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A Measurement of the 𝑔2 Spin Structure Function at Low 𝑄2
Toby BadmanThe University of New Hampshire
For the Jlab g2p collaborationAPS 2016 Salt Lake City, Utah
Inclusive Electron Scattering
2
⇑⇒
↑↓𝑝 = 𝐸, 𝑘
𝑝′ = 𝐸′, 𝑘′
𝑃 = 𝑀, 0
𝑞 = 𝜐, 𝑞
𝑊
𝜃
𝑄2 = −𝑞2 = 4𝐸𝐸′ sin2 𝜃2
𝑥 = 𝑄2
2𝑀𝜐
𝑊2 = 𝑀2 + 2𝑀𝜐 − 𝑄2
Inclusive unpolarized cross section:
𝑑2𝜎
𝑑Ω𝑑𝐸′= 𝜎𝑀𝑜𝑡𝑡
1𝜐
+ 2𝑀
tan2 𝜃2
Inclusive polarized cross section differences:
𝑑2𝜎
𝑑Ω𝑑𝐸′↑⇑−↓⇑ =
4𝛼2
𝑀𝑄2𝜐
𝐸′
𝐸𝐸 + 𝐸′ cos𝜃 −
𝑄2
𝜐
𝑑2𝜎
𝑑Ω𝑑𝐸′↑⇒−↓⇒ =
4𝛼2 sin 𝜃
𝑀𝑄2𝜐2𝐸′2
𝐸𝜐 − 2𝐸
Experimental Technique
3
↑⇑−↓⇑𝑒− 𝑒−
↑⇒−↓⇒𝑒− 𝑒−
Δ𝜎⊥Δ𝜎∥Measured quantities:
𝑔1 =𝑀𝑄2
4𝛼𝑒2
𝑦
(1 − 𝑦)(2 − 𝑦)Δ𝜎∥ + tan
𝜃2Δ𝜎⊥
𝑔2 =𝑀𝑄2
4𝛼𝑒2
𝑦2
2(1 − 𝑦)(2 − 𝑦)−Δ𝜎∥ +
1 + (1 − 𝑦) cos 𝜃
(1 − 𝑦) sin 𝜃Δ𝜎⊥
Δ𝜎⊥contributes only ~5% to 𝑔1 at our kinematics.
Δ𝜎⊥measured during 𝑔2𝑝
experiment, Δ𝜎∥ contributes ~2 − 8% to 𝑔2.
Motivation
• Very little data exists for the proton 𝑔2 structure function.
• Measurements at Jefferson Lab:
RSS 1 < 𝑄2 < 2 GeV2 published
SANE 2 < 𝑄2 < 6 GeV2 analysis
g2p 0.02 < 𝑄2 < 0.2 GeV2 analysis
• A low 𝑄2 measurement will be a useful tool for testing the validity of 𝜒PT and
the studying the moments of 𝑔2.
Existing data:
4
Experimental Setup
Jefferson Lab CEBAF:• 12 GeV maximum beam energy• 200 𝜇A maximum current• 85% electron polarization
Hall A:• All new beam
diagnostics (BPM, BCM, rasters)
• Chicane installed for transverse target field
• 2.5/5T rotatable target field
• Septum magnet for small scattering angles
5
Kinematic Coverage
Model estimated kinematic coverage
Beam Energy(GeV)
Target Field (T)
3.352 5
2.254 5
2.254 2.5
1.706 2.5
1.158 2.5
6
Target Polarization 2-8%
Inelastic XS Model 10%
Dilution 2-8%
Packing Fraction 5-45%
Physics Asymmetry
Preliminary systematics:
𝑔2𝑝
Collaboration, Apr. 12 2016No radiative correctionsPreliminary systematics
7
Unpolarized Cross Section
Packing Fraction 5-45%
Dilution 2-8%
Unpolarized XS model (dilution)
10%
Acceptance 25%
Preliminary systematics:
• Acceptance correction study is still underway.
• An acceptance cut is chosen such that the theta/phi distribution is flat within the cut region.
