Physics Interpretation of PREX Elastic Scattering E 1

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

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

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

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

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

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

Thanks, Alex Brown PREX Workshop 2008 Skx-s 15 E/N Robert Michaels Trento PREX Workshop 09 PREX at

Thanks, Alex Brown PREX Workshop 2008 Robert Michaels Trento PREX Workshop 09 Skx-s 20 PREX at

Thanks, Alex Brown PREX Workshop 2008 Robert Michaels Trento PREX Workshop 09 Skx-s 25 PREX at

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 Robert Michaels Trento PREX Workshop 09 PREX at

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

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

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

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

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

Optimum Kinematics for Lead Parity: <A> = 0. 5 ppm. E = 1 Ge. V if Accuracy in Asy 3% Fig. of merit Min. error in R n maximize: 1 month run 1% in R (2 months x 100 u. A 0. 5% if no systematics) 5 Robert Michaels Trento PREX Workshop 09 n PREX at

Fine-Tuning: At 50 the Optimal FOM is at 1. 05 Ge. V (+/- 0. 05) 1% @ ~1 Ge. V Robert Michaels Trento PREX Workshop 09 PREX at

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

Higher Q 2 Point ? ( e. g. E = 1. 3 Ge. V, 80, q = 0. 92 fm-1 ) For Lead Here ? 5 Robert Michaels Trento PREX Workshop 09 PREX at

Time to make measurements JLab Spectrometers (2 HRS) For PREX (optimal) 1% in RN days Higher Q 2 point ( E = 1. 3 Ge. V, q = 0. 92 fm-1 ) 2% in RN days Robert Michaels Trento PREX Workshop 09 PREX at

Estimates for Other Nuclei: 48 Ca 120 sn • Forward angle use 50 septum • Want thick target 10% X 0 = practical max ~ 0. 4 - 0. 5 Radiative losses estimated ~ Tlen (mm) 48 Ca 1. 6 10. 2 6. 6 120 Sn 6 9. 1 1. 6 208 Pb 11. 4 6. 3 0. 5 Robert Michaels Trento PREX Workshop 09 PREX at

48 Ca 120 sn For effectively 1% in RN Each a 2 month run max E (Ge. V) ppm Sensitivity to RN Rate (MHz / arm) % Error 48 Ca 1. 7 2. 0 3. 4 % 25 3. 5 120 Sn 1. 2 1. 0 2. 9 % 125 2. 6 These should match for 1% in RN Robert Michaels Trento PREX Workshop 09 PREX at

PREX : Summary of • Do PREX better • Higher Q 2 • 138 • 48 • 120 point Future Options RN to ~ 0. 6 % 208 Pb ? ! -- marginal Ba Ca Sn ~ 2 month beam (each) Thanks: C. J. Horowitz, P. Souder, K. Kumar Robert Michaels Trento PREX Workshop 09 PREX at