Trento PREX Workshop 09
Robert MichaelsPREX at
Physics Interpretation of PREX
208Pb
E = 1 GeV,
electrons on lead
05Elastic Scattering
Parity Violating Asymmetry
• Physics Analysis
• Can one Q2 determine RN ?
• Follow-up measurements
other Q2 , other nuclei
• Theory Questions
Trento PREX Workshop 09
Robert MichaelsPREX at
neutron weak charge >> proton weak charge
is small, best observed by parity violation
)()()(ˆ 5 rArVrV
||)()(/
//3 rrrZrdrV )()()sin41(22
)( 2 rNrZG
rA NPWF
22 |)(| QFd
d
d
dP
Mott
)()(4
1)( 0
32 rqrjrdQF PP )()(
4
1)( 0
32 rqrjrdQF NN
)(
)(sin41
22 2
22
2
QF
QFQG
d
d
d
d
d
d
d
d
AP
NW
F
LR
LR
Electron - Nucleus Potential
electromagnetic axial
Neutron form factor
Parity Violating Asymmetry
)(rA
1sin41 2 W
Proton form factor
0
Pb is spin 0208
Trento PREX Workshop 09
Robert MichaelsPREX at
Measured Asymmetry
Weak Density at one Q2
Neutron Density at one Q2
Correct for CoulombDistortions
Small Corrections forG
nE G
sE 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
Trento PREX Workshop 09
Robert MichaelsPREX at
str
mb
d
d
1fmq
Reminder: Electromagnetic Scattering determines
r
r
Pb208
(charge distribution)
1 2 3
Trento PREX Workshop 09
Robert MichaelsPREX at
( 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, dPe/Pe = 1%
Trento PREX Workshop 09
Robert MichaelsPREX at
PREX: pins down the symmetry energy (1 parameter)
( R.J. Furnstahl )
energy cost for unequal # protons & neutrons.../ 3/1
2
4
AaA
ZNaa
A
Esv
PREX
Pb208
)1(
Actually, it’s the density dependence of a4 that we pin down.
Trento PREX Workshop 09
Robert MichaelsPREX at
Skx-s15Thanks, Alex Brown
PREX Workshop 2008
E/N
N
Trento PREX Workshop 09
Robert MichaelsPREX at
Skx-s20Thanks, Alex Brown
PREX Workshop 2008
Trento PREX Workshop 09
Robert MichaelsPREX at
Skx-s25Thanks, Alex Brown
PREX Workshop 2008
Trento PREX Workshop 09
Robert MichaelsPREX at
Relationship of Measured Asymmetry to Theory
),(
),(
dd
d
Add
dA
physics
measured
dd
),(
theoryA
Differential Cross Section
Acceptance Function will be measured, presently simulated
Theoretical Asymmetry
PREX Expt provides these
to be compared
Trento PREX Workshop 09
Robert MichaelsPREX at
Simulated AcceptanceIt will also be measured !
(integrated over azimuth)
Trento PREX Workshop 09
Robert MichaelsPREX at
Acceptance
Examples of Theoretical Models Calculations by C. J. Horowitz
Trento PREX Workshop 09
Robert MichaelsPREX at
Simulation of Observed Asymmetry for various Models
Thanks, C.J. Horowitz
Trento PREX Workshop 09
Robert MichaelsPREX at
Application: Atomic Parity Violation• Low Q test of Standard Model
• Needs RN (or APV measures RN )
2
rdrZrNG
H eePWNF
PNC35/2 )()sin41()(
22
0
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).
Trento PREX Workshop 09
Robert MichaelsPREX at
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 ?
Trento PREX Workshop 09
Robert MichaelsPREX at
Optimum Kinematics for Lead Parity: E = 1 GeV if <A> = 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
Trento PREX Workshop 09
Robert MichaelsPREX at
Fine-Tuning: At 50 the Optimal FOM is at 1.05 GeV (+/- 0.05)
1% @ ~1 GeV
Trento PREX Workshop 09
Robert MichaelsPREX at
Optimization for Barium -- of possible direct use for Atomic PV
1 GeV optimum
Trento PREX Workshop 09
Robert MichaelsPREX at
Higher Q2 Point ? ( e.g. E = 1.3 GeV, 80, q = 0.92 fm-1 )
5
Here ?
For Lead
Trento PREX Workshop 09
Robert MichaelsPREX at
Time to make measurements
IPT
2
7days
strAIP 007.0~,50~,85.0~ JLab Spectrometers (2 HRS)
For PREX (optimal) 1% in RN
Higher Q2 point ( E = 1.3 GeV, q = 0.92 fm-1 ) 2% in RN
IPT
2
19days
Trento PREX Workshop 09
Robert MichaelsPREX at
Estimates for Other Nuclei: 48Ca 120sn
• Forward angle use 50 septum
• Want thick target 10% X0 = practical maxbt
E
Radiative losses estimated ~ ~ 0.4 - 0.5
48Ca 1.6 10.2 6.6
120Sn 6 9.1 1.6
208Pb 11.4 6.3 0.5
3cm
g20 cm
gX Tlen (mm)
Trento PREX Workshop 09
Robert MichaelsPREX at
48Ca 120sn
48Ca 1.7 2.0 3.4 % 25 3.5
120Sn 1.2 1.0 2.9 % 125 2.6
22 ARFOM
E (GeV)
max
Appm
Sensitivity to RN
Rate(MHz / arm)
Each a 2 month run
% Error
A
dA
These should match
for 1% in RN
For effectively 1% in RN
Trento PREX Workshop 09
Robert MichaelsPREX at
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