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

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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.

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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!

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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

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Backup

13

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.

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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

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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−

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Plot courtesy of Melissa Cummings

V.1

V.1

Cross Section Differences

Preliminary systematics:

𝑔2𝑝

Collaboration, Apr. 12 2016No radiative correctionsPreliminary systematics

Unpolarized XS model 10%

Target polarization 2-8%

Acceptance 25%

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