1. PR10-005 Precision Measurement of the Neutron Magnetic Form Factor at Q 2 =16 and 18 (GeV/c) 2 by the Ratio Method Brian Quinn/Carnegie Mellon Univ. Bogdan Wojtsekhowski/JLab Ron Gilman/Rutgers Univ. Carnegie Mellon/ JLab/ Rutgers/ William and Mary/ Santa Maria/ Norfolk/ Glasgow/ Ljubljana/ Richmond/ Kharkov/ U.N.H./ N.C. Central/ Saint Mary’s/ UVa/ Yerevan/ Florida International/ INFN/ Novosibirsk/ Tel Aviv/ Cal State/ MIT/ Edinburgh/ Temple The Hall A Collaboration

2. 2 Context ‘Sister’ experiment to E12-09-019 Two highest points not approved by PAC34 Improved experiment with modified design: BigHAND  HCal –Higher luminosity –Higher (more uniform) efficiency –Better spatial resolution –Reduced beam time Efficient to run contiguously

3. 3 Introduction Elastic scattering from spin ½ target (one photon exchange approx.) where: Use Bodek (Jour. Phys 110 (2008) 082004) for more realistic, more conservative estimate of count rates (Lagrange polynomial corrections to Kelly fit satisfying asymptotic quark-hadron duality constraints)

4. 4 Projected results (Projected E09-019 and present proposal plotted at Bodek prediction) Proposed

5. 5 Motivation Theory Review: The theoretical interest in extending this measurement to the highest possible is very general and unassailable. Among the simplest, most fundamental of hadronic observables Helps provide definitive test of nucleon structure theory (With proton form factor, gives access to isovector form factor, which is ‘easy’ case for l QCD.) Comparison of neutron magnetic form factor to proton magnetic form factor of particular interest - Comparehigh scaling behavior - Extract magnetic form factor for each quark species Quark transverse charge density of neutron related to magnetic form factor Sets sum rule for GPD measurements/predictions

6. 6 Technique Ratio Method: Measure quasi-elastic scattering from deuteron tagged by coincident nucleon: d(e,e’p) and d(e,e’n) Many systematic effects (experimental and theory) cancel in ratio. Expect very small correction for Electric because small form factor and large kinematic weighting of Magnetic

7. 7 Nuclear Corrections Corrections to d(e,e’n) and d(e,e’p) almost identical  cancel in ratio Arenhovel (low Q 2 ) finds small (<1% when wide-angle tail is cut) corrections at 1 GeV/c and decreasing at larger Q 2 Q 2 (GeV/c)FSI corr. 10.99980 20.99971 30.99966 40.99962 5 S. Jeschonnek found ratio of full calc (S. Jeschonnek and J.W. Van Orden Phys. Rev. C 62 (2000) 044613) to PWIA calc. for Kinematics of earlier CLAS e5 measurements. Ratio almost identical for n and p  tiny corrections Additional nuclear effects due to Fermi motion manifest as PWIA calculation of coefficients a,b,c, and d: Q 2 (GeV/c) PWIA corr. 161.0032 181.0046 Using Jechonnek’s code, found R PWIA /R Free (neglecting neutron Electric form factor) for planned kinematics and cuts. < 0.5%

8. 8 Two-photon Corrections Usual complication of two-photon corrections is for separation of small form factor from large one. Small epsilon-dependence has big effects. We extract the larger Magnetic form factor. Corrections may not tend to cancel in ratio ( P.G. Blunden, W. Melnitchouk and J.A.Tjon, Phys. Rev. C 72 (2005) 034612 ). Recent results at these kinematics: Q 2 =16 GeV 2  n -  p =-0.15% Q 2 =18 GeV 2  n -  p = 1.8 % Not specific to ratio technique, affect any elastic cross section measurement at these kinematics

9. 9 Systematics Ratio Method is insensitive to: Target thickness Target density Beam current Beam structure Live time (electron) trigger efficiency Electron track reconstruction Electron acceptance Important to understand: Neutron efficiency/proton efficiency  HCal almost ideal Neutron acceptance/proton acceptance

