VCS GP
measurements
Expected precision on 2000 hr MAINZ run
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Forward Spin Polarizabilities
Neutron
PRL 93 152301 (2004)
Relativistic Baryon ÂPT Bernard, Hemmert,
Meissner PRD 67076008(2003)
Heavy Baryon ÂPT Calculation Kao, Spitzenberg,
Vanderhaeghen PRD 67016001(2003)
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Forward Spin Polarizabilities
Neutron
PRL 93 152301 (2004)
Add by hand major effect for 0 but not for
LT
Relativistic Baryon ÂPT Bernard, Hemmert,
Meissner PRD 67076008(2003)
Heavy Baryon ÂPT Calculation Kao, Spitzenberg,
Vanderhaeghen PRD 67016001(2003)
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Status of ?PT calculations
¼ term not under control in ÂPT calcs. LT
much less sensitive to this term
LT was expected to be easiest quantity for ÂPT
calcs
Q20.1
ÂPT calc
HB poor poor poor good poor bad
RB( VM) good fair good fair good bad
Q20.05
HB good good
RB( VM) good good
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Interest from Theorists
State of the Art ÂPT calculations fail to
reproduce LT. WHY?
B. Holstein, T. Hemmert, C.W. Kao, N. Kochelev,
U. Meissner, M. Vanderhaeghen, C. Weiss
Convergence? Working on NNLO. ¼ term included
properly? Short range effects beyond ¼
N? Isoscalar in nature? t-channel axial vector
meson exchange? An effect of the QCD vacuum
structure?
Isospin separation is critical to understand the
nature of the problem
Contains a Bjorken-like part due to g1 and an
unknown part due to g2
From theoretical point of view, usually easier to
deal with isospin separated quantity
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The Experiment
E0(GeV) µ(deg) Days
1.1 6 1.0
1.7 6 1.5
2.2 6 1.6
3.3 6 2.9
4.4 6 2.7
4.4 9 6.0
Data Taking 15.7
Overhead 8.4
Total Days 24.1
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Beamline Chicane
10 m
4 m
Tungsten calorimeter
Slow raster
SEM BPM
EP
85cm
BCM
Moller
Target center
Fast raster
Major Installation
Chicane Design Jay Benesh (JLab CASA) Two
upstream Dipoles, one with vertical degree of
freedom. Reuse the dipoles from the HKS
experiment. Utilize open space upstream of
target. Minimal interference with existing
beamline equipment.
UVA/Jlab 5 T Polarized Target Upstream Chicane
and supports Slow raster and Basel
SEM. Instrumentation for 50-100 nA beam. Local
beam dump. Hall A Septa.
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Projected Results
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BC Sum Rule
Burkhardt-Cottingham Sum Rule
3¾ violation for proton seen at SLAC
P. L. Anthony et al. , Phys. Lett. B553, 18
(2003).
But, appears to hold for neutron
P. L. Anthony et al. , Phys. Lett. B553, 18
(2003).
M. Amarian et al. Phys. Rev. Lett. 92 (2004)
022301.
Hall C proton analyses at Q21.3 underway
If it holds for one Q2 it holds for all
R. Jaffe
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LT Spin Polarizability
Able to unambiguously test available calcs.
Provide benchmark for any future calc.
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Proton d2(Q2)
Huge systematic from lack of g2p data
SANE
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Extended GDH Sum
Sensitive to behavior which is normally masked in
1 as Q2? 0
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Summary
Hydrogen Hyperfine Structure
Extended GDH SUM
Resonance Structure
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Summary
g2p unmeasured below Q21.3 GeV2. 24 days to
measure g2p at low Q2 and complete the Jlab Spin
Physics program. No existing experiment or 6 GeV
proposal will provide this data. This experiment
is not possible with 12 GeV. Test Integral
relations and Sum Rules BC Sum Rule d2p(Q2)
Extended GDH Sum Eliminate leading systematic
of EG4 measurement of Hall B. Hydrogen Hyperfine
Splitting g2 is large contribution to systematic
uncertainty Contribution dominated by
Q2lt0.4 State of the art ÂPT calcs work well for
many spin-dependent quantities up to 0.1 GeV2 But
fail for LT. WHY? Need isospin separation to
resolve.
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Existing DIS g2 Data
Jlab Hall A x¼0.2
SLAC ltQ2gt 5 GeV2
Proton
Neutron
Deuteron
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Total Systematic
Source ()
Cross Section 5-7
Target Polarization 3
Beam Polarization 3
Radiative Corrections 3
Parallel Contribution lt1
Total 7-9
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Forward Spin Polarizabilities
Scaling of polarizabilities expected at large Q2
Not observed yet for Neutron
PRL 93 152301 (2004)
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Hydrogen Hyperfine Structure
NCG 2006 Utilized CLAS model assuming 100 error
CLAS model Simula model
Elastic piece larger but with similar uncertainty
If we assumed this uncertainty is realistic we
will improve this by order of magnitude
In fact, unknown in this region
0.13 ppm of this error comes from 2
MAID Model
Simula Model
So if the 100 error is realistic, we would cut
error on POL in half
So 100 error is probably too optimistic We will
provide first real constraint on 2