Precision Measurement of the Proton Elastic Cross Section at High Q2 PAC32 12 GeV Proposal : PR12-07-108 Spokespersons: Bryan Moffit (MIT) Shalev Gilad (MIT) Bogdan Wojtsekhowski (JLab) John Arrington (ANL) Bryan Moffit PAC32 Presentation

Motivation Electron – Nucleon Scattering 𝐽 ℎ𝑎𝑑𝑟𝑜𝑛𝑖𝑐 μ Figure from Perdrisat et al. arXiv:hep-ph/0612014 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 = 1 1+ 𝑄 2 0.71 2 𝐺 𝐸 𝑝 = 𝐺 𝐷 , 𝐺 𝑀 𝑝 = μ 𝑝 𝐺 𝐷 , 𝐺 𝑀 𝑛 = μ 𝑛 𝐺 𝐷 Bryan Moffit PAC32 Presentation

Form Factors – Low Q2 Vector Meson Dominance to Dispersion Relations 𝐹 𝑞 2 ~ 𝑎 𝑞 2 − 𝑚 𝑉1 2 + −𝑎 𝑞 2 − 𝑚 𝑉2 2 Figures from Perdrisat et al. arXiv:hep-ph/0612014 Bryan Moffit PAC32 Presentation

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

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

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

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= 1+2 1+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) 142301 Bryan Moffit PAC32 Presentation

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= 1+2 1+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

This Proposal (PR12-07-108) 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

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

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

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 Q2 θ E' ε Hours Events * * * * Bryan Moffit PAC32 Presentation

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

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

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 - 104 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

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 01-046 MSD from CMS (LHC) Electronics adaptation being evaluated by JLab DAQ group. Bryan Moffit PAC32 Presentation

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

Is 2% Achievable? Published Results from JLab: Hall C – E94-110 : 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) 015206 Hall A – E01-001 : p(e,e'p) Total ≈ 3.0% (Acceptance = 2.0%) Published: Phys. Rev. Lett 94 (2005) 142301 Hall A – E05-004 : “LEDEX” Low-Q2 A(Q) From Proposal : Total = 1.8% (Acceptance Uncertainty = 1.0%) Hall A – E05-110 : “Coulomb Sum Rule” (Gas Targets) From Proposal: Total = 2.2% (Acceptance Uncertainty = 1.0%) Completed/Upcoming Experiments Bryan Moffit PAC32 Presentation

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

Start of backup slides Bryan Moffit PAC32 Presentation

Detailed Beamtime Request Bryan Moffit PAC32 Presentation

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

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

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

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/0611046 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

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/0612014 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) 092301 Bryan Moffit PAC32 Presentation

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) 142301 Bryan Moffit PAC32 Presentation

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/0612014 Bryan Moffit PAC32 Presentation

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

Radiative Corrections Data Simulation Data normalized to Simulation Figures from Vanderhaeghen et al. PRC, 62 (2000) 025501 Bryan Moffit PAC32 Presentation

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) 025501 δreal calculated with (E'el – E') = 0.04 E'el Model dependent corrections (δ1 and δ2) evaluated from Maximon and Tjon (nucl-th/0002058) Bryan Moffit PAC32 Presentation

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) 025501 δreal calculated with (E'el – E') = 0.04 E'el Model dependent corrections (δ1 and δ2) evaluated from Maximon and Tjon (nucl-th/0002058) Bryan Moffit PAC32 Presentation

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) 025501 δreal calculated with (E'el – E') = 0.04 E'el Model dependent corrections (δ1 and δ2) evaluated from Maximon and Tjon (nucl-th/0002058) Bryan Moffit PAC32 Presentation

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/0612026 Bryan Moffit PAC32 Presentation

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

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