• Proton XS is calculated as:𝑑𝜎
𝑑Ω𝑑Ε=
𝑒𝑀𝑁𝐻3
𝐴𝜌𝑁𝐻3𝑍𝑁𝐻3𝑓𝑌𝑁𝐻3
𝑔2𝑝
Collaboration, Apr. 12 2016No radiative correctionsPreliminary systematics
8
Radiative Corrections
• Preliminary polarized radiative correction:
𝑅 = 𝐴𝑢𝑛𝑟𝑎𝑑 − 𝐴𝑟𝑎𝑑
• 𝐴 𝑢𝑛 𝑟𝑎𝑑 is generated
from MAID.
• Polarized radiative correction study is still underway, results will be updated when complete.
9
V.1
Proton Spin Structure Functions
Unpolarized XS model 10%
Radiative Corrections Method
40%
Target polarization 2-8%
Acceptance 25%
Preliminary systematics:𝑄2 ≈ 0.1GeV2
𝑔2𝑝
Collaboration, Apr. 12 2016No radiative correctionsPreliminary systematics
10
𝑔2𝑝
Collaboration, Apr. 12 2016Preliminary radiative correctionsPreliminary systematics
Radiative Corrections Applied
Summary
• A measurement of the proton spin structure function 𝑔2 at low 𝑄2 is an important component in the testing of a number of effective theories of QCD.
• The g2p experiment, which measured 𝑔2 in a 𝑄2 region of 0.02 −0.2GeV2, successfully ran at Jefferson Lab during the spring of 2012 and analysis is still ongoing.
• Preliminary methods for determining the acceptance and radiative effects give promising results for the spin structure at a 𝑄2 of 0.1GeV2.
• Current efforts are focused on improving these methods and reducing systematics.
• More results to come shortly!
11
Thank You!
g2p Analysis Team:
StudentsToby BadmanMelissa CummingsChao GuMin HuangJie LiuPengjia ZhuRyan Zielinski
SpokespeopleAlexandre CamsonneJP ChenDon CrabbKarl Slifer
Post DocsKalyan AlladaElena LongJames MaxwellVince SulkoskyJixie Zhang
12
The B.C. Sum Rule
Γ2 =
0
1
𝑔2 𝑥, 𝑄2 𝑑𝑥 = 0
• 0𝑡ℎmoment of 𝑔2:
Brown: SLAC E155xRed: Hall C RSSBlack: Hall A E94-010Green: Hall A E97-110Blue: Hall A E01-012
• Existing data:
• g2p hopes to fill in low 𝑄2
region for the proton.
14
Spin Polarizabilities
• Generalized spin polarizabilities 𝛾𝑜 and 𝛿𝐿𝑇 are benchmark tests of 𝜒PT.
• Some disagreement with neutron polarizabilities.
• No proton data yet!
• 𝛾𝑜 =16𝛼𝑀2
𝑄6 0𝑥𝑜 𝑥2 𝑔1 𝑥, 𝑄
2 −4𝑀2
𝑄2𝑥2𝑔2 𝑥, 𝑄
2 𝑑𝑥
• 𝛿𝐿𝑇 =16𝛼𝑀2
𝑄6 0𝑥𝑜 𝑥2 𝑔1 𝑥, 𝑄
2 + 𝑔2 𝑥, 𝑄2 𝑑𝑥
15
data from E94010
Courtesy V. Bernard et al. Phys. Rev. D 87,054032 (2013).
data from CLAS
Dilution and Packing Fraction
• The physics asymmetry first requires the calculation of two target quantities:
The length ratio of material in the target cup, called the packing fraction.
𝑃𝑓 =𝑌𝑝
𝑌𝐸− 1
𝜒𝑁𝜎𝑁+𝜒𝐻𝜎𝐻
𝜒𝐻𝑒𝜎𝐻𝑒
−1
The fractional composition of proton material in the target, called the dilution factor.
𝑓 = 1 −𝑌𝐵𝐺𝑌𝑃
• The asymmetry is then calculated as:
𝐴𝑝ℎ𝑦 =1
𝑓𝑃𝑏𝑃𝑡
𝑌+−𝑌−
𝑌++𝑌−
16
Plot courtesy of Melissa Cummings
V.1
V.1