Physics Interpretation of PREX Elastic Scattering Parity Violating Asymmetry E = 1 GeV, electrons on lead Physics Analysis Can one Q2 determine RN ? Follow-up measurements other Q2 , other nuclei Theory Questions 208Pb Trento PREX Workshop 09

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

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

Reminder: Electromagnetic Scattering determines (charge distribution) 208 Pb 1 2 3 Trento PREX Workshop 09

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

Pb PREX: pins down the symmetry energy (1 parameter) energy cost for unequal # protons & neutrons ( R.J. Furnstahl ) Actually, it’s the density dependence of a4 that we pin down. 208 Pb PREX Trento PREX Workshop 09

Skx-s15 Thanks, Alex Brown PREX Workshop 2008 E/N Trento PREX Workshop 09

Thanks, Alex Brown PREX Workshop 2008 Skx-s20 Trento PREX Workshop 09

Thanks, Alex Brown PREX Workshop 2008 Skx-s25 Trento PREX Workshop 09

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

Simulated Acceptance It will also be measured ! (integrated over azimuth) Trento PREX Workshop 09

Examples of Theoretical Models Calculations by C. J. Horowitz Acceptance Trento PREX Workshop 09

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

Application: Atomic Parity Violation Low Q test of Standard Model Needs RN (or APV measures RN ) 2 Isotope Chain Experiments e.g. Berkeley Yb Shape dependence enters APV similarly to PVES.  Nearly a direct application. Analysis by Steve Pollock PRC 63, 025501 (2001). (lucky accident of PVES kinematics) 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 How well do we really know these ? Horowitz, et.al. PRC 63 025501 Trento PREX Workshop 09

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

Fine-Tuning: At 50 the Optimal FOM is at 1.05 GeV (+/- 0.05) Trento PREX Workshop 09

Optimization for Barium -- of possible direct use for Atomic PV 1 GeV optimum Trento PREX Workshop 09

Here ? Higher Q2 Point ? ( e.g. E = 1.3 GeV, 80, q = 0.92 fm-1 ) For Lead Here ? 5 Trento PREX Workshop 09

Time to make measurements JLab Spectrometers (2 HRS) For PREX (optimal) 1% in RN days Higher Q2 point ( E = 1.3 GeV, q = 0.92 fm-1 ) 2% in RN days Trento PREX Workshop 09

Estimates for Other Nuclei: 48Ca 120sn Forward angle  use 50 septum Want thick target  10% X0 = practical max Radiative losses estimated ~ ~ 0.4 - 0.5 Tlen (mm) 48Ca 1.6 10.2 6.6 120Sn 6 9.1 1.6 208Pb 11.4 6.3 0.5 Trento PREX Workshop 09

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

PREX : Summary of Future Options Do PREX better RN to ~ 0.6 % ?! Higher Q2 point 208Pb -- marginal 138 Ba 48 Ca 120 Sn ~ 2 month beam (each) Thanks: C. J. Horowitz, P. Souder, K. Kumar Trento PREX Workshop 09