robert michaels prex at trento prex workshop 09 physics interpretation of prex 208 pb e = 1 gev,...
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![Page 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](https://reader035.vdocuments.us/reader035/viewer/2022070305/5514dfa2550346935c8b558d/html5/thumbnails/1.jpg)
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
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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
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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
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Trento PREX Workshop 09
Robert MichaelsPREX at
str
mb
d
d
1fmq
Reminder: Electromagnetic Scattering determines
r
r
Pb208
(charge distribution)
1 2 3
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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%
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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.
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Trento PREX Workshop 09
Robert MichaelsPREX at
Skx-s15Thanks, Alex Brown
PREX Workshop 2008
E/N
N
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Trento PREX Workshop 09
Robert MichaelsPREX at
Skx-s20Thanks, Alex Brown
PREX Workshop 2008
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Trento PREX Workshop 09
Robert MichaelsPREX at
Skx-s25Thanks, Alex Brown
PREX Workshop 2008
![Page 10: Robert Michaels PREX at Trento PREX Workshop 09 Physics Interpretation of PREX 208 Pb E = 1 GeV, electrons on lead Elastic Scattering Parity Violating](https://reader035.vdocuments.us/reader035/viewer/2022070305/5514dfa2550346935c8b558d/html5/thumbnails/10.jpg)
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
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Trento PREX Workshop 09
Robert MichaelsPREX at
Simulated AcceptanceIt will also be measured !
(integrated over azimuth)
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Trento PREX Workshop 09
Robert MichaelsPREX at
Acceptance
Examples of Theoretical Models Calculations by C. J. Horowitz
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Trento PREX Workshop 09
Robert MichaelsPREX at
Simulation of Observed Asymmetry for various Models
Thanks, C.J. Horowitz
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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).
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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 ?
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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
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Trento PREX Workshop 09
Robert MichaelsPREX at
Fine-Tuning: At 50 the Optimal FOM is at 1.05 GeV (+/- 0.05)
1% @ ~1 GeV
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Trento PREX Workshop 09
Robert MichaelsPREX at
Optimization for Barium -- of possible direct use for Atomic PV
1 GeV optimum
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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
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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
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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)
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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
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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