1. Precision Measurement of the Proton Elastic Cross Section at High Q2
PAC32 12 GeV Proposal : PR
Spokespersons: Bryan Moffit (MIT)
Shalev Gilad (MIT)
Bogdan Wojtsekhowski (JLab)
John Arrington (ANL)
Bryan Moffit
PAC32 Presentation

2. Motivation Electron – Nucleon Scattering 𝐽 ℎ𝑎𝑑𝑟𝑜𝑛𝑖𝑐 μ
Figure from Perdrisat et al. arXiv:hep-ph/
Hadronic Current with internal structure
𝐽 ℎ𝑎𝑑𝑟𝑜𝑛𝑖𝑐 μ =𝑖𝑒 𝑁 ˉ 𝑝′ γ μ 𝐹 1 𝑄 2 + 𝑖 σ μν 2M 𝐹 2 𝑄 2 𝑁 𝑝
Electric and Magnetic Form Factors
Global behavior ~ Dipole form:
𝐺 𝐸 = 𝐹 1 −τ 𝐹 2 𝐺 𝑀 = 𝐹 1 + 𝐹 2
𝐺 𝐷 = 𝑄 𝐺 𝐸 𝑝 = 𝐺 𝐷 , 𝐺 𝑀 𝑝 = μ 𝑝 𝐺 𝐷 , 𝐺 𝑀 𝑛 = μ 𝑛 𝐺 𝐷
Bryan Moffit
PAC32 Presentation

3. Form Factors – Low Q2 Vector Meson Dominance to Dispersion Relations
𝐹 𝑞 2 ~ 𝑎 𝑞 2 − 𝑚 𝑉 −𝑎 𝑞 2 − 𝑚 𝑉2 2
Figures from Perdrisat et al. arXiv:hep-ph/
Bryan Moffit
PAC32 Presentation

4. Form Factors – High Q2 Predictions from QCD? QCD Lagrangian:
Nucleon Structure in terms of quark and gluon degrees of freedom
GPDs:
How does the active quark couple to the proton?
𝐹 1 𝑡 = −1 +1 𝑞 𝑑𝑥 𝐻 𝑞 𝑥,ξ,𝑡 𝑑𝑥 𝐹 2 𝑡 = −1 +1 𝑞 𝑑𝑥 𝐸 𝑞 𝑥,ξ,𝑡 𝑑𝑥
Figure from 12 GeV Upgrade pCDR
Bryan Moffit
PAC32 Presentation

5. Form Factor Scaling How high is that? Dimensional Scaling:
At high values of Q2,
asymptotic freedom [small αs(Q2)] allows for pQCD calculations.
How high is that?
Dimensional Scaling:
Form Factors scale
asymptotically as (Q2)-(n-1)
n = participating valence quarks
Figure from 12 GeV Upgrade pCDR
𝑄 4 𝐺 𝑀 𝑝 ∝ 𝑄 4 𝐹 1 𝑝 ~𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
pQCD -> logarithmic departures from Q2 dependence
Bryan Moffit
PAC32 Presentation

6. Form Factor Scaling How high is that? Dimensional Scaling:
At high values of Q2,
asymptotic freedom [small αs(Q2)] allows for pQCD calculations.
How high is that?
Dimensional Scaling:
Form Factors scale
asymptotically as (Q2)-(n-1)
n = participating valence quarks
Figure from 12 GeV Upgrade pCDR
𝑄 4 𝐺 𝑀 𝑝 ∝ 𝑄 4 𝐹 1 𝑝 ~𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
pQCD -> logarithmic departures from Q2 dependence
Bryan Moffit
PAC32 Presentation

7. Cross Section -> Form Factors
𝑑σ 𝑑Ω = σ 𝑀𝑜𝑡𝑡 ε 𝐺 𝐸 𝑝 2 +τ 𝐺 𝑀 𝑝 2 ε 1+τ
τ= 𝑄 2 4 𝑀 𝑝 2
ε= τ tan 2 θ 2 −1
Rosenbluth Separation
Measure Cross Section at same Q2 but different E and θ (varying є)
At sufficiently high Q2, GMP dominates.
Figure from Qattan et al. PRL 94 (2005)
Bryan Moffit
PAC32 Presentation