10. 10 Kinematics Q 2 (GeV/c) 2 E beam (GeV)  e (deg.)  N (deg.) E scatt (GeV) P N (GeV/c) 161151.110.72.59.4 181165.27.01.410.5

11. 11 Apparatus BigBite Spectrometer Instrumented with: -GEM planes from SBS -Electromagnetic Cal. -Gas Cerenkov -timing planes Allows high luminosity

12. 12 Apparatus (2) Hadron Calorimeter (HCal) to be built for Super BigBite Spectrometer (SBS) provides ideal replacement for BigHAND stack Iron/scintillator sampling calorimeter 11X22 identical modules High energy-deposition - High threshold - High Luminosity Excellent spatial resolution - Tight cut on nucleon direction (wrt q-vector) High efficiency for n and p - Nearly equal (cancel in ratio) Iron Scintillator

13. 13 Apparatus (3) Hadron Calorimeter (HCal) Background estimates (7 degrees) 50 MeV(ee) threshold <0.5 MHz (in 3X3 cluster) <0.5% accidental coincidence

14. 14 Apparatus (4)  x =  y =  3 cm Q 2 =16 (GeV/c) 2  n =95.6  n /  p =0.988 Q 2 =18 (GeV/c) 2  n =95.5  n /  p =0.990 Results from Geant4 Simulation (matches published results for COMPASS calorimeter). Assume identical modules, 3X3 cluster size for hits

15. 15 n/p identification Big Ben dipole deflects protons so event-by-event displacement from q-vector direction is ~68 cm Q 2 =16 (GeV/c) 2 ‘kick’=375 MeV/c Q 2 =18 (GeV/c) 2 ‘kick’=442 MeV/c Simulated quasi-elastic neutron and proton hits (shown separately)

16. 16 Simulation Quasi-elastic On shell spectator(  Struck nucleon off shell) Boost to struck nucleon rest frame Isotropic distribution -Weighted by cross section (using Bodek parameterization) Boost back to lab Fold in resolution, make (weighted) increment of spectra Inelastic GENEV physics Monte Carlo (Genoa/CLAS) On-shell initial nucleons (with Fermi momentum) Boost to struck nucleon rest frame Generate GENEV event (with boosted beam energy) Boost back to lab Fold in resolution, increment (un-weighted) spectra Inelastic normalized empirically to quasi-elastic

17. 17 Simulation Results Q 2 = 18 (GeV/c) 2 results without cuts on  pq

18. 18 Simulation Results (2) Q 2 = 18 (GeV/c) 2 : W 2 spectra for different cuts on  pq

19. 19 Error estimates. Q 2 (GeV/c) 2 1618 Proton x-sect (%)1.74. Neutron electric f.f.0.890.39 Nuclear (FSI and PWIA)-- Two-photon1.2. Accidental0.160.11 Target windows0.2 Acceptance0.160.11 Inelastic4.75.4 Nucleon mis-ID0.5 Hcal efficiency0.5 Statistical error on R(%)2.54.1 Total error on G n M (%)2.84.1 Contributions (in %) to systematic error on R

20. 20 Beam Request Q 2 (GeV/c) 2 1618  e (deg.) 45.165.2  N (deg.) 10.77.0 LD 2 44  A 96192 Dummy 44  A 816 LH 2 75  A 612 LH 2 37  A 26 LH 2 75  A BigBen off 612 Total118238  356 hours Commissioning0 1 Energy change8 2 Angle changes20 384hr (16 days)

21. 21 Projected results (Projected E09-019 and present proposal plotted at Bodek prediction) Proposed

22. 22 Neutron statistics (Projected E12-09-019 and present proposal plotted at Bodek prediction c.f. CLAS12 with Bodek or Alberico)

23. 23 Backup Slides.

24. 24 Simulation Results Q 2 = 16 (GeV/c) 2 results without cuts on  pq

25. 25 Simulation Results Q 2 = 16 (GeV/c) 2 : W 2 spectra for different cuts on  pq

26. 26

27. 27 Technique Ratio Method: Measure quasi-elastic scattering from deuteron tagged by coincident nucleon: d(e,e’p) and d(e,e’n) Many systematic effects (experimental and theory) cancel in ratio. Expect very small correction for Electric because small form factor and large kinematic weighting of Magnetic