G M p Simulation and analysis plan

1. GMp Simulation and analysis plan E. Christy (Hampton University), John Arrington (ANL) → Analysis framework based on procedures well tested for precision Cross section measurements, eg. - M.E. Christy, et al., Phys. Rev. C 70, 015206 (2004). - A Qattan, et al., Phys. Rev. Lett. 94, 142301 (2005). → Simulation software also already exists, with multiple tools available

2. Ideally have at least 2 (mostly) independent analyses utilizing: 1. complementary procedures 2. independent software when feasible

3. Cross Section Extraction Methods For each bin in DE', DW, the number of detected electrons is: N- = L*(ds/dWdE')*(DE' DW)*e*A(E',q) + BG with L: Integrated Luminosity (# of beam electrons*targets/area) e: Total efficiency for detection A(E',q): Acceptance for bin BG: Background events. The efficiency and backgroun corrected electron yield is Y = (N- - BG)/e = L*s data *(DE DW)*A(E',q)

4. For A(E',q) accurately modeled by simulation, determine cross section from 1. s data = Y/[(DE DW)*A(E',q)*L] (acceptance correction method) or 2. sdata = smod * [Y(E',q)/YMC(E',q)](MC ratio method) M.E. Christy, et al., Phys. Rev. C 70, 015206 (2004). To get Born cross section: 1. radiatively correct data 2. radiated model

5. Acceptance correction method (single arm MC uniform generation) Apply background subtractions and acceptance corrections in each E'-q bin. Integrate radiative tail in each q bin. Apply radiative corrections (code from SLAC NE11, modified for current target). Use Model to remove q dependence. Do Weighted average over q.

6. E94-110 – acceptance correction E99-118 – SIMC ratio Data – cryo Data – scaled dummy Yield Data - endcap subtracted MC ratio method: SIMC

7. Summary → Methods are complementary and each has advantages and disadvantages → Both rely on reliable model of spectrometer optics and acceptance → Different radiative correction codes for each method => Provide robust cross check of results

8. Backup

9. HMS Momentum 2.75 GeV 2.36 GeV 2.0 GeV 1.75 GeV Acceptance Correction Method • Bin efficiency corrected e- yield indp/p- q.(dp/p = +/- 8%, Dq= +/- 35 mrad) • Subtract scaled dummy yield bin-by-bin to remove e- Al background. • Subtract charge symmetric e- yield bin-by-bin. • Apply acceptance correction for each d-q bin. • Apply radiative corrections bin-by-bin. • Apply q bin-centering correction and average over q => for each d bin.

10. Monte Carlo Ratio Method Generate MC events with s model weighting and radiative contributions included. Scale the MC yield by L data/LMC , where LMC is that needed to produce Ngen for the given smod and phase space generated into. Add background contributions to MC or subtract from data. ds (d, qc) = dsmod(d,qc) * Y(d)/YMC(d) Where Y(d) is the yield for events with any value of q, i.e. this integrates over q. Warning: For inclusive data, radiative events can come from kinematically far away. Comparison of January '05 proton data to MC using E94-110 resonance region model and externally calculated radiative corrections.

11. For comparison of SIMC and MCEEP radiative effects see http://hallaweb.jlab.org/data_reduc/AnaWork2010/mkj_simc_mceep_radcor.pdf