8. Cross Section -> Form Factors
𝑑σ 𝑑Ω = σ 𝑀𝑜𝑡𝑡 ε 𝐺 𝐸 𝑝 2 +τ 𝐺 𝑀 𝑝 2 ε 1+τ
τ= 𝑄 2 4 𝑀 𝑝 2
ε= τ tan 2 θ 2 −1
Rosenbluth Separation
Measure Cross Section at same Q2 but different E and θ (varying є)
At sufficiently high Q2, GMP dominates.
Bryan Moffit
PAC32 Presentation

9. This Proposal (PR )
Measure Proton Elastic Cross Section at High Q2 to high precision.
Second and Independent measure of GMP in an important range of Q2
Improved GMP allows for better extraction of
F1P and F2P
High Precision Cross Section important for extraction of Gmn from Quasi-Elastic measurements of the deuteron
Goal: 2% or better
total uncertainty
Bryan Moffit
PAC32 Presentation

10. Precision Study of Q2 Dependence
Onset of Scaling Behavior
at Q2 ~ 7-8 GeV2 ?
Fit: Q-n
What is the power of the
Q2 dependence?
How does GMP approach the
pQCD limit?
Bryan Moffit
PAC32 Presentation

11. Why at JLab? Availability of Beam Energy
Similar range of ε as other JLab experiments
Precision essential for Physics
Readiness of Instrumentation
Bryan Moffit
PAC32 Presentation

12. Kinematics Ebeam Q2 θ E' ε Hours Events 3 Beam Energies I = 80μA
Both HRSs in symmetric configuration*
3 Redundant Q2
Different ε
21.5 days for LH2
31 days requested
Ebeam Q θ E' ε Hours Events * * * *
Bryan Moffit
PAC32 Presentation

13. Technical Challenges
Accurate measure and stability of beam current and energy
Stability of target density/luminosity
Reduced systematics of Spectrometer acceptance:
Improved analysis techniques
Additional general use equipment
Bryan Moffit
PAC32 Presentation

14. Target Configuration LH2 : 20 cm Racetrack Vertical Flow Design
Dedicated Studies of density stability
Luminosity Monitor in datastream
Solid Aluminum Foils (Dummy)
Endcap subtraction
Carbon Optics Targets
1-2 cm spacing along zlab for extended target optics/acceptance
Picture from 2005 HAPPEX-II
Solid Target / Racetrack Endcaps measured with X-ray attenuation
Bryan Moffit
PAC32 Presentation

15. HRS Detector Package Main Trigger (electrons) - S2m AND Gas Cherenkov
Secondary Triggers
- S0 AND Gas Cherenkov
- S0 AND S2m
Gas Cherenkov with
Lead Glass Counters
pion rejection
- 99.5% electron efficiency
Additional VDC layer
- Improvement in tracking efficiency
- Reduction of non-statistical tails
Figure from Hall A Webpage (modified)
Bryan Moffit
PAC32 Presentation

16. Precision Angle Measurement (PAM)
All targets and detectors
mounted to an aluminum frame
- Accurate placement (~ few μm)
Wire Scanners
- Measure/Calibration of incoming
beam angle
Micro Strip Detector (MSD)
- Accurate measure of scattering
angle and improved HRS
optics/acceptance studies
Figure from Wojtsekhowski JLab TN
MSD from CMS (LHC)
Electronics adaptation being
evaluated by JLab DAQ group.
Bryan Moffit
PAC32 Presentation

17. Systematic Uncertainties
Point to Point
Normalization
Lower numbers indicate values estimated
if PAM device functions as well as desired
Statistics: 0.5 – 0.8%
TOTAL (Scale + Rand. + Stat.) : 1.3 (1.8) %
Goal: 2% or better
Bryan Moffit
PAC32 Presentation

18. Is 2% Achievable? Published Results from JLab:
Hall C – E : p(e,e')p
Point-to-Point = 0.97% (Acceptance Uncertainty = 0.5%)
Normalization = 1.70% (Acceptance Uncertainty = 0.8%)
Published: Phys. Rev. C70 (2004)
Hall A – E : p(e,e'p)
Total ≈ 3.0% (Acceptance = 2.0%)
Published: Phys. Rev. Lett 94 (2005)
Hall A – E : “LEDEX” Low-Q2 A(Q)
From Proposal : Total = 1.8% (Acceptance Uncertainty = 1.0%)
Hall A – E : “Coulomb Sum Rule” (Gas Targets)
From Proposal: Total = 2.2% (Acceptance Uncertainty = 1.0%)
Completed/Upcoming Experiments
Bryan Moffit
PAC32 Presentation

