Physics Interpretation of PREX

1
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
2
Electron - Nucleus Potential
axial
electromagnetic
is small, best observed by
parity violation
208
Pb is spin 0
neutron weak charge gtgt proton weak charge
Neutron form factor
Proton form factor
Parity Violating Asymmetry
3
Measured Asymmetry
PREX
Physics Analysis
Correct for Coulomb
Distortions
2
Weak Density at one Q
Mean Field
Small Corrections for
s
n
Other
G
G
MEC
Atomic Parity Violation
E
E
Models
2
Neutron Density at one Q
Assume Surface Thickness Good to 25 (MFT)
Neutron Stars
from C.J. Horowitz
R
n
4
Reminder Electromagnetic Scattering
determines
(charge distribution)
208
Pb
1
2
3
5
PREX
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
6
PREX
pins down the symmetry energy (1 parameter)
energy cost for unequal protons
neutrons
( R.J. Furnstahl )
Actually, its the density dependence of a4
that we pin down.
208
Pb
PREX
7
Thanks, Alex Brown PREX Workshop 2008
Skx-s15
E/N
8
Thanks, Alex Brown PREX Workshop 2008
Skx-s20
9
Thanks, Alex Brown PREX Workshop 2008
Skx-s25
10
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
11
Simulated Acceptance
It will also be measured !
(integrated over azimuth)
12
Examples of Theoretical Models
Calculations by C. J. Horowitz
Acceptance
13
Simulation of Observed Asymmetry for
various Models
Thanks, C.J. Horowitz
14

• 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)
15
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
16
Optimum Kinematics for Lead Parity E 1
GeV if
ltAgt 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
17
Fine-Tuning At 50 the Optimal FOM is
at 1.05 GeV (/- 0.05)
1 _at_ 1 GeV
18
Optimization for Barium -- of possible
direct use for Atomic PV
1 GeV optimum
19
Higher Q2 Point ? ( e.g. E 1.3
GeV, 80, q 0.92 fm-1 )
For Lead
Here ?
5
20
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
21
Estimates for Other Nuclei 48Ca
120sn

• Forward angle ? use 50 septum
• Want thick target ? 10 X0
  practical max

0.4 - 0.5
Radiative losses estimated
Tlen
(mm)
48Ca 1.6 10.2
6.6 120Sn 6
9.1 1.6 208Pb
11.4 6.3 0.5
22
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
23
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