1. Robert Michaels PREX at Trento PREX Workshop 09 Physics Interpretation of PREX 208 Pb E = 1 GeV, electrons on lead Elastic Scattering Parity Violating Asymmetry Physics Analysis Can one Q 2 determine R N ? Follow-up measurements other Q 2, other nuclei Theory Questions

2. Robert Michaels PREX at Trento PREX Workshop 09 neutron weak charge >> proton weak charge is small, best observed by parity violation Electron - Nucleus Potential electromagnetic axial Neutron form factor Parity Violating Asymmetry Proton form factor Pb is spin 0 208

3. Robert Michaels PREX at Trento PREX Workshop 09 Measured Asymmetry Weak Density at one Q 2 Neutron Density at one Q 2 Correct for Coulomb Distortions Small Corrections for G n E G s E MEC Assume Surface Thickness Good to 25% (MFT) Atomic Parity Violation Mean Field & Other Models Neutron Stars R n PREX Physics Analysis from C.J. Horowitz

4. Robert Michaels PREX at Trento PREX Workshop 09 Reminder: Electromagnetic Scattering determines Pb 208 (charge distribution) 123

5. Robert Michaels PREX at Trento PREX Workshop 09 ( R.J. Furnstahl ) Measurement at one Q is sufficient to measure R 2 N proposed error * Why only one parameter ? (next slide…) PREX: * 2/3 this error if 100 uA, dP e /P e = 1%

6. Robert Michaels PREX at Trento PREX Workshop 09 PREX: pins down the symmetry energy (1 parameter) ( R.J. Furnstahl ) energy cost for unequal # protons & neutrons PREX Pb 208 Actually, its the density dependence of a 4 that we pin down.

7. Robert Michaels PREX at Trento PREX Workshop 09 Skx-s15 Thanks, Alex Brown PREX Workshop 2008 E/N

8. Robert Michaels PREX at Trento PREX Workshop 09 Skx-s20 Thanks, Alex Brown PREX Workshop 2008

9. Robert Michaels PREX at Trento PREX Workshop 09 Skx-s25 Thanks, Alex Brown PREX Workshop 2008

10. Robert Michaels PREX at Trento PREX Workshop 09 Relationship of Measured Asymmetry to Theory Differential Cross Section Acceptance Function will be measured, presently simulated Theoretical Asymmetry PREX Expt provides these to be compared

11. Robert Michaels PREX at Trento PREX Workshop 09 Simulated Acceptance It will also be measured ! (integrated over azimuth)

12. Robert Michaels PREX at Trento PREX Workshop 09 Acceptance Examples of Theoretical Models Calculations by C. J. Horowitz

13. Robert Michaels PREX at Trento PREX Workshop 09 Simulation of Observed Asymmetry for various Models Thanks, C.J. Horowitz

14. Robert Michaels PREX at Trento PREX Workshop 09 Application: Atomic Parity Violation Low Q test of Standard Model Needs R N (or APV measures R N ) 2 Isotope Chain Experiments e.g. Berkeley Yb Shape dependence enters APV similarly to PVES. Nearly a direct application. (lucky accident of PVES kinematics) Analysis by Steve Pollock PRC 63, 025501 (2001).

15. Robert Michaels PREX at Trento PREX Workshop 09 Theory Questions : Corrections to the Asymmetry Coulomb Distortions ~20% = the biggest correction. Under control Transverse Asymmetry (to be measured) Two – photon exchange effects -- including Dispersion Corrections (intermediate excited state) Strangeness Electric Form Factor of Neutron Parity Admixtures Meson Exchange Currents Shape Dependence Isospin Corrections Radiative Corrections Excited States Target Impurities Horowitz, et.al. PRC 63 025501 How well do we really know these ?

16. Robert Michaels PREX at Trento PREX Workshop 09 Optimum Kinematics for Lead Parity: E = 1 GeV if = 0.5 ppm. Accuracy in Asy 3% n Fig. of merit Min. error in R maximize: 1 month run 1% in R n (2 months x 100 uA 0.5% if no systematics) 5

17. Robert Michaels PREX at Trento PREX Workshop 09 Fine-Tuning: At 5 0 the Optimal FOM is at 1.05 GeV (+/- 0.05) 1% @ ~1 GeV

18. Robert Michaels PREX at Trento PREX Workshop 09 Optimization for Barium -- of possible direct use for Atomic PV 1 GeV optimum

19. Robert Michaels PREX at Trento PREX Workshop 09 Higher Q 2 Point ? ( e.g. E = 1.3 GeV, 8 0, q = 0.92 fm -1 ) 5 Here ? For Lead

20. Robert Michaels PREX at Trento PREX Workshop 09 Time to make measurements days JLab Spectrometers (2 HRS) For PREX (optimal) 1% in R N Higher Q 2 point ( E = 1.3 GeV, q = 0.92 fm -1 ) 2% in R N days

21. Robert Michaels PREX at Trento PREX Workshop 09 Estimates for Other Nuclei: 48 Ca 120 sn Forward angle use 5 0 septum Want thick target 10% X 0 = practical max Radiative losses estimated ~ ~ 0.4 - 0.5 48 Ca 1.6 10.2 6.6 120 Sn 6 9.1 1.6 208 Pb 11.4 6.3 0.5 T len (mm)

22. Robert Michaels PREX at Trento PREX Workshop 09 48 Ca 120 sn 48 Ca 1.7 2.0 3.4 % 25 3.5 120 Sn 1.2 1.0 2.9 % 125 2.6 E (GeV) max ppm Sensitivity to R N Rate (MHz / arm) Each a 2 month run % Error These should match for 1% in R N For effectively 1% in R N

23. Robert Michaels PREX at Trento PREX Workshop 09 PREX : Summary of Future Options Do PREX better R N to ~ 0.6 % ?! Higher Q 2 point 208 Pb -- marginal 138 Ba 48 Ca 120 Sn ~ 2 month beam (each) Thanks: C. J. Horowitz, P. Souder, K. Kumar