19. We request 31 days of beamtime to perform this measurement.
Summary
Precision Measurement of the Proton Elastic Cross Section at High Q2
Second and Independent measure of GMP in an important range of Q2
Precision of σep and GMP will allow
Better extraction of nucleon Form Factors F1, F2, GMN
Provide additional experimental constraints for GPD and pQCD calculations
Goal: 2% or better
total uncertainty
We request 31 days of beamtime to perform this measurement.
Bryan Moffit
PAC32 Presentation

20. Start of backup slides
Bryan Moffit
PAC32 Presentation

21. Detailed Beamtime Request
Bryan Moffit
PAC32 Presentation

22. Beam Energy
Require use of eP and Upgrade ofArc energy methods for JLab 12 GeV
Precision ~ 3-4 x 10-4
Monitor stability and energy spread with
OTR
Tiefenback
Synchotron Light Interferometer (SLI)
Figure from Kevin Kramer Ph.D. Thesis (2003)
Figure from Alcorn et al. NIM A522 (2004)
Bryan Moffit
PAC32 Presentation

23. Additional Wire Chamber
Current usage:
Tight cuts on # hits/chamber
Correct for lost events
0.5% correction on σep for E01-001
One additional Wire Chamber for each spectrometer
Added redundancy to account of multiple hit clusters per event.
Higher tracking efficiency
Additional Wire Chamber Options:
Use “Spare” and build another “spare” from on-site components
Use Multi-Wire Drift Chambers from BigBite Spectrometer
Use front drift chambers from Focal Plane Polarimeter
Bryan Moffit
PAC32 Presentation

24. PAM Impact All components mounted on a single aluminum frame:
Each measured accurately to a few micron.
Micro Strip Detector (MSD)
Used only in calibrations (removed during production)
Reduced uncertainty in angles (when used with Tungsten wire):
Incoming beam angle ( 0.1 mrad -> 0.05 mrad)
Scattering angle ( 0.2 mrad -> 0.05 mrad)
Redundancy with optics survey
Survey takes time.. and sometimes wrong (by ~ 0.5°)!
Redundancy with optics/sieve data
Better understanding of optics with MSD directly before any magnetic elements.
Bryan Moffit
PAC32 Presentation

25. Form Factors – High Q2 Predictions from QCD? QCD Lagrangian:
Nucleon Structure in terms of quark and gluon degrees of freedom
GPDs:
How does the active quark couple to the proton?
Parametrization 1
Parametrization 2 Q2
Figure from S. Ahmad et al. arXiv:hep-ph/
𝐹 1 𝑡 = −1 +1 𝑞 𝑑𝑥 𝐻 𝑞 𝑥,ξ,𝑡 𝑑𝑥 𝐹 2 𝑡 = −1 +1 𝑞 𝑑𝑥 𝐸 𝑞 𝑥,ξ,𝑡 𝑑𝑥
Figure from 12 GeV Upgrade pCDR
Bryan Moffit
PAC32 Presentation

26. Polarization Transfer
𝐺 𝐸 𝑝 𝐺 𝑀 𝑝 = 𝑃 𝑥 𝑃 𝑧 𝐸 𝑒 + 𝐸 𝑒′ 2M tan θ 𝑒 2
Figure from Perdrisat et al. arXiv:hep-ph/
Form Factor Extraction (Method 2):
Polarization Transfer
Measure components of the scattered proton polarization transferred from polarized electron
Figure from Gayou et al. PRL 88 (2002)
Bryan Moffit
PAC32 Presentation

27. Measured GE/GM Ratio (e,e') Rosenbluth Separation (e,p)
Super-Rosenbluth
Polarization Transfer
𝑒 𝑝⇒𝑒 𝑝
Discrepancy explained by
Two-Photon Exchange?
Figure from Qattan et al. PRL 94 (2005)
Bryan Moffit
PAC32 Presentation

28. Two-Photon Exchange TPE Corrections Significant Є dependence
Difficult to extrapolate from SLAC to JLab kinematics
Does not impact σe-p for other experiments at JLab kinematics
Only important for GMP extraction
Figure from Perdrisat et al. arXiv:hep-ph/
Bryan Moffit
PAC32 Presentation

29. Radiative Corrections
Standard Corrections large,
but well understood
High Statistics ->
Better Confirmation of
Radiative Tail Calculations
Two-Photon Corrections
still quite uncertain.
Large progress in calculations and experimental input to verify them.
Not relevant for GEP or neutron FF extraction at JLab kinematics
Bryan Moffit
PAC32 Presentation

30. Radiative Corrections
Data
Simulation
Data normalized to Simulation
Figures from Vanderhaeghen et al. PRC, 62 (2000)
Bryan Moffit
PAC32 Presentation

31. Radiative Corrections 6.6 GeV
𝑑σ 𝑑Ω 𝑡𝑜𝑡𝑎𝑙 = 𝑑σ 𝑑Ω 𝐵𝑜𝑟𝑛 1+ δ 𝑣𝑒𝑟𝑡𝑒𝑥 + δ 𝑣𝑎𝑐𝑝𝑜𝑙 + δ 𝑟𝑒𝑎𝑙 +𝑍 δ 1 + 𝑍 2 δ 2
Radiative Correction calculations provided by M. Vanderhaeghen et al.
Physical Review C 62 (2000)
δreal calculated with (E'el – E') = 0.04 E'el
Model dependent corrections (δ1 and δ2) evaluated from
Maximon and Tjon (nucl-th/ )
Bryan Moffit
PAC32 Presentation

32. Radiative Corrections 8.8 GeV
𝑑σ 𝑑Ω 𝑡𝑜𝑡𝑎𝑙 = 𝑑σ 𝑑Ω 𝐵𝑜𝑟𝑛 1+ δ 𝑣𝑒𝑟𝑡𝑒𝑥 + δ 𝑣𝑎𝑐𝑝𝑜𝑙 + δ 𝑟𝑒𝑎𝑙 +𝑍 δ 1 + 𝑍 2 δ 2
Radiative Correction calculations provided by M. Vanderhaeghen et al.
Physical Review C 62 (2000)
δreal calculated with (E'el – E') = 0.04 E'el
Model dependent corrections (δ1 and δ2) evaluated from
Maximon and Tjon (nucl-th/ )
Bryan Moffit
PAC32 Presentation

33. Radiative Corrections 11 GeV
𝑑σ 𝑑Ω 𝑡𝑜𝑡𝑎𝑙 = 𝑑σ 𝑑Ω 𝐵𝑜𝑟𝑛 1+ δ 𝑣𝑒𝑟𝑡𝑒𝑥 + δ 𝑣𝑎𝑐𝑝𝑜𝑙 + δ 𝑟𝑒𝑎𝑙 +𝑍 δ 1 + 𝑍 2 δ 2
Radiative Correction calculations provided by M. Vanderhaeghen et al.
Physical Review C 62 (2000)
δreal calculated with (E'el – E') = 0.04 E'el
Model dependent corrections (δ1 and δ2) evaluated from
Maximon and Tjon (nucl-th/ )
Bryan Moffit
PAC32 Presentation

34. First three u-quark moments of
Impact on GPD Analysis
From P. Kroll:
High quality, large Q2 data on GMp would have the following impact on a GPD analysis:
if the trends of our previous analysis are correct then such data would essentially provide better information on the u-quark moment of the Dirac form factor and hence would improve the GPD Hu
Additional large Q2 data on GMn and GEp would allow to test the mentioned trends, e.g. the dominance of u over d quarks in the proton.
These form factors would therefore lead to improved GPDs Hd and Eu, Ed (provided one knows what to do with GEn).
First three u-quark moments of
Dirac form factor
Figure from P. Kroll arXiv:hep-ph/
Bryan Moffit
PAC32 Presentation

35. Plots including Gep and TPE errors
Error Bars include:
2% Total Error in σep
1% GEP Error
2% TPE Error
Bryan Moffit
PAC32 Presentation

36. Plots including Gep and TPE errors
Error Bars include:
2% Total Error in σep
1% GEP Error
2% TPE Error
Bryan Moffit
PAC32 Presentation